Talk:Straightedge and compass construction

3597: 1184:

circle, and b) has a length of 1 between the other intersection with the circle and the intersection with an extended diameter. You can easily do this by sliding around a marked ruler whose marking has length 1, but it's impossible otherwise (since it trisects the angle, for one). Another way to look at it is: no particular distance is unconstructable, because the plane doesn't have a preferred coordinate system. Only once you draw your first circle do you establish a metric. So if you have any marked ruler you can trivially make the marking a constructible length by making it the unit distance in your coordinates.

3593: 195: 185: 164: 1152:

straightedge can start with the creation of an arbitrary distance using the compass). Likewise, no new constructions are possible using a ruler with any number of marks on it as long as the ratio of any two distances between marks is constructible using compass and straightedge (i.e. any ratio must be a solution to a quadratic equation). A ruler would only permit new constructions if a ratio of distances between marks is not constructible (for example, a ruler with three marks at 0, 1 and

290: 269: 799:

straightedge and compass. So you are still restricted as to how you can use elements of this "grid" and you will not be able to double the cube, etc. Now if you were to actually violate the rules for a Euclidean construction somehow, you can double the cube. For example, see the particular example Arthur gave. In that example, one creates a point of intersection between two lines by measuring along a marked straightedge, which is disallowed under the normal rules. --

1677:"compass and straightedge" over "compass and straightedge construction" -- The preference is shorter, therefore presumably better barring some other argument. The former is quite unambiguous, in the sense that the pairing of these two tools is universally understood to apply equally to the set of tools, to the operations that may be performed with them, and to the theory which governs all. Thus there is no need to disambiguate by adding the needless word "construction". 2721:

large number are needed) will be changed to being direct. By the way, I hope my slightly more formal section on the interpretation of geometric constructions as operations in the complex field is helpful. Further work needed includes removing some of the repetitions in other sections, and a description with a diagram (or alternatively a link) for the geometric construction for each arithmetic operation.

32: 98: 300: 133: 3354:

working mathematician I feel the need to point out that there are professional standards for published mathematical works and the paper being talked about fails to meet those standards in many ways. The fact that the author of the paper is also a founding editor of the journal in which this paper appears may explain how it got published in the first place. Comments?

4124:

allow one to generate various interesting subsets of the ones that can be constructed using compass and ruler and there's other constructions that lead to wider fields like the one with unit distances you found. I can't find an appropriate article on a quick search but there probably is one or one could be set up easily. It could include for instance the ones where

2942:

and a point; and then draw a line which passes through the given point and intersects both lines, and such that the distance between the points of intersection equals the given segment." Between which points of intersection -- all three? How does a distance "equal" a segment? Can we stop jamming "for example" appositives everywhere they are grammatically legal? (

1660:. Note that the "common usage" argument fails to endorse "ruler", because a ruler is marked in common usage. Adherence to strict interpretation fails as well: if "ruler" is strictly interpreted to be unmarked then this jerks the rug from under any claim to "common usage" for "ruler and compass". "Straightedge" is unambiguous, strict, and still commonly understood. 3144:"An example of a simple achievable construction is to divide a line into two sections of ratio 1 : N (integer). First construct perpendicular lines at each end of the target line, next construct, with the compass, one target line length 'down' on the 'left' and N target line lengths 'up' on the 'right'. Join the two resultant points for a 1:N intersection." 4037:.(In particular this is not original research) 2. I asked you to discuss before making changes, I think you should do it next time. (Note that it is not me who started this "war".) 3. For the rest I gave the answers already --- I will wait couple of days and undo you changes. I am 100% sure think this type of construction worth to be mentioned here. -- 4072:

directly linking unit graphs and trisection. And really I can't see why you are going on about that here, the linkages do the job straightforwardly and pretty much equivalent in idea and more to the point there are citations showing the link. No we don't leave things in if it is obvious they don't belong and there is consensus about that.

757:

be zero, using the compass set to the unit radius mark off one unit from zero. Move the point of the compass to the first unit, mark of the second unit, .... The same procedure can be repeated for any straight edge in the diagram, effectivly giving the same construction possible as with a marked streight edge and compass. --

2929:

cannot represent all of the real numbers - so one can produce an infinitely good approximation, given infinite time, but can never produce an exact answer in the strictly mathematical sense (because they lack the expressive power in the same way as the rational numbers cannot express the exact solution).

4419:

This is the first time I have contributed anything to Knowledge (XXG) besides donations, so I'm not sure what exactly I'm doing here. And I am not a mathematician for sure, but I wanted to at least point out something in this article that may no longer reflect current knowledge. The latest Scientific

4277:

Euclid seems to have had a broader view of what a "construction" is than this. For example, proposition 3.1 constructs the center of a circle from the circle. That can't be done with the basic constructions because there are no intersections to make a point from and no points to make a line or circle

3444:

I just did a check using "straightedge-and-compass construction" on Google Books and that did bring up the hyphens somewhat. There were six without hyphens and four with on the first page, the first five did not have a hyphen. It was 9 hyphens and 20 without and one I couldn't tell on the first three

3353:

I would say that the section should be struck. In support of this I note that according to Math Reviews, the paper that this section references has never been cited by any other mathematical article. As a Knowledge (XXG) editor I should not be commenting on the quality of referenced sources, but as a

3190:

The most famous ruler-and-compass problems have been proven impossible in several cases by Pierre Wantzel, using the mathematical theory of fields. In spite of these impossibility proofs, some mathematical novices persist in trying to solve these problems. Many of them fail to understand that many of

2886:

It might be worth mentioning that it _is possible to solve these problems to arbitrary accuracy (just not exactly). Simlply draw a cartesian grid of whatever scale is required (if you make it fine/big enough you can get any desired level of accuracy). Only mathematicians make a distiction between "as

2305:

See my response right above; the Monthly definitely is not endorsing a particular terminology. What if someone else decides to put another Monthly ref indicating "ruler and compass" is preferred? Where will this end? Anyway, I'm going to create a "books" subsection then. I think there are several

1899:

I'd like to ask Oleg: What do you mean by "existing (terminology)"? Do you mean the inconsistent text (at least 16 alternate forms) that existed before I standardized on one form? Do you mean the consistent text that existed before Paul's counter-move? Or do you mean the inconsistent text that exists

1861:

To answer these questions someone should really survey the literature for the opinions of "experts" (by the way, there are roughly zero references in the article). In lieu of doing that tedious work, I vote for what I see as correctness: name the article "compass and straightedge", mention all of the

1607:

I don't care a fig for what is the most common usage; only what is more correct. We're not in the business of perpetuating error. Fine to have redirects from all possible variations, including those with "ruler" in the title. Not okay to title the article page itself that way; that's just plain wrong

1484:

I don't agree with the move of the page to ""Compass and straightedge". As i wrote above I think that "ruler and compass constructions" is the most common name for the subject of this article. In any case if we were to replace "ruler" by "straightedge", the article should be rewritten to reflect that

1193:

Thank you for pointing this out. I was assuming neusis was not a permitted construction (it is far less direct than normal compass and straightedge constructions), but including it leads to an important superset of the compass and straightedge constructions. In light of this, I change my vote back to

977:

I think the article itself says it best, "The ruler to be used has no markings on it and only one edge, and is known as a straightedge." In my humble experience, I have always heard such constuctions referred to as "compass and straight-edge constructions." IMHO, I think straightedge is clearer and

4234:

I did like the link to Euclidea an online compass and straightedge construction game that was added 18 march 2016, but was removed soon after with as reason (revert - rm promotional link; this is not a web directory) I did like the link and would like it reinstated, because it is related , I like

3801:

Could we make a section with much used constructions, so that readers have some directory linking to much used (but not bascic) constructions, I know the list should not be to long or maybe a seperate page for a longer list. but on this page a list refering to "midpoint of segment", "angle bisector"

3486:

a compound noun, denoting a class of constructions, but one can also refer to the tools used in such a construction, in which case the hyphens should not appear. In using the compound noun, one can say that construction X is a straightedge-and-compass construction, but this article is concerned with

3140:

IMO, this article spends most of its time reviewing (a) what can't be done and (b) complicated proofs of this and complicated proofs of some thinghs that can be done. It appears to lack almost completey a review of what can be done and of how to do (some) of these constructions. I was tempted to add

2982:

This is false - for example, given (0,0), (0,1), (0,-1), (1,0), (-1,0), and (1/√2,1/√2), the points that can be constructed with only a straightedge have coordinates in Q. Even supposing specific special points (x1,y1), ..., (x6,y6) (rather than arbitrary points), all points constructible with only

2720:

A 2/3 majority is quite a strong endorsement for the suggested, less ambiguous title. On a related point, I have noticed that at present we have some double redirects to the article. Hopefully, if the name is changed (or if, as now seems unlikely, decided to be not changed) all redirects (of which a

2187:

As someone who learned about this (twice) in undergraduate and graduate studies within the past several years, I would note that it was introduced both times as "straightedge and compass" with both professors, at different institutions, commenting on the difference between a straightedge and a ruler

1183:

It's not just a matter of being able to construct the length between the marked segments; it's the fact that you can construct it in an unconstructable position. Have a look at Archimedes' trisection of the angle. The key step is to produce a line segment which a) passes through a given point on a

1043:

for reasons mentioned above. Additionally, one should not use Google hits, but rather limit the references to authoritative sources (cf list of books below). My perusal of that list so far shows that neither term is overwhelmingly preferred by the authors of advanced mathematics books. In fact, I

4123:

If you really feel the need to stick that citation into some article you should find an appropriate article or set one up. An article on the various types of points that can be constructed using different axioms would be a notable topic I think - for instance subsets of Hilbert's axioms of Geometry

3481:

I was also jarred by this move and did a little investigation myself. I have certainly seen the hypenated version but only rarely and a quick pass through my bookshelf did not turn up any instances of it. I also looked for the ruler and compass version with or without hyphens. The variations may be

3272:

Regardless of the algorithm we use, we can only perform a finite number of steps. Therefore, no matter what algorithm we use to determine them, there will always be points that we cannot mark by crossing of two lines (same holds if we mark the point as intersection of a line and a circle, or of two

1921:

Existing terminology is "ruler and compass" as far as I am concerned. I am not taking it as a confrontation, but please don't stress so much that "all linking articles use one term and the article itself uses another". That is easy to fix one way or another. Let us be patient for a few days and see

828:

The issue of the marked straightedge is of a class distinct from that of the non-collapsing compass. Euclid I.2 and .3 justify the non-collapsing compass and show that any construction possible with the non-collapsing compass can be performed with the collapsing. The definition of the compass never

814:

The distinction is essential, which is why I am involved. You can, indeed, create a scale of any constructible numbers along a line. If you were to look at that, it would appear to be a ruler, in common speech. In order to use it as a new tool, though, you would have to cut it out from the paper on

756:

Does it actually matter if a ruler is marked or not. It is a trivial matter to produce a marked straight edge from an un marked straight edge and a compass. Step 1: draw a small circle, call the radius of the circle your unit. Next draw a straight line with the ruler, pick some point on the line to

582:

there is a slight distortion. the only true way to draw a real hexagon is to 1. bisect the circle at any point 1/2 way between the center and an edge to form point 2. using point as a center, draw a line perpendicular to the angle formed between and 3. mark the two points where intersects the

4071:

I was aware you could get the further shapes if you extend those origami axioms but it isn't so easy to do them and there is no straightforward connection to trisecting. The basic axioms do that fine and there are citations for it. The thing you have to do to get any further here is get a citation

2986:

I suspect that this false generalisation is due to a misinterpretation of another result - given those 6 points, one can construct arbitrarily many points of the circle given by those 5 equidistant points, as well as its center. If one actually had the circle and its center, that would be enough,

2941:

Whether moved or not, the second sentence in the section on marked rulers is completely obtuse. Someone who understands it in detail should just yank this particular sentence and rewrite it wherever it belongs. "This would permit them, for example, to take a line segment, two lines (or circles),

2073:

You seem to be saying "I worked my ass fixing all of those articles and links, therefore, how dare you all people argue with me?" Maybe that's not what you mean, but if that is what you mean, that's a lame way of making a point. And we are not arguing about inconsistency here, we are arguing about

2000:

Understand that I'm only talking about titles of articles here. Elsewhere, there is more latitude. For example one may choose to describe things rather than name them. So for example if I wanted to describe these constructions I might write "constructions using only a straightedge and compass" for

1865:

Apparently the larger issue is how to refer to these constructions in other articles; I submit that anyone reading the phrase "compass and straightedge construction" will automatically translate it into "ruler and compass construction" or whatever their favorite variant is, so accomodating popular

798:

One can indeed create a Cartesian grid (as described in the article) with equally spaced out points along the axes. However, although it may look like you've effectively constructed a replacement for a marked straightedge, the point is that you are still only allowed certain operations with your

3905:

F. Klein described another linkage machine in his "Famous problems of Elementary Geometry" (? - not sure I got that right, I'm not at home) that can do this as well, and we already have a page on it (sorry, don't remember the name). Perhaps we can extend this section to include these and the unit

3348:

I would like to call into question the value of this section. First, the paper referred to is now 14 years old ... not particularly recent in my mind, so I find the section title a bit misleading. The section has been in the article since Sept. 2002, with no change in content (but there have been

702:

speaking, a "ruler" is a straightedge only, a tool for ruling (drawing straight lines). A tool for measuring is a "scale"; thus the commonplace object found in home and office is truly a ruler with a scale printed upon it -- a dual-purpose tool. It is, however, ambiguously called a ruler; and the

3529:

The usual rule for hyphens is to include them between words that together form a single adjective for something else in the sentence, and to leave them out when the words form a noun phrase that's not functioning as an adjective. For example, "a high-school opera" ("high-school" functions as an

2928:

I disagree - I think there should be some mention of this, to inform the casual reader, (without being overly technical) that compass and straight edge are at least as powerful as the rational numbers, and can be used to solve any problem to arbitrary precision. The important point is that they

1349:

I was going to jump in and vote oppose when I first saw the vote started, but I thought I'd wait and see if any arguments swayed me, first. Having been in the 'neutral' camp for a day or two, I've now plumped for oppose. I've never heard of 'straightedge'; the "ruler and compass" words seemed

1300:

I'd never heard of "straightedge and compass" or "compass and straightedge" before this discussion. (And I was designated crank-reader at Caltech for a short period of time, so I saw a lot of bad "ruler-and-compass" angle trisections. This doesn't necessarily indicate the correct term, but it

384:

I think these two sentences are contradictory. The first seems to imply a collapsing compass, as you must pre-define the radius and center point in order to draw the circle there. If a rigid compass were permissible then you need only a center point in order to draw a circle whose radius youve

4119:

policy says we should not put things like that into articles. You should not be trying to push things like that in here unless somebody in the world at large has thought it worthwhile to publish a connection. I have explained this before, you seem to deny that is a real reason but it is pretty

4114:

I do not object to a trisection linkage which has a good relevant citation. The classical impossible constructions are an important part of the article and there are citations talking about compass and ruler and the classical problems and directly connecting linkages with those. I do object to

3821:

I have just removed an addition dealing with unit distance graphs. The quoted result says that for any algebraic number there is a graph (in the Euclidean plane) with a pair of vertices at this distance for any unit distance graph representation. If this was related to compass and straightedge

3428:

I did the checking by putting "compass-and-straightedge" with the quotes into Google Books. I did not do any special checking that hyphens were inappropriate and therefore an entry should be ignored. If some demonstration can be made that there is some criteria I should use which is better and

1367:

be constructed with compass and straightedge - are simply not true in general for ruler and straightedge. Therefore the current name could be seen as misleading. On the other hand, it's naming policy to use the most widely familiar name, even where that name contains factual inaccuracies. Such

3730:

Unless I missed something, the article currently contains no history prior to Gauss, except a brief mention that a proposition of Euclid's implies that it doesn't matter whether a compass is collapsible, a brief statement that the requirements can be expressed in terms of Euclid's first three

4397:

The History section doesn't explain the origins of the compass and straightedge restriction, nor does it distinguish between eras in which the restriction was considered absolute and eras where constructions using other tools were considered legitimate but less aesthetic, less fundamental or

2756:

Hopefully...all redirects (of which a large number are needed) will be changed to being direct. By the way, I hope my slightly more formal section on the interpretation of geometric constructions as operations in the complex field is helpful. Further work needed includes removing some of the

2897:

Firstly, this is an article about a topic in mathematics, not about practical drafting methods. That should really be clear from the article. Secondly, it is true but rather a minor point that approximate constructions for squaring the circle, etc, exist: approximate constructions exist for

1151:

I think I must not have expressed myself clearly enough. An infinite ruler with two marks on it only provides a single unit of length which can be used anywhere in a construction. As we are only interested in ratios, this cannot allow any new constructions (any construction with compass and

3563:

I think including the hyphens follows the ordinary rules for punctuation, and forms the common name. Or am I misunderstanding you? I don't have an opinion (yet) on whether "compass" or "straightedge" customarily comes first. I'll do a little googling and see if my results agree with yours.

3644:

Here's what I think is going on regarding the hyphens: While the hyphenated version clearly follows standard English punctuation for compound attributive nouns, sometimes copyeditors omit the hyphens when they seem unwieldy and there's no real ambiguity. This happens especially often in

2126:

and did the work required. Now I find I'm asked to spend an equal amount of time debating the issue. My work is beginning to seem a poor investement; perhaps I should have permitted the mess to fester as it was. But if you will not do the work yourself, I ask that you allow me to do so.

848:

One of the biggest issues I have with a marked ruler - beyond the fact that it is capable of extending constructibilty - is the simple fact that it introduces measure, a metric, into the plane. This turns geometry from something more abstract and geometric, to something more algebraic.

815:

which it was drawn and translate it. If translation by a non-constructible distance is permitted -- and we generally understand that two objects may be offset, relative to one another, by any real-number distance -- then this opens the door to all three classic forbidden constructions.

1764:

Until I started work, nobody had made any effort to untangle the rat's nest of links, descriptions, redirects, categories, and general blundering surrounding this subject. Now, with the exception of the rewrite of the main article (and perhaps one other task, that of an article for

833:

be expanded on demand. This is important; the actual process of duplicating a given line segment is hellishly complex compared to the ease of simply drawing a new circle with the old radius held in the compass. But the latter operation is only justified by the proof of the former.

3062:

In my long-lost undergraduate days, I came across a sourcebook with an interesting letter from Newton in which he defined what we now know as the derivative with *exactly* the "modern" notion of a limit (given verbally, but precisely). It's bizarre that this took centuries to be

3675:

Well I think that established 'Straightedge and compass construction' as a preferable title for Knowledge (XXG), but should we even include the 'construction' bit? It seems a bit unnecessary to me and people more often just say something like 'using straightedge and compass'.

4002:

mentioned above talk explicitly about trisecting and they do everything necessary and relevant as far as this article is concerned compared to that general paper. And it is normal to not put things back in but discuss it first when you are in a minority about the insertion.

545:

The regular polygon with the largest number of sides that was ever actually drawn with a ruler and compass had 1,024 sides. It was drawn by graduate student Mr. Sam Bronstein at the University of Kentucky in 1963, a feat that took him 33 days and a sheet of paper 9 meters

4099:

Could you provide some reasons, why you object to include the linkage-construction? So far I did not see any. Please make it clear, maybe number them and either I will agree or I could explain what is wrong with them. (At the moment our discussion goes nowhere).

3578:

Googling books is what I did so please go ahead and check for yourself. I understand common name as meaning the name that is more common as written down in the major reliable sources rather than the name that follows grammar or is otherwise official in some way.

2290:

I agree with you that it's wise to annotate each ref with the term chosen by the ref's author. I don't agree that web refs are automatically uncitable. I do agree that a random smattering of web refs is substandard. I chose refs such as an article published in

81: 1074:

I can live with either title and there are good arguments on both sides. Whatever you do, it's crucially important that the reader be made aware of the fact that, even though rulers sometimes have marks, the technical term "ruler and compass construction"

2001:

clarity, while if I wanted to refer to them by name I might write "traditionally called ruler and compass constructions", perhaps noting what is meant by "ruler". Or if I was writing for mathematicians I would just write "ruler and compass constructions".

3459:

Just noticed I used "straightedge and compass construction" instead of "compass and straightedge construction". In fact straightedge and compass construction came up 1560 times on Google books but compass and straightedge construction only came up 900

2229:

John, I would prefer if we only added book references, preferably well-known textbooks and the like. I don't believe getting a cross section of Google hits will be nearly as helpful or representative of what may be considered "authoritative" usage.

3286:

be constructed, even though there are infinitely many of them. The real impossibility proof is that the number of constructible points is countably infinite but there are uncountably infinitely many reals. If anyone wants to write it up, go for it.

694:

construction. For practical purposes the ruler is the more generally useful tool, certainly the more popular; thus it's not hard to see why the term is also more popular. But this is one of those times that the Google test gives a false indication.

3992:

says says in its nutshell "Articles may not contain any new analysis or synthesis of published material that serves to reach or imply a conclusion not clearly stated by the sources themselves." For the origami trisection there is a citation in the

1451:

Whatever the outcome be, IMO it would be bad idea to chase each and every reference in wikipedia articles and replace by one and the same. This would be imposing a POV bias unto the readers, since in real world both terms are used interchangeably.

4304:

While there are certainly problems with Euclid's "proof" in III.1, I don't see where your objection is coming from. The circle has to be given (determined) in some manner, and Euclid does this by talking about the circle through the three points,

3548:

that I can see and that is part of a Knowledge (XXG) policy. Is there a good reason to prefer grammar to common name in this instance? Also straightedge and compass construction is more common in books than compass and straighterdge construction.

4470:

Article could use some cleanup, many external links have gone bad. I'd do it myself but I'm not a member so I don't know how to mark them and I don't want to start removing unsourced material if it can just be redirected to a different source.

3266:

Suppose an algorithm that gives you a point as a result. The point will always be given by intersection of two lines (or line and circle or two circles. See previous elemental operations), but there are infinite points in a classical euclidean

3600:

came up with 2,660. The books in the first couple pages of the latter seem more authoritative than the former: Springer-Verlag, etc. In the first 19 books in the straightedge-and-compass group, about a third had hyphens and two-thirds didn't.

2435:

the text in the section sez "Note that our ruler may be used only to draw straight lines through constructed points. We are not allowed to use it for measurement. Sometimes it is referred to as a "straight-edge" to make this point clear."

837:

It is exactly this kind of subtle distinction between permitted and forbidden operations that invites so many cranks to waste their lives on fallacy. And this is why I feel so strongly about the issue of term used to describe this subject.

3997:

article explicitly talking about trisecting angles in origami and giving the construction and there's other citations which could be given giving the connection to the axioms if you'd like citations here. The linkage constructions I and

3822:

constructions, it would be saying that all algebraic numbers are constructible - which is clearly false. If I am somehow mistaken, the section would have to indicate how it is related to the topic of this article before being replaced.

1499:

I think "Straightedge-and-compass constructions" would be better. "Ruler" is technically incorrect, as one can construct cube roots (not normally considered a ruler-and-compass construction) using a straightedge with two marks and a

2259:(edit conflict) Are we now to take this as endorsement by AMM? Or are you going to go through all AMM articles and see if one usage is preferred? A simple JSTOR search shows the Monthly lets authors use whatever term they like. -- 2100:

Thank you, Oleg; you are exactly correct, although I might have put it more delicately. I paid for my preference in the only coin of value here. The more that you denigrate my effort, the less respect I have for your point of view.

413:

At some time in the past I Heard the commentators for professional wrestling refer to the ring in which activity takes place as the "squared circle". This is an excellent example of pseudo-science in the service of pseudo-sport.

2037:

To me the issues are one and the same. I think that, as a project, we should agree on one correct term for every concept and replicate it throughout all articles, much as we settle on one correct style for, say, taxoboxes. There

1944:

At what time in the history of this project has "ruler and compass" been the standard term for this concept? It has been mentioned in many other articles, with a wide range of terms. The last time you (Oleg) edited the text of

1368:

inaccuracies should be clarified in the article text, ideally in the intro, not corrected in the title. If the "compass and straightedge" name were equally widespread, or even half as widespread, I might agree to prefer it.

1137:

I'd hate you to think I was criticizing your vote; I'm not. But you do suggest that a ruler marked in constructible ratios could not be employed to perform impossible constructions; it's my understanding that it can indeed.

3530:

adjective for "opera") but "an opera performed in high school" ("high school" is a noun, the object of "in"). Similarly, "compass-and-straightedge constructions" but "constructions made with compass and straightedge". —

3191:

these problems are trivially solvable provided that other geometric transformations are allowed: for example, doubling the cube is possible using geometric constructions, but not possible using ruler and compass alone..

3030:

he had invented (differential equations), which would have been more natural. He chose this more awkward method so as to demonstrate that the theory would have been accessible to the ancient pythagorans, unaware that

1115:

I believe using a marked ruler allows essentially the same constructions (unless the markings are in unconstructible ratios), but the suggested term more clearly describes the intended meaning. A google search shows

4357:

where it seems 'Straightedge and compass construction' is more common. Also the version without hyphens seems more common but seems to occur about a third of the time. Any objections to a move now? Prefer hyphens?

4278:

from. However, Euclid does it by drawing a chord through the circle at random, relying on the fact that the construction works no matter which chord one draws. Perhaps the definition of construction has changed?

1468:

I agree with the recommendation, although I don't see it as a PoV issue. If we leave this alone, eventually the inward links should divide in proportion to all editor's feelings. This is the wiki process at work.

3243:

The discussion on moving the article seems to have stalled a while ago with no decision. As a purely practical matter, it's usually much easier to make a link to the article when the article name is singular.--

45: 3413:

I've checked Google books and only found two instances of the name with hyphens in instead of spaces. Therefore this new hyphens name is not a common name and the article should be move back to its old title.

1384: 2847:; even the Galois theory article makes this assertion. However, the proofs just rely on basic field theory with no need of Galois groups, etc. The current phrasing would even seem to take credit away from 3373:

Is there any analogous model where instead of limiting the compass and straightedge constructions to a single 2D plane, that we instead use them on a number of intersecting 2D planes in 3 dimensional space?

3837:

Yes all algebraic numbers are constructable using unit-distance-graph constuructins. And yes unit-distance-graph constuructins is a type of geometric constructions (not worse that origami-constructions).

3219:" in that sentence appears in blue, perhaps with an underline? That means that you can click on it, and read in detail about the problem of doubling the cube. In that article there is a section titled 4377:, there are no hyphens and putting compass first is somehow jarring. I believe that this is a case where the rules of grammar are being ignored in favor of common practice, and we should follow suit. -- 3711:

An alternate method for constructing polygons is by taking any two sides of a right-angle triangle as radii of a circle & its sectors,some of the results will be apeiroga,but most give good results.

4433:

Just trying to make Knowledge (XXG) better in my own diminutive way. I'll check back to see which part of subterranean garbage this post has been banished to bc that's how I learn. Thanks. Glenn Wiens

464:

It is definitely the fault of mathematicians here. Some VERY famous names aided and abetted this myth, without checking into it themselves. You'd think being math people, they would question things.

251: 3758:

What did they say about squaring the circle, doubling the cube, and trisecting the general angle? Did they think that these could be solved? Which trisectible angles did they know how to trisect?

3736:

The following three construction problems, whose origins date from Greek antiquity, were considered impossible in the sense that they could not be solved using only the compass and straightedge.

1621:

I'd like to make it clear that no consensus existed in the project before I did my work over these last few days. The subject was referred to by no less than 16 alternate, inconsistent titles.

1582:

It took me over 7 hours to correct every link in every related article, fix every category tag, and rewrite several snippets of text. I'm really sorry I haven't gotten around to the rewrite of

2693:

your support or opposition was marginal or indecisive, can you imagine any circumstance under which you might consider reversing your position or becoming fully neutral? What might that be?

2191:

I know that I am jumping in late here, but I support the more accurate title, and I think that historical precedence is an absurd reason to continue the propagation of ambiguous terminology.

457:

No, the people doing the history are mathematicians specialising in history of math, not the other way around. (True for most sciences...you have to have some understanding of the material.)

598:(Also, this proposed construction seems rather vague. How do you draw a line perpendicular to an angle? What does "180 from across " mean? It is decipherable, but it takes some work.) 4426:

by Emily Riehl which seems to indicate that it is now possible to construct "with an imaginary straightedge and compass, of a cube with a volume twice that of a different, given cube".

3638: 3634: 2295:

and the highly-respected and popular Math Forum at Drexel. Certainly some nutball crank in a high school in Outer Okeefenokee who happens to have a page on cube doubling is uncitable.

1969:

easy to fix -- not one way, not at all. I spent at least 7 hours fixing links, text, and redirects. Now that I've paid for my concerns in sweat, yes, it's easy for you to run a bot --

4210: 4166: 2164:

is better; this is about the process of construction in general, more than a list of constructions. On the whole, I prefer the shorter name: it is also a direct link in phrases like

3393:

Replacing circles with spheres so you look at points where lines or spheres intersect is the obvious extension. However you still don't get anything beyond doing square roots.

1794:

Common usage should decide; Knowledge (XXG) is no place for "correctness" - but only if it is -er- decisive. I am not convinced that "ruler and compass" dominates the field.

4472: 4319:. Yes, that choice is arbitrary, but it is not part of the construction, rather it is part of the given. There is no aspect of the construction that uses random elements. -- 1350:

familiar as soon as I saw them, and I didn't make an assumption that the ruler was used for length measurement; the resources identified below are by no means unambiguous.

2978:

A further generalisation of this theorem (due to K. Venkatachala Iyengar) gives constructions using only a ruler given a point and five distinct points equidistant from it.

735:

The verb "rule" is sometimes synonymous with "measure" or "judge". Therefore, I suggest that all wording in this article be changed to "straightedge" instead of "ruler".

3962:. By the way, if one consider multiple folds in origami constructions then you also get all algebraic numbers. I will undo your edits. Next time please discuss first. -- 1992:

John, you seem to be conflating the issue of what we title the article with how we describe or refer to these constructions in other articles. As I tried to explain in

3753:

What lengths, angles, and figures could they construct? (E.g., could they do the regular pentagon? Did they think that all regular polygons ought to be constructible?)

1172: 4333:

The other possibility is that the circle is determined by a center and a radius - but in that case one already has the center and so here is no need to construct it.

2775:

article. Now that the page is "hot", there have been plenty of edits so I'll hold off on a comprehensive rewrite; it may not be necessary with many hands on the page.

356: 381:

Circles can only be drawn starting from two given points: the centre and a point on the circle. The compass may or may not collapse when it's not drawing a circle.

3928:

The difference with origami is there is an explicit construction for trisecting an angle at the article pointed at as an important part of the whole business, see

3880:

Yes that doesn't belong here, it is too general and unrelated, but a construction using linkages with no sliders would and that is practically the same thing. See

2122:. I saw a raggedy, mixed-up scatter of references to the subject, some clearly ignorant, others thoughtless. Regardless of the merits of my preference, at least I 4033:

1. you should read carefully what I wrote (I did not say that get all algebraic numbers with the Huzita–Hatori axioms for origami). See for example Theorem 1 in

4514: 3691:

I think "construction" is definitely necessary in the title. It's part of the standard terminology of geometry, which distinguishes constructions from proofs. —

346: 3043:, which Newton knew about, and used; it's in Euclid. Newton published his results with Euclidean proofs because these proofs were, and were understood to be, 2215:

Ok, sorry, I missed this comment earlier. I think we should at least annotate the refs though so it's easy to see at a glance what the ref's position is. --

1904:, wherein all linking articles use one term and the article itself uses another? Please don't take this as a confrontation; I'd like to know your preference. 4494: 2629:

Although the term "ruler" is sometimes used instead of "straightedge," the Greek prescription prohibited markings that could be used to make measurements.

1973:

I brought order from chaos. Don't stress the inconsistency? If you don't think it's important what we call it, why oppose the effort to gain consistency?

4504: 241: 322: 2757:

repetitions in other sections, and a description with a diagram (or alternatively a link) for the geometric construction for each arithmetic operation.

2983:

a straightedge would have coordinates in Q, which cannot capture the closure of Q under square roots (which is what ruler and compass can construct).

525:

I think there's room for a lot of reorganization here. Some pages should be merged; some new ones should be split off. I just ran into a problem with

1876:

I perfectly agree with Paul August. It is not Knowledge (XXG)'s purpose to decide which is the most correct way, rather, the most used way is chosen.

217: 2801:

I can provide good graphics for any construction if someone will kindly indicate what's required. Let's get together in a corner and thrash it out.

3463:

I think on this evidence the article should be titled "Straightedge and compass construction" rather than "Compass-and-straightedge construction".

1996:, whatever we choose to title this article, we can describe to these constructions in different ways, in different contexts. Here is what I wrote: 1124:

by 100,000 to 90,000 so a few redirect pages are going to be necessary. Fortunately, the term "Compasses" seems to be hardly used in this context.

117: 41: 1485:

change, and the title should be "Compass and straightedge constructions". I am going to move the article back until we can arrive at a consensus.

2796:? should stand for all or each should have its own page. I intend to slim down description of these subjects in the main article, in proportion. 1732:"compass and straightedge" over "straightedge and compass" -- All constructions can be performed with compass alone; thus it is the senior tool. 615:"A regular n-gon can be constructed with compass and straightedge if n is the product of a power of 2 and any number of distinct Fermat primes." 4509: 4424: 1749:"compass and straightedge" over "compass-and-straightedge" (and all hyphenated forms) -- In this case, hypenation is simply poor English style. 989: 595:

I'm not a mathematician, but I don't see why the hexagon construction doesn't work. Is it because pi is irrational? Can someone clarify this?

3278:

This sounds nonsensical to me. A finite (but unbounded) number of operations can certainly produce an infinite number of possible points. All

2365:

Had an interesting note about how in ancient Greece, they did not have access to marked rulers, so for them a ruler was just a straight edge.

2205:

It's important that we sign our own comments, but I don't think it's appropriate for us to take credit for public references in this section.

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Regarding the end of this last sentence: If an example is offered, it should be given, not withheld. Doubling the cube is "possible" using

713:

Being a quibbler by nature, I cannot resist pointing out that the "unambiguous umarkedness" of the straightedge may not be straightforward:

313: 274: 3167: 1881:

Writing an encyclopedia is hard enough without us spending time on aruging which terminology is the right one. Just use the existing one.

1563:

What evidence is there that it's the most common? I myself never hear it, and never use it, and have been indoctrinated against its use.

529:; somebody got carried away with the difference between real and ideal construction. That's a whole subject in itself; but it's not math. 208: 169: 4450:

Please disregard my entry as it isn't relevant to the matter at hand. My bad - I'll stick with conventional contributions in the future.

4373:

I'd favor the move to "Straightedge and compass construction" (no hyphens). In analogy with the technically incorrect, but still common,

3349:

minor changes in how the reference is given). The single sentence is pure hype and does not add anything to the article. On the basis of

779:

for a "ruler (straightedge with two marks)" and compass construction which cannot be simulated by a "ruler and compass" construction. —

436:

Mathematicians are notoriously incompetent historians. Gauss NEVER gave a proof of the necessity of the constructibility of the regular

850: 1590:

article title; it is also the linking text and other references to the subject scattered throughout the project. I have corrected them

1427:

Google hits are misleading here. If you click search results to the very end, you will notice that both give nearly the same number of

2943: 44:. Please view the links under Article milestones below to see why the nomination was archived. For older candidates, please check the 2591:

in subtitle; notable in that this is a broad cross-section of related pages, presumably collected by author without a narrow outlook

2937:

Shouldn't this be moved to the "Constructible Number" article, since they have little to do with compass and straightedge directly?

2493: 517:

and all the other articles on specific impossibility proofs. These overlap a lot, yet none of them should try to cover every topic.

1965:

Don't stress the inconsistency? This is the root of the whole problem. Inconsistency makes us look like fools and amateurs. It was

4115:

putting in things which don't mention a direct connection, that paper doesn't mention compass or ruler or anything like that. The

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under impossible constructions is poorly worded. It needs to be brought up to the level normally present on Knowledge (XXG). --

499:? Because that way I don't have to move the article, and anyway "ruler and compasses construction" is less agreeable to the ear. 2672: 3781:

I found a source and got a good start on a history section, but it needs to be beefed up with more material and more sources.

2380:

explicitly mentions the distinction between a marked ruler and plain straightedge in explaining preference for "straightedge"

1956:. Did you think, then, that you were right but you think, now, you were wrong then? Or it just doesn't matter what we call it? 144: 4476: 4257:

Doesn't seem to be add anything to the topic, it is just a nice game. Unfortunately I agree it comes under not a directory.

579:

technically, using a compass and a straightedge to draw a hexagon is impossible, since the circumference is 2Πr. not 2(3)r.

612:

I did a little research, and it seems to me that the hexagon construction is fine. From the "Constructible polygon" page:

3741:(I thought they kept trying rather than assuming impossibility--is that not right? The above assertion needs a citation.) 3491:

was singularized. I think that the title should either be hyphenated with constructions, or no hyphens with construction.

2906:

in the plane (I have added a statement to this effect). Hence adding this note would be like adding a note in the article

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graph result. My earlier suggestion was made without looking at that page and I didn't realize that it was so limited.

2739:

Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

876:

Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.

1118:"straight edge and compass" OR "straightedge and compass" OR "compass and straightedge" OR "compass and straight edge" 665:

think of a ruler as being a "marked" one (technically called a "measure"). However a ruler can also be unmarked. See

390: 2178:. How general is this, do you suppose? (I don't think this should decide the issue by itself, but it is an issue.) 2143:

I do not see consensus here, but I have added the normal move vote format above, this page should also be listed on

3487:

straightedge-and-compass constructions. When the move was made, there were two changes, the hyphens were added and

2914:

could be approximated as accurately as one wished with a rational number. This is true, but also true of all other

31: 3748:

Did the ancient Greeks come up with the requirements of a straightedge and compass construction? In what context?

2826:

Great job to everyone who has been working on all the article. I will try to get some time to help out also. --

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the most appropriate name. In short, yes, you did a lot of work, but you are also making too much fuss about it.

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Since "straigtedge and compass" is more precise but should not confuse anyone used to "ruler and compass", etc.

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I would never have been so bold as to overturn a clear consensus of any kind if that is what I had seen. I did

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very much suspect that "ruler and compass" is something of an artifact and not preferred by modern authors. --

1016: 440:-gon. WANTZEL proved this in 1837. If you read otherwise, it's because mathematicians are sloppy historians. 2793: 150: 3988:

You do not get all algebraic numbers with the Huzita–Hatori axioms for origami. The original research policy

3856:

Then this is not constructible using straightedge and compass and so doesn't belong in this article. Perhaps

2007:

I don't think such variations are "inconsistent", nor do I think this make us look like "fools and amateurs".

2843:

Currently the intro mentions that the proofs of impossibility of the famous classical constructions rely on

1339: 901: 854: 4423:) features an article on math entitled "Infinity Category Theory Offers a Bird's-Eye View of Mathematics"] 4281: 3545: 3506: 3350: 2319:

I tabulated, retaining your division into three classes. We may argue about it, but at least we will do so

620:

We let n=6 (representing a hexagon). We know that 2^1=2 and that 3 is a Fermat prime, so we can say 3*2=6.

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I must agree that the "compass and straightedge" has its points. For one thing, it permits the marked, or

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Not endorsement by AMM; but an AMM article is a credible source, just like somebody's algebra textbook.

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on Knowledge (XXG). If you would like to participate, please visit the project page, where you can join

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on Knowledge (XXG). If you would like to participate, please visit the project page, where you can join

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used a compass and straightedge construction to illustrate his theory of gravitation, rather than the

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be exceptions, but each requires a local justification. You may not see it that way and I don't think

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A ruler is commonly understood to be marked; this type of construction specifically forbids markings.

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changes throughout Euclid; but later constructions are simplified. It is understood that any of them

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Is it mentioned anywhere how to construct 60 degree angles? It is one of the simpler constructions.

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Even if you don't buy this, the construction itself comes straight from Proposition 15 in Euclid's

305: 97: 4451: 4434: 2147:, I suppose, but those of us talking about it now should probably get their chance to vote first. 1694:

Note that any argument supporting "construction" might apply to "method". No extra word is needed.

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Now for the boring, point-by-point argument -- feel free to skip this if you already know better:

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This is the more colloquilal name, and you don't need marks on the stick, i.e. 'a ruler' per se.

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Shouldn't this define what is meant by an angle of finite order or link to a definition? --

2766:. I'll take a look and check to see that all are still correct and all rds direct and single. 17: 4403: 3954:

It is mentioned in "Extended constructions", and it is an extended constructions. Yes it is

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changes the statistics enough to favour the hyphens from the 2% I found I'd like to see it.

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And I quote from the first subsection "compass and straightedge tools", first bullet point:

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a permitted construction, but I understand what you mean. Anyway, glad I could help.

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in title; note consistent use of this term across dozens of related Math Forum pages

2310: 2263: 2234: 2219: 1769:), we have it all correct. Please, for heaven's sake, let's not screw it all up now. 1456: 1435: 1048: 803: 518: 465: 458: 441: 3932:. The straightforward axioms can deal with cubics but not more complex polynomials. 3099:

These two section appear to have almost identical content. Should they be merged? --

3039:

Unsourced; and largely false. Archimedes' more "advanced analytical method" was the

2792:, this is one of the 3 classic impossible constructions. I think either one article 818:

If cut-and-translate is permitted, then it's not even necessary to produce a scale.

447:

Or is it the historians who are sloppy, notoriously incompetent mathematicians? ;-)

3288: 3224: 3079: 3023: 721: 318: 2556: 3166:"Infinite in length and only having one side." Isn't that physically impossible? 2814:- this article is probably a good enough place to refer in general to all three. 2480:

section with this title; repeated use of straightedge and no mention of "ruler".

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Before the move discussion, I'd intended to finish up my work with a rewrite of

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I went around to all linking articles and fixed all links to point directly to

1805:

a different article, however. If it redirects here, is there really a problem?

1541:

Agree with moving it back. "Ruler and compass" is by far the most common name.

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due to some grammatical rules (and I am no expert on those). The hyphens make

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is the place for metaphysical argument. But I don't generally like misleading

1787:, object to be called a ruler within the article, and then we can discuss the 1351: 979: 931:

followed by an optional one-sentence explanation, then sign your opinion with

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Personally, I find the version without hyphens jarring because it leads to a

3047:; Newton's fluxions were not, and would become so for another two centuries. 4359: 4334: 4258: 4213: 4096: 4073: 4004: 3933: 3884: 3677: 3580: 3550: 3510: 3464: 3446: 3430: 3415: 3394: 3201: 2903: 2671:. This is not a clear consensus but neither is it a ringing endorsement of 2615: 2583: 394: 104: 1625:

but it's just plain silly to war over it. I think we all know what's right.

3652:

interpretation after "compass and". I'd prefer to stay with the hyphens. —

3141:

the following (next para) but thought I'd put it here for comment first.

3022:

Obsessed as he was with a belief that gravity was known to the ancients,

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You missed nothing, friend. I just put it there. Thought it made sense.

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marked ruler -- even one with but two arbitrary marks -- is sufficient.

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with obviously the same meaning. Both words are acceptable according to

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I think it would be worthwhile to have a history section that answers:

3035:

had infact known of greatly more advanced analytical geometric methods.

3027: 1818:- Soon to be quoted in a news story about Knowledge (XXG), to be sure. 1391:. Not scientific by any measure, obviously, but worth keeping in mind. 561: 2242:

Annotate if you like, but Mathworld and AMM are pretty authoritative.

2174:

I am also somewhat concerned by Nightstallion's never having heard of

1594:, with a few notable exceptions, each of which I'm prepared to defend. 3078:

Do you think that the article is ready to become a featured article?

2607:

follow links to individual constructions to see each word in context

3797:

Add a section " much used constructions" (name open for discussion)

3185:

The fourth paragraph of the introductory section reads as follows:

2667:

The poll seems to have stalled, with about a 2 to 1 preference for

1656: 1586:, but I intend to do so. Please note that the issue is not merely 1519: 1406:

How many does it return for compass and straightedge constrution?

1231:- Straight edge is more accurate and the googling is inconclusive 703:

less-common "straightedge" is clearly and unambiguously unmarked.

683: 666: 2733:

The above discussion is preserved as an archive of the debate.

2451:

discussing Gauss' construction of the 17-sided regular polygon.

2306:

others besides me that would find a separate section useful. --

870:

The following discussion is an archived debate of the proposal.

3329:

thumbnail doesn't seem to animate, tho the gif itself does. --

2902:

single point in the plane, since the constructible points are

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and such an article would be fine for a unit distance graph.

4035:

One-, Two-, and Multi-Fold Origami Axioms by Alperin and Lang

1862:

variations in the intro, and then redirect all of them here.

1608:-- and I think everyone tangent to this discussion knows why. 1031:: "ruler" can mislead, "straightedge" is a better term here. 389:

You could fix it however you like, possibly best to point to

3116:

Compass and straightedge constructions as complex arithmetic

3094:

Compass and straightedge constructions as complex arithmetic

2527:

by Joseph A. Montagna of Yale-New Haven Teachers Institute.

1383:

For all that's worth, the google returns 110,000 answers to

1265:, referes to it as Ruler and Compass. Good enough for me. -- 4413:== Regarding Doubling the cube: Is it still impossible? == 2911: 2780:

One particular plan of mine for this field is to deal with

2487:

A First Course in Abstract Algebra:Rings, Groups and Fields

2864:

Ok, I fixed it. Hopefully it is acceptable. The page on

2529:"This book was written for students of middle school age." 1835::The criterion for inclusion is verifiability, not truth. 1415:

Woa, never mind, i did it and it's only 5 digits. weird.

1301:

certainly indicates the term popular among crackpots.) —

4235:

it (but that is personal and is not within the scope of

2501:

cited in Newsletter of the European Mathematical Society

420:

We need more on doubling the cube and angle trisection.

2851:, giving it to Galois. I think a change is needed. -- 2642: 1950: 1791:

constructions which permit the ssolution of quartics.

1623:

The actual title of the article is not the biggest deal

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move to straightedge, after reading the table below. -

103:

A fact from this article appeared on Knowledge (XXG)'s

74: 3802:, "mirror point in line" and maybe 7 more is in order. 2675:. Let's see if we can get together behind something. 491:, but for the sake of consistency I'm changing all to 488: 4174: 4130: 1158: 4420:

American Magazine (October 2021 Volume 325, Issue 4

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How much of the above shows up in Euclid, and where?

2706:

No matter your position on the poll, please propose

2636:

Geometry Constructions with Compass and Straightedge

1174:). Would you agree with this view of the situation? 751:

Does it actually matter if a ruler is marked or not?

637:

For the record, a regular hexagon is constructible.

317:, a collaborative effort to improve the coverage of 212:, a collaborative effort to improve the coverage of 2710:titles for the article that satisfy your concerns. 4204: 4160: 2458:Mathematical thought: from ancient to modern times 1166: 3637:: 832 books, 4 out of the first 20 with hyphens. 3930:Mathematics of paper folding#Trisecting an angle 3509:unless it comes up wit something really stupid. 2987:but having arbitrarily many points on it isn't. 4349:Move to 'Straightedge and compass construction' 3114:I absolutely agree that they should be merged. 2448:'Euclidean' constructions, by ruler and compass 374:introduction to the compass... a contradiction? 3118:seems a touch more understandable to me, BTW. 1816:Knowledge (XXG) is no place for "correctness" 690:straightedge; this is explicitly forbidden in 587:above unsigned comment 17:39, 8 December 2005 4242:but that would have I guess the same result. 2918:and that wouldn't be the right place for it. 2678:I'd like to ask 2 questions, very different. 2544:Compass and straightedge in the Poincare disk 8: 3325:Trisecting a segment with ruler and compass. 2973:Constructing with only ruler or only compass 2201:Discussion of List of terminology references 2336: 993:(or singular "construction" if preferred). 583:circles radius 4. repeat 180 from across 4279: 1851:Which is the correct (most accurate) term? 1363:The negative statements - the things that 1122:"Ruler and compass" OR "compass and ruler" 912:Move of page to "Compass and straightedge" 263: 158: 53: 26: 4353:No move was done after the discussion at 4194: 4181: 4175: 4173: 4150: 4137: 4131: 4129: 2525:The Early Greeks Contribution to Geometry 1247:Stick to the most widespread definition. 1157: 953:For the reasons that Joshua Davis gives. 4400:Shmuel (Seymour J.) Metz Username:Chatul 3598:"straightedge and compass constructions" 3594:"compass and straightedge constructions" 2477:construction by straightedge and compass 1854:Which is the common (most popular) term? 1162: 331:Knowledge (XXG):WikiProject Architecture 3639:"straightedge and compass construction" 3635:"compass and straightedge construction" 1857:Which of these should name the article? 669:) for a fuller discussion of all this. 265: 226:Knowledge (XXG):WikiProject Mathematics 160: 130: 3883:. I like the name isoklinostat too :) 3731:postulates, and the dubious statement 3162:About the definition of "straightedge" 990:Compass and straightedge constructions 4495:Knowledge (XXG) Did you know articles 4239:. Also I would like to add a link to 4205:{\displaystyle {\sqrt {a^{2}-b^{2}}}} 4161:{\displaystyle {\sqrt {a^{2}+b^{2}}}} 2443:Introduction to the theory of numbers 2188:specifically to eliminate confusion. 2156:I find David Kernow's preference for 1385:Straightedge and Compass construction 550:Is it really as imprtant to be here? 474: 38:Straightedge and compass construction 7: 4515:Mid-importance Architecture articles 2429:constructions with ruler and compass 2394:with the text saying unmarked ruler 1954:compass and an unmarked straightedge 1827:Oh, I'm sure; but it is policy: See 513:MERGE: This needs to be merged with 311:This article is within the scope of 206:This article is within the scope of 3505:Well I think we should just follow 2750:At the end of the move discussion, 149:It is of interest to the following 3262:Moved this here from the article: 385:already defined with the compass. 25: 4505:Mid-priority mathematics articles 2868:though now needs to be fixed. -- 1522:. I recommend moving it back. — 1229:Very weak support, almost neutral 393:, they're completely equivalent. 334:Template:WikiProject Architecture 3860:would be a better place for it. 3633:More results from Google books: 3090:Constructible points and lengths 2933:"Extended constructions" section 2887:close as you like" and exact. -- 1952:), you chose to retain the text 1866:usage is not really so crucial. 479:The article mixes the two words 298: 288: 267: 229:Template:WikiProject Mathematics 193: 183: 162: 131: 96: 30: 4120:fundamental to Knowledge (XXG). 2673:Ruler and compass constructions 2597:Geometry Construction Reference 2515:String, Straightedge and Shadow 1653:"straightedge" over "ruler" -- 978:less likely to cause confusion. 351:This article has been rated as 246:This article has been rated as 4375:ruler and compass construction 3223:that answers your question. — 2959:"Constructible Angles" section 2333:List of terminology references 1922:which way the consensus goes. 1389:ruler and compass construction 1323:Never heard of straightedge. — 1: 4510:B-Class Architecture articles 4473:2601:14F:8000:B3B0:0:0:0:5733 4387:18:34, 8 September 2018 (UTC) 4368:09:54, 8 September 2018 (UTC) 4354: 4343:09:17, 8 September 2018 (UTC) 4329:03:53, 8 September 2018 (UTC) 4298:23:04, 7 September 2018 (UTC) 4082:18:25, 29 November 2015 (UTC) 4047:17:00, 29 November 2015 (UTC) 4013:13:44, 28 November 2015 (UTC) 3972:11:27, 28 November 2015 (UTC) 3942:14:20, 27 November 2015 (UTC) 3916:19:39, 27 November 2015 (UTC) 3893:13:57, 27 November 2015 (UTC) 3870:13:25, 27 November 2015 (UTC) 3848:12:54, 27 November 2015 (UTC) 3832:04:01, 26 November 2015 (UTC) 3596:came up with 2250 books, and 3403:10:51, 19 December 2012 (UTC) 3388:05:25, 19 December 2012 (UTC) 3339:07:54, 28 February 2011 (UTC) 3320:04:03, 28 November 2009 (UTC) 3297:18:17, 1 September 2009 (UTC) 3068:21:22, 20 February 2007 (UTC) 3057:19:03, 20 February 2007 (UTC) 3012:01:39, 17 November 2006 (UTC) 2547:American Mathematical Monthly 2462:straightedge and compass only 881:The result of the debate was 745:07:39, 18 December 2007 (UTC) 632:05:56, 10 December 2005 (UTC) 603:05:30, 10 December 2005 (UTC) 325:and see a list of open tasks. 220:and see a list of open tasks. 18:Talk:Compass and straightedge 4500:B-Class mathematics articles 4460:00:48, 22 October 2021 (UTC) 4443:06:25, 20 October 2021 (UTC) 4393:From whence the restriction? 4237:Knowledge (XXG):NOTDIRECTORY 4222:02:24, 3 December 2015 (UTC) 4110:22:38, 2 December 2015 (UTC) 3995:Mathematics of paper folding 3791:22:40, 11 January 2015 (UTC) 3776:19:17, 11 January 2015 (UTC) 3544:Maybe but it doesn't follow 3005:Mathematics of paper folding 2952:21:47, 14 January 2011 (UTC) 1019:as the traditional wording. 859:16:57, 11 January 2024 (UTC) 555:03:37, 18 October 2005 (UTC) 1079:refers to unmarked rulers. 1002:See comment in discussion. 391:Compass equivalence theorem 4531: 4267:00:06, 19 March 2016 (UTC) 4252:18:36, 18 March 2016 (UTC) 3721:08:53, 21 April 2014 (UTC) 3351:Knowledge (XXG):Notability 3233:06:36, 28 March 2009 (UTC) 3210:23:01, 26 March 2009 (UTC) 3083:18:44, 23 March 2007 (UTC) 2994:18:33, 9 August 2006 (UTC) 2923:21:42, 25 April 2006 (UTC) 2892:15:21, 25 April 2006 (UTC) 2819:00:21, 13 April 2006 (UTC) 2405:compass and straightedge. 2401:Algebra: A Graduate Course 2328:05:31, 30 March 2006 (UTC) 2314:05:12, 30 March 2006 (UTC) 2300:05:02, 30 March 2006 (UTC) 2276:17:34, 31 March 2006 (UTC) 2267:05:12, 30 March 2006 (UTC) 2247:04:56, 30 March 2006 (UTC) 2238:04:43, 30 March 2006 (UTC) 2223:04:37, 30 March 2006 (UTC) 2210:04:28, 30 March 2006 (UTC) 2183:15:13, 30 March 2006 (UTC) 2152:16:46, 29 March 2006 (UTC) 2132:23:05, 30 March 2006 (UTC) 2084:05:03, 30 March 2006 (UTC) 2055:03:21, 31 March 2006 (UTC) 2017:16:41, 30 March 2006 (UTC) 1994:our discussions on my talk 1978:04:53, 30 March 2006 (UTC) 1932:23:34, 29 March 2006 (UTC) 1909:23:06, 29 March 2006 (UTC) 1891:16:19, 29 March 2006 (UTC) 1871:14:23, 29 March 2006 (UTC) 1840:16:40, 29 March 2006 (UTC) 1823:14:23, 29 March 2006 (UTC) 1810:23:55, 28 March 2006 (UTC) 1774:21:08, 28 March 2006 (UTC) 1568:02:29, 29 March 2006 (UTC) 1551:18:53, 28 March 2006 (UTC) 1531:18:40, 28 March 2006 (UTC) 1511:18:37, 28 March 2006 (UTC) 1493:17:08, 28 March 2006 (UTC) 1474:20:48, 31 March 2006 (UTC) 1463:18:16, 31 March 2006 (UTC) 1442:18:12, 31 March 2006 (UTC) 1420:17:25, 31 March 2006 (UTC) 1411:17:22, 31 March 2006 (UTC) 1401:21:46, 29 March 2006 (UTC) 1359:10:06, 31 March 2006 (UTC) 1345:11:38, 30 March 2006 (UTC) 1319:07:07, 30 March 2006 (UTC) 1310:00:24, 30 March 2006 (UTC) 1292:20:38, 29 March 2006 (UTC) 1275:19:09, 29 March 2006 (UTC) 1257:17:53, 29 March 2006 (UTC) 1236:20:18, 31 March 2006 (UTC) 1147:22:56, 31 March 2006 (UTC) 1129:17:48, 31 March 2006 (UTC) 1108:17:22, 31 March 2006 (UTC) 1096:15:34, 31 March 2006 (UTC) 1084:16:23, 31 March 2006 (UTC) 1067:23:07, 30 March 2006 (UTC) 1052:04:07, 30 March 2006 (UTC) 1036:01:23, 30 March 2006 (UTC) 1024:23:48, 29 March 2006 (UTC) 1007:15:13, 30 March 2006 (UTC) 998:23:37, 29 March 2006 (UTC) 983:22:30, 29 March 2006 (UTC) 970:21:29, 29 March 2006 (UTC) 958:17:45, 29 March 2006 (UTC) 946:16:46, 29 March 2006 (UTC) 843:23:32, 30 March 2006 (UTC) 807:09:10, 30 March 2006 (UTC) 788:00:46, 29 March 2006 (UTC) 767:00:09, 29 March 2006 (UTC) 708:23:55, 28 March 2006 (UTC) 677:16:47, 28 March 2006 (UTC) 656:19:18, 26 March 2006 (UTC) 642:23:36, 30 March 2006 (UTC) 569:23:33, 30 March 2006 (UTC) 534:22:15, 27 March 2006 (UTC) 357:project's importance scale 82:Featured article candidate 42:featured article candidate 3364:03:33, 1 April 2012 (UTC) 3253:05:40, 27 June 2009 (UTC) 3215:Do you see how the text " 2968:13:52, 18 July 2006 (UTC) 2882:Approximate constructions 2876:08:29, 7 April 2006 (UTC) 2859:16:42, 4 April 2006 (UTC) 2834:16:34, 4 April 2006 (UTC) 2806:05:00, 4 April 2006 (UTC) 2726:00:17, 3 April 2006 (UTC) 2683:23:00, 2 April 2006 (UTC) 2571: 2537: 2350: 2196:19:54, 3 April 2006 (UTC) 1373:01:35, 2 April 2006 (UTC) 1314:Use the most common term 1212:18:59, 1 April 2006 (UTC) 1199:17:28, 1 April 2006 (UTC) 1189:16:30, 1 April 2006 (UTC) 1179:15:50, 1 April 2006 (UTC) 907:07:07, 3 April 2006 (UTC) 729:05:29, 9 April 2006 (UTC) 647:"Ruler" or "Straightedge" 575:Drawing A Regular Hexagon 521:13:08, 14 Nov 2004 (UTC) 505:18:43, 2004 Mar 13 (UTC) 454:18:43, 2004 Mar 13 (UTC) 403:19:09, 13 July 2018 (UTC) 350: 283: 245: 178: 157: 56: 52: 4481:20:45, 1 June 2024 (UTC) 4408:13:35, 20 May 2021 (UTC) 4398:otherwise second class. 3812:08:55, 8 June 2015 (UTC) 3701:05:21, 29 May 2013 (UTC) 3686:13:38, 27 May 2013 (UTC) 3662:05:44, 29 May 2013 (UTC) 3611:19:03, 25 May 2013 (UTC) 3589:16:27, 25 May 2013 (UTC) 3574:16:21, 25 May 2013 (UTC) 3559:16:09, 25 May 2013 (UTC) 3540:14:48, 25 May 2013 (UTC) 3519:19:33, 24 May 2013 (UTC) 3501:18:11, 24 May 2013 (UTC) 3484:straightedge-and-compass 3473:16:22, 24 May 2013 (UTC) 3455:16:14, 24 May 2013 (UTC) 3439:14:52, 24 May 2013 (UTC) 3424:22:43, 23 May 2013 (UTC) 3200:geometric constructions? 3181:Information-free example 3176:02:59, 3 June 2008 (UTC) 3157:23:10, 31 May 2008 (UTC) 3130:16:13, 15 May 2007 (UTC) 3109:23:37, 10 May 2007 (UTC) 2794:Impossible constructions 2764:Compass and straightedge 2736:Please do not modify it. 2669:Compass and straightedge 2650:Compass and Straightedge 2625:straightedge and compass 2623:in title; text includes 2604:Compass and straightedge 2588:Compass and Straightedge 2561:Compass and straightedge 2498:straightedge and compass 2377:Straightedge and Compass 2168:compass and straightedge 1847:There are three issues: 1584:Compass and straightedge 1518:. Already discussed at 1060:Compass and straightedge 1017:Compass and straightedge 873:Please do not modify it. 692:compass and straightedge 475:'Compass' vs 'compasses' 468:13:09, 14 Nov 2004 (UTC) 461:13:08, 14 Nov 2004 (UTC) 314:WikiProject Architecture 252:project's priority scale 2160:tempting. Of the two, 661:As you say most people 560:No, but it might go to 540:largest regular polygon 209:WikiProject Mathematics 4206: 4162: 2980: 2812:proof of impossibility 2620:Geometric Construction 2613:Geometric Construction 1831:. Equally quotable is 1168: 1167:{\displaystyle \pi \;} 139:This article is rated 4207: 4163: 3726:Needs history section 2976: 2578:The Geometry Junkyard 2554:Chaim Goodman-Strauss 1203:Of course, neusis is 1169: 885:, by a 13:7 margin. — 698:To the quibble: Yes, 337:Architecture articles 143:on Knowledge (XXG)'s 4230:linking to euclidea 4172: 4128: 3858:Constructible number 3817:Unit distance graphs 3282:points on the plane 3239:Reviving name debate 3041:Method of exhaustion 2782:Trisecting the angle 2517:, Viking Press, 1965 1156: 515:Constructible number 232:mathematics articles 4273:Basic Constructions 4168:can be got but not 2790:Squaring the circle 2746:General improvement 2485:M.Anderson,T.Feil: 2465:repeated reference 1801:any effort to make 306:Architecture portal 4466:Bad external links 4202: 4158: 3384:of Knowledge (XXG) 3344:Recent (?) Results 3003:The brief plug to 2441:Hardy and Wright, 2417:ruler and compass 2370:Dummit and Foote, 2362:Ruler and Compass 2166:can be drawn with 1947:Euclidean geometry 1283:Dummit and Foote, 1164: 1163: 988:Support rename to 201:Mathematics portal 145:content assessment 57:Article milestones 4300: 4284:comment added by 4200: 4156: 3369:Three dimensions? 3217:doubling the cube 3055: 2786:Doubling the cube 2754:wrote (in part): 2663:Seeking consensus 2660: 2659: 2646:Drexel University 2538:Journal articles 2472:Topics in algebra 2391:ruler and compass 1803:ruler and compass 777:Doubling the cube 726: 371: 370: 367: 366: 363: 362: 262: 261: 258: 257: 125: 124: 91: 90: 16:(Redirected from 4522: 4379:Bill Cherowitzo 4321:Bill Cherowitzo 4318: 4211: 4209: 4208: 4203: 4201: 4199: 4198: 4186: 4185: 4176: 4167: 4165: 4164: 4159: 4157: 4155: 4154: 4142: 4141: 4132: 4000:Bill Cherowitzo 3908:Bill Cherowitzo 3862:Bill Cherowitzo 3824:Bill Cherowitzo 3493:Bill Cherowitzo 3386: 3356:Bill Cherowitzo 3318: 3316: 3311: 3302:60 degree angles 3074:Featured Article 3051: 2738: 2513:Diggins, Julia, 2505:Mar 2006 review 2422:Michael Artin's 2387:Rings and Fields 2372:Abstract Algebra 2337: 1767:angle trisection 1455: 1434: 1337: 1332: 1327: 1285:Abstract Algebra 1173: 1171: 1170: 1165: 941:See discussion. 899: 894: 889: 875: 725: 629:Imaginaryoctopus 600:Imaginaryoctopus 527:Regular polytope 339: 338: 335: 332: 329: 308: 303: 302: 292: 285: 284: 279: 271: 264: 234: 233: 230: 227: 224: 203: 198: 197: 187: 180: 179: 174: 166: 159: 142: 136: 135: 127: 100: 77: 54: 34: 27: 21: 4530: 4529: 4525: 4524: 4523: 4521: 4520: 4519: 4485: 4484: 4468: 4395: 4351: 4306: 4275: 4232: 4190: 4177: 4170: 4169: 4146: 4133: 4126: 4125: 3819: 3799: 3728: 3709: 3411: 3374: 3371: 3346: 3327: 3314: 3309: 3307: 3304: 3260: 3258:Incorrect proof 3241: 3183: 3164: 3138: 3097: 3076: 3063:rediscovered.-- 3049:Septentrionalis 3019: 3001: 2991:David.applegate 2975: 2961: 2935: 2908:Rational number 2884: 2841: 2748: 2743: 2734: 2665: 2470:I.N. Herstein, 2335: 2273:Septentrionalis 2244:Septentrionalis 2203: 2180:Septentrionalis 2149:Septentrionalis 2076:Oleg Alexandrov 1924:Oleg Alexandrov 1883:Oleg Alexandrov 1837:Septentrionalis 1807:Septentrionalis 1543:Oleg Alexandrov 1482: 1471:Septentrionalis 1453: 1449: 1432: 1393:Oleg Alexandrov 1387:and 378,000 to 1335: 1330: 1325: 1249:Oleg Alexandrov 1154: 1153: 1004:Septentrionalis 943:Septentrionalis 919: 914: 897: 892: 887: 871: 753: 649: 577: 542: 511: 477: 411: 382: 376: 336: 333: 330: 327: 326: 304: 297: 277: 231: 228: 225: 222: 221: 199: 192: 172: 140: 73: 23: 22: 15: 12: 11: 5: 4528: 4526: 4518: 4517: 4512: 4507: 4502: 4497: 4487: 4486: 4467: 4464: 4463: 4462: 4394: 4391: 4390: 4389: 4350: 4347: 4346: 4345: 4331: 4274: 4271: 4270: 4269: 4231: 4228: 4227: 4226: 4225: 4224: 4197: 4193: 4189: 4184: 4180: 4153: 4149: 4145: 4140: 4136: 4121: 4094: 4093: 4092: 4091: 4090: 4089: 4088: 4087: 4086: 4085: 4084: 4058: 4057: 4056: 4055: 4054: 4053: 4052: 4051: 4050: 4049: 4022: 4021: 4020: 4019: 4018: 4017: 4016: 4015: 3979: 3978: 3977: 3976: 3975: 3974: 3958:and yes it is 3947: 3946: 3945: 3944: 3923: 3922: 3921: 3920: 3919: 3918: 3898: 3897: 3896: 3895: 3875: 3874: 3873: 3872: 3851: 3850: 3818: 3815: 3798: 3795: 3794: 3793: 3765: 3764: 3760: 3759: 3755: 3754: 3750: 3749: 3739: 3738: 3727: 3724: 3713:AptitudeDesign 3708: 3705: 3704: 3703: 3673: 3672: 3671: 3670: 3669: 3668: 3667: 3666: 3665: 3664: 3646: 3642: 3622: 3621: 3620: 3619: 3618: 3617: 3616: 3615: 3614: 3613: 3526: 3525: 3524: 3523: 3522: 3521: 3476: 3475: 3461: 3457: 3410: 3407: 3406: 3405: 3385: 3370: 3367: 3345: 3342: 3326: 3323: 3303: 3300: 3277: 3275: 3274: 3269: 3268: 3259: 3256: 3240: 3237: 3236: 3235: 3182: 3179: 3168:207.62.186.233 3163: 3160: 3137: 3134: 3133: 3132: 3096: 3086: 3075: 3072: 3071: 3070: 3037: 3036: 3018: 3015: 3000: 2997: 2974: 2971: 2960: 2957: 2956: 2955: 2934: 2931: 2926: 2925: 2883: 2880: 2879: 2878: 2849:Pierre Wantzel 2840: 2839:Galois theory? 2837: 2824: 2823: 2822: 2821: 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3849: 3845: 3841: 3836: 3835: 3834: 3833: 3829: 3825: 3816: 3814: 3813: 3809: 3805: 3796: 3792: 3788: 3784: 3780: 3779: 3778: 3777: 3773: 3769: 3762: 3761: 3757: 3756: 3752: 3751: 3747: 3746: 3745: 3742: 3737: 3734: 3733: 3732: 3725: 3723: 3722: 3718: 3714: 3706: 3702: 3698: 3694: 3690: 3689: 3688: 3687: 3683: 3679: 3663: 3659: 3655: 3651: 3650:"garden-path" 3647: 3643: 3640: 3636: 3632: 3631: 3630: 3629: 3628: 3627: 3626: 3625: 3624: 3623: 3612: 3608: 3604: 3599: 3595: 3592: 3591: 3590: 3586: 3582: 3577: 3576: 3575: 3571: 3567: 3562: 3561: 3560: 3556: 3552: 3547: 3546:WP:COMMONNAME 3543: 3542: 3541: 3537: 3533: 3528: 3527: 3520: 3516: 3512: 3508: 3507:WP:COMMONNAME 3504: 3503: 3502: 3498: 3494: 3490: 3489:constructions 3485: 3480: 3479: 3478: 3477: 3474: 3470: 3466: 3462: 3458: 3456: 3452: 3448: 3443: 3442: 3441: 3440: 3436: 3432: 3426: 3425: 3421: 3417: 3408: 3404: 3400: 3396: 3392: 3391: 3390: 3389: 3383: 3379: 3378: 3368: 3366: 3365: 3361: 3357: 3352: 3343: 3341: 3340: 3336: 3332: 3324: 3322: 3321: 3317: 3312: 3301: 3299: 3298: 3294: 3290: 3285: 3281: 3271: 3270: 3265: 3264: 3263: 3257: 3255: 3254: 3250: 3246: 3238: 3234: 3230: 3226: 3222: 3218: 3214: 3213: 3212: 3211: 3207: 3203: 3199: 3194: 3192: 3186: 3180: 3178: 3177: 3173: 3169: 3161: 3159: 3158: 3154: 3150: 3145: 3142: 3135: 3131: 3127: 3123: 3122: 3117: 3113: 3112: 3111: 3110: 3106: 3102: 3095: 3091: 3087: 3085: 3084: 3081: 3073: 3069: 3066: 3061: 3060: 3059: 3058: 3054: 3050: 3046: 3042: 3034: 3029: 3025: 3021: 3020: 3016: 3014: 3013: 3010: 3006: 2998: 2996: 2995: 2992: 2988: 2984: 2979: 2972: 2970: 2969: 2966: 2958: 2953: 2949: 2945: 2940: 2939: 2938: 2932: 2930: 2924: 2921: 2917: 2913: 2909: 2905: 2901: 2896: 2895: 2894: 2893: 2890: 2881: 2877: 2874: 2871: 2867: 2866:Galois theory 2863: 2862: 2861: 2860: 2857: 2854: 2850: 2846: 2845:Galois theory 2838: 2836: 2835: 2832: 2829: 2820: 2817: 2816:131.107.0.106 2813: 2809: 2808: 2807: 2804: 2800: 2799: 2795: 2791: 2787: 2783: 2779: 2778: 2774: 2770: 2769: 2765: 2761: 2760: 2759: 2758: 2753: 2745: 2740: 2737: 2731: 2730: 2727: 2724: 2719: 2718: 2715: 2713: 2712: 2711: 2709: 2705: 2698: 2696: 2695: 2694: 2692: 2689: 2685: 2684: 2681: 2676: 2674: 2670: 2662: 2656: 2652: 2649: 2647: 2644: 2640: 2637: 2634: 2633: 2630: 2626: 2622: 2619: 2617: 2614: 2611: 2610: 2606: 2603: 2601: 2598: 2595: 2594: 2590: 2587: 2585: 2582: 2579: 2576: 2575: 2570: 2567: 2563: 2560: 2558: 2555: 2551: 2548: 2545: 2542: 2541: 2536: 2533: 2530: 2526: 2522: 2519: 2516: 2512: 2511: 2508: 2504: 2500: 2497: 2495: 2494:1-58488-515-7 2492: 2488: 2484: 2483: 2479: 2476: 2473: 2469: 2468: 2464: 2461: 2459: 2455: 2454: 2450: 2447: 2444: 2440: 2439: 2434: 2431: 2428: 2425: 2421: 2420: 2416: 2413: 2412:Galois Theory 2409: 2408: 2404: 2402: 2398: 2397: 2393: 2390: 2388: 2384: 2383: 2379: 2376: 2374:, 2nd edition 2373: 2369: 2368: 2364: 2361: 2359: 2358:Galois Theory 2355: 2354: 2349: 2345: 2342: 2339: 2338: 2332: 2330: 2329: 2326: 2322: 2315: 2312: 2309: 2304: 2303: 2302: 2301: 2298: 2294: 2288: 2277: 2274: 2270: 2269: 2268: 2265: 2262: 2258: 2257: 2256: 2255: 2254: 2253: 2248: 2245: 2241: 2240: 2239: 2236: 2233: 2228: 2227: 2224: 2221: 2218: 2214: 2213: 2212: 2211: 2208: 2200: 2198: 2197: 2194: 2189: 2185: 2184: 2181: 2177: 2172: 2171: 2169: 2163: 2159: 2154: 2153: 2150: 2146: 2133: 2130: 2125: 2124:made a choice 2121: 2117: 2116: 2115: 2114: 2113: 2112: 2111: 2110: 2099: 2098: 2097: 2096: 2095: 2094: 2093: 2092: 2085: 2081: 2077: 2072: 2071: 2070: 2069: 2068: 2067: 2056: 2053: 2049: 2045: 2041: 2036: 2035: 2034: 2033: 2032: 2031: 2030: 2029: 2028: 2027: 2018: 2015: 2012: 2009: 2006: 2002: 1998: 1997: 1995: 1991: 1990: 1989: 1988: 1987: 1986: 1985: 1984: 1979: 1976: 1972: 1968: 1964: 1963: 1962: 1961: 1955: 1951: 1948: 1943: 1942: 1941: 1940: 1933: 1929: 1925: 1920: 1919: 1918: 1917: 1916: 1915: 1910: 1907: 1903: 1898: 1897: 1896: 1895: 1892: 1888: 1884: 1880: 1879: 1875: 1874: 1873: 1872: 1869: 1863: 1856: 1853: 1850: 1849: 1848: 1841: 1838: 1834: 1830: 1826: 1825: 1824: 1821: 1817: 1814: 1813: 1812: 1811: 1808: 1804: 1800: 1795: 1792: 1790: 1786: 1775: 1772: 1768: 1763: 1762: 1761: 1760: 1759: 1758: 1748: 1747: 1746: 1745: 1744: 1743: 1742: 1741: 1731: 1730: 1729: 1728: 1727: 1726: 1725: 1724: 1714: 1710: 1709: 1708: 1707: 1706: 1705: 1704: 1703: 1693: 1692: 1691: 1690: 1689: 1688: 1687: 1686: 1676: 1675: 1674: 1673: 1672: 1671: 1670: 1669: 1659: 1658: 1652: 1651: 1650: 1649: 1648: 1647: 1646: 1645: 1637: 1636: 1635: 1634: 1633: 1632: 1624: 1620: 1619: 1618: 1617: 1616: 1615: 1606: 1605: 1604: 1603: 1602: 1601: 1593: 1589: 1585: 1581: 1580: 1579: 1578: 1577: 1576: 1569: 1566: 1562: 1561: 1560: 1559: 1558: 1557: 1552: 1548: 1544: 1540: 1539: 1538: 1537: 1532: 1529: 1525: 1521: 1517: 1514: 1513: 1512: 1509: 1505: 1501: 1497: 1496: 1495: 1494: 1491: 1488: 1479: 1475: 1472: 1467: 1466: 1465: 1464: 1461: 1458: 1446: 1444: 1443: 1440: 1437: 1431:google hits. 1430: 1421: 1418: 1414: 1413: 1412: 1409: 1405: 1404: 1403: 1402: 1398: 1394: 1390: 1386: 1381: 1380: 1374: 1371: 1366: 1362: 1360: 1357: 1353: 1348: 1346: 1343: 1342: 1338: 1333: 1328: 1322: 1320: 1317: 1313: 1311: 1308: 1304: 1299: 1298: 1293: 1290: 1286: 1282: 1281: 1280: 1279: 1276: 1272: 1268: 1264: 1263:Galois Theory 1261:. I Stewart: 1260: 1258: 1254: 1250: 1246: 1245: 1244: 1243: 1237: 1234: 1230: 1227: 1226: 1213: 1210: 1206: 1202: 1201: 1200: 1197: 1192: 1191: 1190: 1187: 1182: 1181: 1180: 1177: 1159: 1150: 1149: 1148: 1145: 1141: 1136: 1135: 1134: 1133: 1130: 1127: 1123: 1119: 1114: 1111: 1109: 1106: 1102: 1099: 1097: 1094: 1090: 1087: 1085: 1082: 1078: 1073: 1070: 1068: 1065: 1061: 1058: 1055: 1053: 1050: 1047: 1042: 1039: 1037: 1034: 1030: 1027: 1025: 1022: 1018: 1015: 1012: 1008: 1005: 1001: 1000: 999: 996: 992: 991: 986: 984: 981: 976: 973: 971: 968: 964: 961: 959: 956: 952: 949: 947: 944: 940: 937: 936: 932: 930: 926: 921: 920: 916: 911: 909: 908: 905: 904: 900: 895: 890: 884: 877: 874: 868: 867: 865: 860: 856: 852: 851:134.204.1.226 847: 846: 845: 844: 841: 835: 832: 826: 825: 823: 816: 808: 805: 802: 797: 796: 795: 794: 789: 786: 782: 778: 774: 773: 772: 771: 768: 764: 760: 755: 754: 750: 746: 742: 738: 734: 733: 730: 727: 723: 719: 717: 715: 712: 711: 710: 709: 706: 701: 696: 693: 689: 685: 678: 675: 672: 668: 664: 660: 659: 658: 657: 654: 646: 644: 643: 640: 633: 630: 626: 622: 619: 614: 613: 611: 608: 607: 604: 601: 597: 594: 593: 592: 591: 590: 584: 580: 574: 570: 567: 563: 559: 558: 557: 556: 553: 548: 547: 539: 535: 532: 528: 524: 523: 522: 520: 516: 508: 506: 504: 498: 494: 490: 486: 482: 467: 463: 460: 456: 455: 453: 449: 446: 445: 444: 443: 439: 434: 433: 429: 424: 423: 418: 417: 416:Eclecticology 409:older entries 408: 404: 400: 396: 392: 388: 387: 386: 379: 373: 358: 354: 348: 345: 344: 341: 324: 320: 316: 315: 307: 301: 296: 294: 291: 287: 286: 282: 276: 273: 270: 266: 253: 249: 243: 240: 239: 236: 219: 215: 211: 210: 202: 196: 191: 189: 186: 182: 181: 177: 171: 168: 165: 161: 156: 152: 146: 138: 134: 129: 128: 120: 119: 114: 112: 111:Did you know? 106: 102: 99: 95: 94: 86: 84: 83: 79: 76: 72: 71: 67: 64: 61: 60: 55: 51: 47: 43: 39: 36: 33: 29: 28: 19: 4469: 4432: 4431: 4430: 4418: 4417: 4416: 4412: 4411: 4396: 4374: 4352: 4315: 4311: 4307: 4280:— Preceding 4276: 4233: 3959: 3955: 3820: 3800: 3766: 3743: 3740: 3735: 3729: 3710: 3674: 3488: 3483: 3427: 3412: 3381: 3375: 3372: 3347: 3328: 3305: 3283: 3279: 3276: 3261: 3242: 3197: 3195: 3189: 3187: 3184: 3165: 3146: 3143: 3139: 3136:General Tone 3120: 3115: 3098: 3093: 3089: 3088:Sections on 3077: 3044: 3038: 3024:Isaac Newton 3002: 2989: 2985: 2981: 2977: 2962: 2944:140.232.0.70 2936: 2927: 2916:real numbers 2910:to say that 2899: 2885: 2842: 2825: 2772: 2755: 2749: 2735: 2732: 2707: 2703: 2701: 2690: 2687: 2686: 2677: 2666: 2654: 2628: 2624: 2565: 2549: 2531: 2528: 2520:straightedge 2514: 2502: 2486: 2471: 2457: 2442: 2432: 2423: 2411: 2400: 2386: 2371: 2357: 2320: 2318: 2289: 2286: 2204: 2190: 2186: 2176:straightedge 2175: 2173: 2165: 2162:construction 2161: 2157: 2155: 2142: 2123: 2119: 2043: 2039: 1999: 1970: 1966: 1953: 1901: 1868:Joshua Davis 1864: 1860: 1846: 1820:Joshua Davis 1815: 1798: 1796: 1793: 1788: 1784: 1782: 1712: 1654: 1622: 1591: 1587: 1524:Arthur Rubin 1515: 1504:Arthur Rubin 1498: 1483: 1450: 1428: 1426: 1382: 1378: 1377: 1364: 1340: 1303:Arthur Rubin 1284: 1262: 1241: 1240: 1228: 1204: 1139: 1121: 1117: 1112: 1100: 1088: 1076: 1071: 1056: 1040: 1028: 1013: 995:David Kernow 987: 974: 967:Joshua Davis 963:Weak Support 962: 950: 939:Weak Support 938: 928: 924: 922: 902: 882: 880: 872: 869: 863: 836: 830: 827: 819: 817: 813: 781:Arthur Rubin 699: 697: 691: 687: 681: 662: 650: 636: 624: 609: 586: 585: 581: 578: 549: 544: 543: 512: 496: 492: 484: 480: 478: 437: 435: 425: 419: 412: 383: 377: 352: 328:Architecture 319:Architecture 312: 275:Architecture 248:Mid-priority 247: 207: 173:Mid‑priority 151:WikiProjects 116: 108: 87:Not promoted 80: 40:is a former 37: 3221:"Solutions" 2600:Paul Kunkel 2356:I Stewart: 2193:Marc Harper 2011:Paul August 1487:Paul August 1447:Consequnces 1379:Google hits 1316:AdamSmithee 1194:"Support". 1033:Jonathunder 671:Paul August 223:Mathematics 214:mathematics 170:Mathematics 4489:Categories 4286:Mrperson59 4244:WillemienH 3804:WillemienH 3693:Ben Kovitz 3654:Ben Kovitz 3603:Ben Kovitz 3566:Ben Kovitz 3532:Ben Kovitz 3382:Sectioneer 3377:siNkarma86 3101:Salix alba 3053:PMAnderson 3033:Archimedes 2552:Jan 2001, 2474:(2nd ed.), 2410:E. Artin: 2343:preference 1565:Ryan Reich 1516:Never mind 1480:Discussion 1417:Kevin Baas 1408:Kevin Baas 1289:Ryan Reich 1267:Salix alba 1209:Ryan Reich 1186:Ryan Reich 1105:Kevin Baas 1021:Thumbelina 955:Ryan Reich 759:Salix alba 495:. Why not 115:column on 4355:#Bad move 3331:Arkelweis 3009:Whiteknox 2803:John Reid 2708:alternate 2680:John Reid 2616:MathWorld 2584:UC Irvine 2572:Websites 2564:in title 2523:cited by 2445:(5th ed.) 2325:John Reid 2297:John Reid 2207:John Reid 2129:John Reid 2052:John Reid 2048:pipelinks 1975:John Reid 1906:John Reid 1771:John Reid 1233:abakharev 1144:John Reid 1081:AxelBoldt 1064:John Reid 840:John Reid 705:John Reid 653:John Reid 639:John Reid 627:Book IV. 625:Elements, 610:Addition: 589:Kargoneth 566:John Reid 531:John Reid 497:compasses 489:Webster's 485:compasses 432:The Anome 422:The Anome 105:Main Page 4294:contribs 4282:unsigned 3707:polygons 3409:Bad move 3380:—Expert 3280:rational 3273:circles) 3149:SGBailey 3065:OinkOink 3045:rigorous 3028:fluxions 2965:OinkOink 2639:Dr. Math 2426:(1st ed) 2414:(2nd ed) 2399:Isaacs: 2340:citation 1797:I would 1785:markable 1500:compass. 917:Opinions 822:Tomahawk 700:strictly 663:commonly 519:Revolver 466:Revolver 459:Revolver 442:Revolver 426:Thanks, 4452:GAWiens 4435:GAWiens 3956:related 3645:titles. 3445:pages. 3289:Arvindn 3225:Dominus 3080:Tomer T 2999:Origami 2784:. Like 2433:however 2424:Algebra 2385:Ellis: 1971:because 1326:Nightst 1113:Support 1101:Support 1089:Support 1072:Abstain 1057:Support 1041:Support 1029:Support 1014:Support 975:Support 951:Support 925:Support 888:Nightst 722:Lambiam 562:Polygon 546:square. 493:compass 481:compass 355:on the 250:on the 141:B-class 107:in the 65:Process 46:archive 3783:Loraof 3768:Loraof 3460:times. 3310:SharkD 3267:space. 3245:RDBury 3017:Newton 2920:Elroch 2873:(Talk) 2856:(Talk) 2831:(Talk) 2752:Elroch 2723:Elroch 2351:Books 2321:neatly 2311:(Talk) 2264:(Talk) 2235:(Talk) 2220:(Talk) 2101:Sorry. 1799:oppose 1789:neusis 1528:(talk) 1508:(talk) 1429:unique 1307:(talk) 1242:Oppose 1196:Elroch 1176:Elroch 1126:Elroch 1120:beats 1077:always 1049:(Talk) 929:Oppose 804:(Talk) 785:(talk) 737:SharkD 688:marked 503:Herbee 452:Herbee 428:Pierre 147:scale. 68:Result 4117:WP:OR 4102:Tosha 4039:Tosha 3990:WP:OR 3964:Tosha 3840:Tosha 3315:Talk 2904:dense 2900:every 2346:note 2145:WP:RM 1829:WP:UE 1657:Ruler 1520:ruler 1457:mikka 1436:mikka 1365:can't 1352:Noisy 1336:llion 1093:lethe 980:Lunch 923:Add * 898:llion 831:could 686:is a 684:ruler 667:ruler 552:Tosha 509:merge 4477:talk 4456:talk 4439:talk 4404:talk 4383:talk 4364:talk 4360:Dmcq 4339:talk 4335:Dmcq 4325:talk 4290:talk 4263:talk 4259:Dmcq 4248:talk 4218:talk 4214:Dmcq 4106:talk 4097:Dmcq 4078:talk 4074:Dmcq 4043:talk 4009:talk 4005:Dmcq 3968:talk 3938:talk 3934:Dmcq 3912:talk 3889:talk 3885:Dmcq 3866:talk 3844:talk 3828:talk 3808:talk 3787:talk 3772:talk 3717:talk 3697:talk 3682:talk 3678:Dmcq 3658:talk 3607:talk 3585:talk 3581:Dmcq 3570:talk 3555:talk 3551:Dmcq 3536:talk 3515:talk 3511:Dmcq 3497:talk 3469:talk 3465:Dmcq 3451:talk 3447:Dmcq 3435:talk 3431:Dmcq 3420:talk 3416:Dmcq 3399:talk 3395:Dmcq 3360:talk 3335:talk 3293:talk 3249:talk 3229:talk 3206:talk 3202:Daqu 3198:what 3172:talk 3153:talk 3121:Root 3105:talk 3092:and 2948:talk 2810:Ref 2788:and 2773:this 2627:and 2491:ISBN 2080:talk 2044:this 1928:talk 1887:talk 1833:WP:V 1713:have 1655:see 1588:this 1547:talk 1397:talk 1370:Deco 1356:Talk 1271:talk 1253:talk 933:~~~~ 927:or * 883:move 855:talk 820:See 775:See 763:talk 741:talk 483:and 399:talk 395:Dmcq 62:Date 3284:can 3147:-- 3126:one 2889:Pog 2870:C S 2853:C S 2828:C S 2557:PDF 2550:108 2507:PDF 2308:C S 2293:AMM 2261:C S 2232:C S 2217:C S 2120:not 2040:may 1967:not 1902:now 1592:all 1460:(t) 1439:(t) 1341:(?) 1205:not 1140:Any 1046:C S 903:(?) 801:C S 347:Mid 242:Mid 4491:: 4479:) 4458:) 4441:) 4406:) 4385:) 4366:) 4341:) 4327:) 4314:, 4310:, 4296:) 4292:• 4265:) 4250:) 4220:) 4188:− 4108:) 4100:-- 4080:) 4045:) 4011:) 3970:) 3940:) 3914:) 3891:) 3868:) 3846:) 3838:-- 3830:) 3810:) 3789:) 3774:) 3719:) 3699:) 3684:) 3660:) 3609:) 3587:) 3572:) 3557:) 3538:) 3517:) 3499:) 3471:) 3453:) 3437:) 3422:) 3401:) 3362:) 3337:) 3295:) 3251:) 3231:) 3208:) 3193:" 3174:) 3155:) 3128:) 3107:) 2950:) 2912:Pi 2704:2. 2691:If 2688:1. 2641:, 2503:59 2323:. 2230:-- 2170:. 2082:) 2050:. 1930:) 1889:) 1711:I 1549:) 1526:| 1506:| 1502:— 1454:`' 1433:`' 1399:) 1354:| 1305:| 1273:) 1255:) 1160:π 1062:. 857:) 783:| 765:) 743:) 720:. 682:A 564:. 430:! 401:) 4475:( 4454:( 4437:( 4402:( 4381:( 4362:( 4337:( 4323:( 4316:C 4312:B 4308:A 4288:( 4261:( 4246:( 4216:( 4196:2 4192:b 4183:2 4179:a 4152:2 4148:b 4144:+ 4139:2 4135:a 4104:( 4076:( 4041:( 4007:( 3966:( 3936:( 3910:( 3887:( 3864:( 3842:( 3826:( 3806:( 3785:( 3770:( 3715:( 3695:( 3680:( 3656:( 3605:( 3601:— 3583:( 3568:( 3564:— 3553:( 3534:( 3513:( 3495:( 3467:( 3449:( 3433:( 3418:( 3397:( 3358:( 3333:( 3291:( 3247:( 3227:( 3204:( 3188:" 3170:( 3151:( 3124:( 3103:( 2954:) 2946:( 2078:( 2014:☎ 1949:( 1926:( 1885:( 1545:( 1490:☎ 1395:( 1331:a 1269:( 1251:( 893:a 853:( 824:. 761:( 739:( 674:☎ 501:— 450:— 438:n 397:( 359:. 254:. 153:: 121:. 113:" 109:" 48:. 20:)

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