Talk:Geometry/Archive 1

459:

was trying to make at great length though was the synthetic part instead of the a priori part which does not quite mean an inherent truth, though this is a somewhat reasonable approximation, it just means they can be appreciated by pure logic rather than through experience (a posteriori). The argument he made central to his system was that these were synthetic truths, against the nigh-universal contemparary view, as held by Hegel or Hume (hance some philosophers), that they were analytic. Analytic means they can't be denied without contradiction, whereas synthetic means they can be denied without a logical contradiction arising. If they were Analytic non-Euclidean geometry would be impossible, as it would generate a contradiction, if they were synthetic they would be possible, in this sense he was proved right in the end with the creation of non-euclidean geometry, the a priori part is another debate. I don't suppose the issue is too important though, I doubt someone's understanding of geometry or Kant will be destroyed either way by the compromise in place, though as I said it doesn't read too fluently.

1900:

in Einstein's works. He was neither most brilliant nor of most merit in the field. He did have several ideas, undoubtedly. However, as it seems to be common to attach this expression to him, the famous E=mc2 was first derived by Poincare! This is only one of the examples, perhaps most trivial, where mr Einstein is being brought up to a rank of super-scientist, which he most certainly was not... On top of that, there is no such thing as Einstein summation convention. Yes, he seems to have made it popular, but he most certainly did not invent it (If I remember correctly it was Gibbs who first applied it). Any thoughts?

483:? Does anyone else here agree with me that the section should be reinserted into the article? The reason I feel this way is because the article does not deal with the issue of parallel lines which is the most important difference between Euclidean geometry and the two non-Euclidean geometries, hyperbolic geometry and elliptic geometry and because in general I think that this article does not give a sufficient overview of the differences between the concepts in different geometries and because in general I think this article is a second rate article which does provide enough information on geometry. 3278:), that is the main-stream point of view. Your edit does respect this fundamental pronciple, as it suggests that "point, line, plane, distance, angle, surface, and curve" are not fundamental concepts in modern geometry. This is definitively wrong, even if the properties that remain true without some of these concepts have been widely studied. Also, neutrality implies that emphasis must not be given to relatively minor subtopics, such as connections, when fundamental subareas such as algebraic geometry, fractals, or computational geometry are not even mentioned. 821:

necessarily isomorphic to the canonical hyperbolic space. But this isn't really how the terms are used commonly. Both Euclidean geometry and hyperbolic geometry more commonly refer to the study of objects living in these spaces that are invariant up to some kind of transformation. So in Euclidean geometry (the kind we all learned in junior high), we study congruence laws of triangles, and the like. Hyperbolic geometry, at this level, might study the fact that there are an infinite number of lines through a point that fail to intersect a given line.

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stated it was Analyic which is precisely what he denied. He stated it was synthetic a priori truths, such that it was truths about the world directly understandable by the human mind by pure reason alone but but that also it could be denied without contradiction, which it could as non-euclidean geometry shows. This does not however mean it was not a priori, i.e. truths about the way the world works as it does, we do after all live in Euclidean 3 space, however much we may be able to conceive other geometries.

31: 2084: 2676: 1753:. Pearce was a very bad choice from both of these points of view: it's a student essay, so it has very little reliability, and it's explicitly an advocacy piece. The Sulba Sutras are already mentioned in our article, by the way, in the first paragraph on history. If you think that should be expanded, bear in mind how briefly the same paragraph treats the mathematics of Babylon, Egypt, and China. — 2784:). In any case, the techniques of complex geometry are a combination of tools from both differential and algebraic geometry, along with many novelties, and the field is broad enough and active enough in contemporary mathematical research to be at least comparable in importance to convex geometry or discrete geometry, both of which have sections here. For example, in his preface Huybrechts writes 472:

article are not told anywhere in the article about what the difference between Euclidean and non-Euclidean geometry is. That is a very important aspect of geometry that should included in this article. There ought to be a section of the article explaining what Euclidean geometry is and what non-Euclidean geometry is and how they differ and also explaining what the other forms of geometry are.

3112: 1077:. Attention is needed to populate its entries with the most relevant and general information. The image can also be changed, but please choose one that is iconic for the topic of geometry, one that anyone can feel identified. A historic image can be a good choice but also a nice modern diagram with many of the most well known geometry theorem/problems would be appropriate. 1192: 3169: 2741: 350:. Should this wikipedia page be for advertising everything that has the word "geometry" in it, regardless of whether or not it is deemed relevant or useful? I don't really know much about this "variable shape geometry" but it seems strange that it is here while more mainstream forms of geometry such as non-commutative geometry, is not here. 930:

drawing out lines and configurations. :Also worth reading in Motte's translation of the principia is Cotes's preface to the second edition, whereby Newton's procedural method of analysis is explained and favorably compared to alternative methods.

435:, making this claim into one of the central arguments of his philosophical system. His position, its influence, and its subsequent assessment throughout 19th and 20th century are amply documented and deserve to be mentioned, but if presently another interpretation of Kant's view has become dominant, we should acknowledge it. 2723:

disproving string theory." The sentence suffers from being unsourced, poorly written, and wildly speculative. I see no value in it, especially since many of its phrases are gibberish: (currently), (theoretical dimensions),(purely defined),(technical reasons)(geometric reason), etc. It should be removed.

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That's because when there's no article for things like "elementary geometry," editors on wikipedia who don't want to wait or write the article tend to oversimplify the meaning of things by linking them to an article that they think is close enough to the meaning. What happens next is elementary terms

1922:

While I tend to agree that Einstein's reputation is hyped-up, your reading of what is in this article is off base. The statement was that differential geometry has become important for mathematical physics, not the other way around as you claim in the title here. Your tirade against Einstein is a bit

1899:

Quite unlikely. I wish to remind the author of that section, that before Einstein there were many scientists interested in the field of Classical Mechanics or theory of elasticity, plasticity and other related (to many to give names, not to omit anyone important). I do not understand this fascination

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I fear that the problem here is indeed that of different understandings of philosophy, hence I suggested removing the reference at all. I think the problem is understanding the subtleties of the idea of synthetic a priori truths, which Kant did indeed make the centre of his philosophy. The point he

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Geometry.I bet that's what you are thinking. Well, there wasn't one. What was here was the article "History of geometry" posted under the wrong name. This problem had been pointed out years ago by Larry Sanger, and has been a recurring theme on the talk page since, so I took the liberty to correct

2722:

The Dimension section ends with this sentence:"Currently, the existence of the theoretical dimensions is purely defined by technical reasons; it is likely that further research may result in a geometric reason for the significance of 10 or 11 dimensions in the theory, lending credibility or possibly

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To my mind, the word "space" usually describes a specific space, i.e., a concrete geometric object. This is usually presented as a model of the space in question—hyperbolic space has three common models that all represent the same space, for example. These are typically homogeneous and isotropic.

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Give me a little time, and I'll support this with a quote from Weil. Yes, infinitely near point is something that was recovered when birational geometry was put on a foundation. Cf. Manin talking about 'bubble space', when you blow up the projective plane everywhere, and again and again ... There is

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Although, I'd be hard pressed to find anything called 'geometry' that doesn't include at least one of those topics. Do you have any examples of geometry without points, lines, planes, distances, angles, surfaces, curves, topologies or manifolds? (Edit: I just looked over your proposed edits and saw

3329:

How can the concepts be fundamental in modern geometry when they are missing from broad fields of Geometry? Even in the 19th Century length and angle were no longer fundamental, and Projective Geometry is far from an unimportant byway in modern geometry, a fact that you implicitly accepted when you

1843:

Yes it does. It is hardly possible to explain what 'geometry' means in the 21st century without some history. The fact that you have been adding a late nineteenth century version of 'forms of geometry' rather tends to support that. Please don't remove historical context from mathematics article. It

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I had a dream the other day, in which I was studying to become a "geometrist" and I wondered (when I woke up), whether this is a real term, one I made up (which could be real), or the by product of all the drugs. Any insight into this problem would be appreciated. In any case it's my new favorite

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The emphasis on research: Quine said there are people interested in philosophy, and people interested in the history of philosophy, and the implication was (partisan and) that these were different bunches of people. The history having moved out, it was interesting to me to tackle the question from

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While I like the new article so far a lot better than the previous one as a general introduction to geometry, it all seems (except for the history summary) very much aimed at describing current research-level mathematics. Shouldn't there be something about high-school-level geometry, very early in

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Many students taking geometry at the middle- and high-school level will probably be visiting this article for help understanding the subject. Therefore, this article should be written with them in mind, as well as provide an overview to the overall subject leading to the various advanced subtopic

3086:

Well, no. Latin, in general, does not derive from Sanskrit; both derive from a common ancestor, proto-Indo-European. And in the specific case of "geometry", reliable sources trace it to Greek. The dating of the Sulba Sutras as a document to the 8th century BC is dubious; it was an oral tradition,

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Well, I've read some of your blogs and appreciate your level of understanding as well as your modesty and concern for consensus. I would say, go ahead and make your changes, refer to this talk discussion, and we'll all take it from there. You have been more than polite. I trust that you will do a

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Since the "space" articles seem to have a more clear purpose and definition, it might be best to start there, and then use the corresponding "geometry" article to treat the subjects that don't make it into the space article. Things like "history" would probably be better in the geometry article.

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but of course the case when the manifold is simply connected is the most important case and fully deserves its own article. This was kept up because some people (including me) thought that the layman would probably search for hyperbolic geometry not hyperbolic space, the latter term being less

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It might be good to note why those articles are that way. Originally, hyperbolic geometry started as an elementary article on the concept of nonEuclidean geometry, and hyperbolic space was created as a more technical treatise on the hyperbolic manifold called hyperbolic space. There is another

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I think that there should be a section of this article explaining the different forms of geometry and the differences between their concepts. That is why I wrote that section about the different forms of geometry. But every time I put a section in about it it gets removed. But the readers of this

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I believe the discussion under the Geometry beyond Euclid heading is wrong. Kant never denied the possibility of of non-euclidean geometry. He stating Geometry was A priori does not mean that non-euclidean geometry can not be developed or that he denied the possibility. That would mean that he

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This is the general article on geometry, and your edit concern the general introduction of this article. This means that only the most important aspects of the subject can appear in the introduction. As the introduction must be accessible to the most general audience (including college students,

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in the section on contemporary geometry, perhaps right after algebraic geometry (and definitely after both algebraic geometry and differential geometry). Complex geometry is a field of study that is partially encapsulated by both algebraic and differential geometry, but can also sit outside them

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is supposed to be short (people can go to the longer article if they want more detail), and is written in chronological order. I think it would be reasonable to add one paragraph about classical Indian geometry following the paragraph about Greek geometry. Hopefully someone can write something

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Persons interested in the subject matter of geometry should read and take note of Isaac Newton's discussion of Geometry in his preface to his Principia. In this he explains the need for geometrical (conceptually accurate) concepts in order for people to carry out what he calls the "mechanics" of

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Thank you, I think this is a better compromise, give my edit was almost as POV as the original content, though the article does now read rather clumsily at that point. Maybe it would be best to remove the reference to Kant at that point, instead just sayng 'some philosophers' or something else,

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The latin word is derived from the Sanskrit word jya (place)-mithi (measurement) which dates further back than the greek usage. It would be good to research this topic further and clearly mention the full origin. An 8th century text (about at least 2 centuries before pythagoras) talks about the

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The word "geometry" on the other hand, is a bit trickier. In full generality, it is the study of all spaces that have local properties that correspond to the space in question. So hyperbolic geometry is really the study of hyperbolic manifolds, spaces that are locally hyperbolic, but aren't

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I think that intuitive aspects are best summarised on both pages, as they help the reader to understand the rest. But I am not sure where to discuss finite projective spaces/geometries, i.e. PG. In a sense these are different spaces, but they are usually referred to as geometries and treated

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On the other hand, if we can't find reliable sources for the quote as it stands, I think deleting it would be just fine. It has one source, but I'm not sure how 'mainstream' it is. An easy fix would be to say that these concepts are fundamental to 'much of geometry', which is certainly

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It's quite a common error made among even among literature on the subject as the a priori, a posteriori, synthetic, analytic distinction is quite subtle, especially for those not well versed in the philosophy in question. As I said though, I don't suppose it's that important an issue.

647:, and I am wondering if the Knowledge community have established any guidelines as to which aspects (e.g. axiomatic development, analytical treatment, visualisations, history, etc.) should primarily come under the space or the geometry article or both for readability? -- -- Cheers, 164:

I noticed that the illustrations so far are historical. Perhaps some pictures, somehow illustrative of some aspects of "contemporary geometry" could be included. I think it would be cool for the lay-reader to see something like that, even if it appears quite mysterious.

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go back the Babylonians, and on the other hand school students might well expect to find the Big Bang, age of the Universe 14.5 billion years, dark matter discussed. It has been interesting so far ( a day or so): I hope some more can be added that does illuminate geometry.

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I wrote the offending sentence. I am far from an expert in philosophy, but all literature on history of mathematics that I am familiar with is critical of Kant's contribution, and some authors did call him 'wrong' on that, including, if I am not mistaken, Felix Klein, in

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are a tertiary source, and one whose reliability is in doubt where this topic is concerned. I think it would be better to name the secondary sources directly in this case (e.g. look at the references on that web site and choose carefully which ones support your text).

3313:

While geometry has evolved significantly throughout the years, there are some general concepts that are fundamental to geometry. These include the concepts of point, line, plane, distance, angle, surface, and curve, as well as the more advanced notions of topology and

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Edit: Just wanted to point out that I'm the one that wrote that line years ago, and I was just a silly young graduate student instead of the silly adult I am now. I just searched google books for definitions of geometry and chose one that I saw, and put the reference

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The photograph you added seems to be of a scholar who is not currently mentioned in the article. Please add a reliable source instead of a photograph. The book you linked does not seem to be in English, so it is hard for me to gauge how reliable the publisher is.

1013:

Are you sure you're talking about the right article? This one is Geometry, not Geology. And the first two pictures span a range from the very ancient to the very modern. I don't think it's possible to encapsulate the whole field of geometry in a single picture.

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The Cartesian approach currently predominates, with geometric questions being tackled by tools from other parts of mathematics, and geometric theories being quite open and integrated. This is to be seen in the context of the axiomatization of the whole of

1317:, which went on in the period c.1900–c.1950: in principle all methods are on a common axiomatic footing. This reductive approach has had several effects. There is a taxonomic trend, which following Klein and his Erlangen program (a taxonomy based on the 1872:

If you're going to do a History of Geometry article, why no mention of India and Pre-7th century BCE Vedic alter construction? Are you all just daft or does History only begin when Greece learned to civilize itself and come out of caves? Cheers- JBalz

3498:, I was waiting that it was signed by Chatul himself or a bot. Unfortunately, this has not been done, and I had to sign it myself. Also, I have fixed the indentation of the last Chatul's posts as well as two section links, because they were confusing. 3382:

The resolution to this problem is very simple. Just find some reliable sources that support your opinion. If there's a contest, we look to most mainstream point of view. What sources are you quoting to establish that point, line, etc. are no longer

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for that), and the place of modern geometry is reduced to half a sentence. This cannot be fixed by changing some sentences as Chatul tried. I have not yet a clear idea for a convenient lead, so I'll come back here later for suggesting a new lead.

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Geology is a broad field of study. So there should be a picture that gives a general idea or example of geology. Something that should be recognisable to the layman. The current picture would only be recognised by experts on the field of Geology.

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until a consensus is reached, and anyone is welcome to contribute to the discussion. The nomination will explain the policies and guidelines which are of concern. The discussion focuses on high-quality evidence and our policies and guidelines.

1832:

Since this is a mathematics article does it really need to have a history section. I think the article should focus on current geometry and math concepts and the history of geometry should only be discussed in the history of geometry article.

1034:

I think we should include basic geometry structures images into the article, such as basic shapes, solid figures, images related to trigonometry rather than exotic and less-known for wider audience structures. What do you think about that?

2253:

Etiquette! i thought it best to gain a consensus through discussion before changing anything. My knowledge grow but is not extensive enough to be definitive. In any case, my thought was just to put in hyperlinks to the articles already in

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Complex geometry is a highly attractive branch of modern mathematics that has witnessed many years of active and successful research and that has recently obtained new impetus from physicists' interest in questions related to mirror

3196:

Geometry includes the study of manifolds in which the concepts of line and plane are meaningless, spaces in which the concept of angles is meaningless and spaces in which the concept of distance is meaningless. Some examples:

725:

It is a good question, and I'm not sure how to answer it. Obviously we can't have two articles with identical content, so duplicating the axiomatic treatment, etc, seems to be a bad idea. You might consider having a look at

3607:" is an anachronism, as you assert yourself that the problem is that he did not follow the modern rules of rigor that have been established more than 2,000 years later. On the contrary, the sentence "geometry was put into an 707:

Sorry, by "space" I meant to imply "geometric space". Perhaps I should also specify "spatial geometries" as opposed to more abstract kinds. The point is, why have two articles on what is essentially one topic? -- Cheers,

2384:

It would be nice for the article to say something about the importance of knowledges of geometry in physics, chemistry, engineering, geology, astronomy, biology, navigation, cartography, etc... There are plenty of uses!

1976:

I have found online sources that state that ज्यामिति (jyamiti) means "geometry", but they are not sources that could be considered reliable. Most online sources trace "geometry" to Greek roots without going any

1536:). Examination of the sources used by this editor often reveals that the sources have been selectively interpreted or blatantly misrepresented, going beyond any reasonable interpretation of the authors' intent. 1639:

If the book is self-published it is not an acceptable source. For Aryabhata if he wrote many treatises it should not be difficult to source one of them, and add a sentence more informative than the photo.

1543:, and check the edits to ensure that any claims are valid, and that any references do in fact verify what is claimed. I searched the page history, and found 10 edits by Jagged 85 (for example, see 3521:, but this is not for the reasons given (implicitly) by Chatul. This is because it gives a too large place to the history of Euclidean geometry (we have a section "History", and also the articles 1666:

One of the sources you recently added is by Ian Pearce. This is not a reliable source. Please personally check the reliability of whatever you add. Incremental change is the key to success.

2000:

Thanks for that. I have completed a brief survey of the subject boundary of geometry, particularly in the west, and this is consistent with my findings, i think. Please checkout and comment on

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Does anyone have a response to what I just said and would it be possible to reinsert a revised version of my explanation of the different forms of geometry into the article as a section titled

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Users may edit the page during the discussion, including to improve the page to address concerns raised in the discussion. However, do not remove the deletion notice from the top of the page.

919:

Examples don't seem appropriate. References should be restricted to general reading on contemporary geometry. References for individual topics make much more sense on a per article basis.

411:. I believe that he was, but others (including some experts) disagree. So the article no longer makes the assertion. Other points of view (including yours) are treated in a footnote. 3671:

Here there is no claim that is mathematically false. There is only an epistmologic assertion that is controversial, which you have modified in a way that is even more controversial.

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instead of here. The procedure is almost the same and they show up automatically with the same names here, but are usable directly on other language editions of Knowledge as well. —

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certainly helps the general reader, it may help mathematicians and physicists outside their specialisms; and we anyway have thousands of purely technical mathematical articles.

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The lead and the article can certainly be improved, but this is not an easy task. So, any significant change of the lead must reach a consensus here before being implemented.

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especially since Kant arguably allowed for the possibility of non-euclidean geometry by arguing geometry was synthetic rather than analytic truths as did say Hume or Hegel.

2699: 1859:. Your proposed "different forms of geometry" is just a mess. Really, you should learn more mathematics before attempting to characterize the "different forms". -- 1512:

I think the phrase "The approach to geometric problems with geometric or mechanical means is known as synthetic geometry" is just plain wrong, so I've deleted it.

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the problem. It's pretty amazing to find a stub on such a high-profile subject, isn't it? I'm sure Knowledge's mathematics experts will have fun with this one.

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physicists, engineers and computer scientists who are interested in image processing), technical details and advanced subtopics have not their place here (see

2026:

I am suggesting that you add a link or a note referring to the work and influence of the Grassmanns in he section in which you discuss Riemann's Contribution.

532:

Um,I've added a proof of Euclid's Butterfly Theorem as well. I'd love to furnish the Napoleonic triangle proof. Could someone tell me how to upload a picture?

3004:

Hori, K., Thomas, R., Katz, S., Vafa, C., Pandharipande, R., Klemm, A., ... & Zaslow, E. (2003). Mirror symmetry (Vol. 1). American Mathematical Soc.

2936:

Kline (1972) "Mathematical thought from ancient to modern times", Oxford University Press, p. 1032. Kant did not reject the logical (analytic a priori)

2004:

I started at where i thought the problem arose, not because i was unaware of the Harappan and Akkadian/Sumerian influences, in addition to the Egyptian.

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the development of non-Euclidean geometry, cf. Leonard Nelson, "Philosophy and Axiomatics," Socratic Method and Critical Philosophy, Dover, 1965; p.164.

3087:

with the oldest written texts only being much later. Also, your capitalization is odd; why capitalize Sanskrit but not Latin, Greek, and Pythagoras? —

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and that, in fact, some of the stated theorems do not follow from the stated axioms and postulates. Should this not be discussed when mentioning the

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Reverted 1 edit by Chatul (talk): Non-neutral point of view. If you disagree with the current formulation of the lead, discuss first in the talk page

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to the subject, and illuminated the relations between complex geometry and algebraic geometry. The primary objects of study in complex geometry are

2098:

For nearly two thousand years since Euclid, while the range of geometrical questions asked and answered inevitably expanded, basic understanding of

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algebraically (i.e. abstractly) as a family. Or, should they have a page of their own (as they did until I unthinkingly tagged them onto the end of

2150:), published only after his death.There was also an influential contemporary Alternative view of Geometry expounded in the works of the Grassmanns 3395:

that you included examples!) I think it's an 'at least one of these apply', not 'every one of these apply'. Perhaps that could be made more clear.

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Sometimes, the obvious takes a while to surface. The articles on "space" assume 3 dimensions. Those on "geometry" should be agnostic. -- Cheers,

2944:, "Ideas of Space Euclidean, Non-Euclidean, and Relativistic", Oxford, 1989; p. 85. Some have implied that, in light of this, Kant had in fact 1576:

I am puzzled how the history of Geometry makes no mention of any Indian and Geometry works! Is this a joke? The references are provided for too.

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Also, connections are not minor, either in Mathematics per se or in applications of Mathematics. In particular, thye play an important role in

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All articles with "space" in the title could look roughly the same. (I haven't really checked to see if they do;in fact, they probably don't.)

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http://web.archive.org/web/20140220182415/http://my.opera.com/jehovajah/blog/2013/06/01/from-plato-to-legendre-geometry-in-aristotelian-crisis

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I think the subject is contentious. I have restored the previous version, but with some modifications toning down the bald suggestion that

2836: 2724: 2570: 1907: 1880: 1153: 1106: 689:. I'm pretty sure I could list a bunch of others if I felt like looking around a bit. So the word "each" above may be a bit exaggerated. 398: 2580: 1950: 999: 959: 3611:" is together another anachronism and a understatement, and sould be written something like: "Euclid introduced what is now called the 2560: 2204:. What matters is the consensus of the editors who remain interested in this article. So probably you would be best off taking this to 3078: 1146:

How many points are needed to determine a line? How many points are needed to form a plane? How many lines may pass through a point?

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One has to be careful with hypothetical arguments concerning what someone did or did not allow for. Kant did not deny possibility of

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When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

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When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

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You write a great deal about this on your blogs. Why don't you write about it yourself? The Grassmanns are certainly very notable.

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and then has no mention of the term "plane figure" on that page either. Bottom line, wikipedia is not elementary school-friendly.

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which consider very general spaces in which the notion of length is distinguished and defined, is a mainstay of modern geometry.″

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Yes, to upload a picture, you can click "File upload wizard" on the sidebar under the "interaction" heading, which takes you to

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The page number 52(pdf page) of the book (35 by printed page number) clearly mentions the line in English mentioned as it is.

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Wells, R. O. N., & García-Prada, O. (1980). Differential analysis on complex manifolds (Vol. 21980). New York: Springer.

1333:, at one point in the 19th century taken to be the prospective master geometric theory, is just one aspect of the general 1140:

How many lines can pass through A & B? B & C? What is the least numberof lines that can contain the three points?

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was for many years a mathematical backwater, competing in three dimensions against other popular theories in the area of

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The first of them duplicates other content; the second is highly polemical. Neither adds much of quality to the article.

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the other end: what would be an acceptable survey of the 'state of the art'? Another analogy: a cosmology basic article

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Serre, J. P. (1956). Géométrie algébrique et géométrie analytique. In Annales de l'institut Fourier (Vol. 6, pp. 1-42).

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is only one possibility for development of geometry. A broad vision of the subject of geometry was then expressed by

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Another consequence of the contemporary approach, attributable in large measure to the Procrustean bed represented by

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being a particularly brilliant figure. In contrast to such approaches to geometry as a closed system, culminating in

83:(Note: I couldn't find the message I composed to explain the move, so here it is to best of my ability from memory:) 2860: 2856: 2777: 547: 38: 2032:

It is not appropriate to do more than a brief entry in this page , but it is less appropriate to leave them out!

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I have written extensively on the Grassmanns in my blogs which you will find if you google "jehovajah Grassmann".

1250:. From the foundational point of view, on manifolds and their geometrical structures, important is the concept of 129:

Definitely, this article is one of our most important summary articles so needs to cater for a wide readership. --

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This article has been edited by a user who is known to have misused sources to unduly promote certain views (see

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pythagoras theorem with its original name. It would be good to fully research there and make the text accurate.

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to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the

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to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the

3517:'s comments on the disputed sentence. I agree also with Chatul's assertion that the lead violates the rules of 3215: 3092: 2728: 2367: 2213: 2185:

If yoou did not write it or contribute to it , i am sorry. However could you direct me to who did in that case?

2065: 1911: 1758: 1469:. As in that case, the concepts may be recovered by fresh approaches and definitions. Those may not be unique: 1381: 1019: 110: 1884: 1223:; they otherwise have rather different directions and interests. Geometry now is, in large part, the study of 1157: 1110: 394: 1954: 963: 3444: 3118: 2646: 2552: 2516: 2442: 1494: 1228: 1003: 694: 66: 3156: 3074: 2812:. Complex geometry lies at the intersection of differential geometry, algebraic geometry, and analysis of 2415: 2390: 2119: 1807: 1770: 1734: 1687: 1620: 1579: 955: 749: 662: 635:

Each article on a specific kind of space tends to have an associated article on the geometry, for example

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over these spaces. Special examples of spaces studied in complex geometry include Riemann surfaces, and

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If you have discovered URLs which were erroneously considered dead by the bot, you can report them with

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https://web.archive.org/web/20060906203141/http://www.math.niu.edu/~rusin/known-math/index/tour_geo.html

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If you have discovered URLs which were erroneously considered dead by the bot, you can report them with

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I saw the comment after I saved edits. I had mentioned references, exactly as mentioned in the website .

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is more general than Euclidean geometry, and more special than projective geometry. The whole theory of

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https://web.archive.org/web/20071004174210/http://www.gresham.ac.uk/event.asp?PageId=45&EventId=618

2551:. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit 2441:. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit 533: 3152: 2155: 3354: 3348: 3066: 2683: 2667: 2407: 2312:

redirects to this article, but the subject is not defined here. Can somebody remedy this? -- Cheers,

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https://web.archive.org/web/20160318034045/http://www.maths.tcd.ie/pub/HistMath/People/Riemann/Geom/

686: 3526: 3252:; I assume that he did not first check whether I had, in fact, discussed it. How should I proceed? 3201: 3088: 2891: 2868: 2781: 2363: 2351: 2309: 2294: 2259: 2228: 2209: 2190: 2171: 2061: 2044: 2009: 1973:"The word geometry comes from the sanskrit word jyamithi meaning the mathematics of constructions." 1754: 1708: 1434: 1389: 1354: 1015: 776: 731: 644: 575: 364: 332: 311: 264: 119: 76: 3657:

The issue isn't how much detail to go into, but rather whether a false claim should be corrected.

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Forster, O. (2012). Lectures on Riemann surfaces (Vol. 81). Springer Science & Business Media.

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On 07:25, 1 June 2013, ‎117.193.150.234 provided the following etymology for the word "geometry":

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https://web.archive.org/web/20090321024112/http://math.kennesaw.edu:80/~mdevilli/JavaGSPLinks.htm

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Griffiths, P., & Harris, J. (2014). Principles of algebraic geometry. John Wiley & Sons.

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Huybrechts, D. (2006). Complex geometry: an introduction. Springer Science & Business Media.

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Huybrechts, D. (2006). Complex geometry: an introduction. Springer Science & Business Media.

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before doing mass systematic removals. This message is updated dynamically through the template

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before doing mass systematic removals. This message is updated dynamically through the template

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give your conclusion about your findings in #s1,2 & 3 by answering the following questions.

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and regarded as of important pedagogic value, most contemporary geometry is a matter of style.

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Miranda, R. (1995). Algebraic curves and Riemann surfaces (Vol. 5). American Mathematical Soc.

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Kleiner, Israel (December 1991). "Rigor and Proof in Mathematics: A Historical Perspective".

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I agree with Charles. Your insertions show a rather misguided idea of what "geometry" means

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friendly. These reasons should hold also for projective geometry and projective space. --

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Should this wikipedia page be for advertising everything that has the word "geometry" in it

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contains the analytical results, and a description of the models of the geometry, whereas

636: 286: 272: 229:), devotes Lecture 19 (pp.145–158) to “Infinitely Near Singularities” including points in 130: 3697:

The claim that the proofs in The Elements are rigorous is false, and I gave references.

3615:, for a unified presentation of geometry as a succession of rigorously proved theorems". 3304: 3275: 2887: 2597:, "External links modified" talk page sections are no longer generated or monitored by 2467:, "External links modified" talk page sections are no longer generated or monitored by 2290: 2255: 2224: 2186: 2040: 2005: 1746: 1455:, which were dropped since they did not well fit into the pure mathematical world post- 1365: 1321:

concept) arranges theories according to generalization and specialization. For example

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definitely! what is doing a calabi-yau manifold as leading image? I will work on that.

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One of the discoveries since the ancient Greeks is that there are incorrect proofs in

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in the early 1900s. Contemporary treatment of complex geometry began with the work of

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If you found an error with any archives or the URLs themselves, you can fix them with

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If you found an error with any archives or the URLs themselves, you can fix them with

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good job and that any misunderstandings among us will be quickly resolved. Good luck!

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Serre, J. P. (1955). Faisceaux algébriques cohérents. Annals of Mathematics, 197-278.

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Thank you, ‎117.193.150.234, for bringing up a very interesting bit of information.

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Note that you also deleted the sourced changes with regard to lapses of rigor in

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If you wish to start a new discussion or revive an old one, please do so on the

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studies the nature of geometric structures modelled on, or arising out of, the

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How many types of Geometry are there? Name and give a definition of each one.

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is a conscious use of geometric language to express phenomena of the theory of

2872: 2603:. No special action is required regarding these talk page notices, other than 2473:. No special action is required regarding these talk page notices, other than 2335: 1446: 1426: 1036: 234: 207: 490:

Are degrees considered parallel lines in the spherical geometry of antiquity?

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has lines and planes but no angles or distances. The closest analog is the

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Complex geometry first appeared as a distinct area of study in the work of

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Beeson, Michael; Narboux; Wiedijk, Freek (2017). "Proof-checking Euclid".

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about the definition of synthetic geometry. Can anybody help? -- Cheers,

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i was wondering if geometry was ever based on other forms of mathematics

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I will change the article to reflect this if no one has any objections.

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In section 2.9, change "Length, area, and volume describe the size or

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emphasizes the axioms, history, and intuitive aspects of the theory.

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neighborhoods (a.k.a. infinitely near points). How lost is that? --

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Some of the representative leading figures in modern geometry are

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What about equiform geometry? It doesn't mention in the article.

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Moreover, our articles must present a neutral point of view (see

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misplaced here ... try an article that actually talks about him.

86:"What the #%&%%^?! What happened to the geometry article?!" 3147:

of an object" to "Length, area, and volume describe the size or

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Donaldson, S. (2011). Riemann surfaces. Oxford University Press.

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The above inquiry has brought me here, where i petition my case.

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on manifolds that have a geometric meaning, in the sense of the

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should be linked.) Nor am I convinced by the claim. For example

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Einstein relativity theory as a start to differential geometry?

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It seems to me that most of the deleted text really belongs at

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Please help by viewing the entry for this article shown at the

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An infobox for this article has been created. It is located at

3106: 2871:, and these spaces find uses in string theory. In particular, 867:: Axioms, history, elliptic property, homogeneous coordinates. 448:, but does it follow that he 'anticipated' them in any sense? 25: 3580:?. In that context it would be appropriate to mention, e.g., 2575:

http://www.math.niu.edu/~rusin/known-math/index/tour_geo.html

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The usual word for someone who does geometry is "geometer". —

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http://www.gresham.ac.uk/event.asp?PageId=45&EventId=618

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Hi, how are these edits irrelevant in the history section?

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redirects to the geometry page. I was attempting to access

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for additional information. I made the following changes:

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for additional information. I made the following changes:

2144:Über die Hypothesen, welche der Geometrie zu Grunde liegen 1433:, it became a beneficiary of the Bourbaki presentation of 196:

axiomatization trying to complete the work of Hilbert and

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I look forward to seeing what you guys/gals come up with.

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http://www.maths.tcd.ie/pub/HistMath/People/Riemann/Geom/

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http://www.maths.tcd.ie/pub/HistMath/People/Riemann/Geom/

1617:'s, who wrote many treatises, its caption text mentioned. 429:

Lectures on the development of mathematics in XIX century

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I'd like to add that it's preferable to add pictures to

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predicts that the extra 6 dimensions of 10 dimensional

2835:. Work in the spirit of Riemann was carried out by the 2548: 2438: 1806:..असक्तः सततं कार्य कर्म समाचर | असक्तः हि आचरन् कर्म.. 1769:..असक्तः सततं कार्य कर्म समाचर | असक्तः हि आचरन् कर्म.. 1733:..असक्तः सततं कार्य कर्म समाचर | असक्तः हि आचरन् कर्म.. 1686:..असक्तः सततं कार्य कर्म समाचर | असक्तः हि आचरन् कर्म.. 1619:..असक्तः सततं कार्य कर्म समाचर | असक्तः हि आचरन् कर्म.. 1578:..असक्तः सततं कार्य कर्म समाचर | असक्तः हि आचरन् कर्म.. 1547: 1544: 1449:. The history of 'lost' geometric methods, for example 643:. I have started making some changes to the article on 206:

Frankly, this sounds like obscure ax grinding. (Surely

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It wasn't me, but it doesn't matter who wrote it; see

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The history of 'lost' geometric methods, for example

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is suitable for inclusion in Knowledge according to

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by an inner faculty of mind: Euclidean geometry was

958:. You might want to consider removing that redirect. 3717:Meder, A. E. (1958). "What is wrong with Euclid?". 2771:I suggest the addition of a small subsection about 2607:using the archive tool instructions below. Editors 2477:using the archive tool instructions below. Editors 2455:

http://math.kennesaw.edu/~mdevilli/JavaGSPLinks.htm

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and so on. There is reference section in each page.

3603:The assertion that "there are incorrect proofs in 2338:too, but is inaccurate because it doesn't include 1943:Geometry is little cool because its all over you 1473:is an approach to infinitesimals from the side of 1285:'s reduction of geometry to algebra by means of a 571: 2875:of strings are modelled by Riemann surfaces, and 2700:Knowledge:Miscellany for deletion/Portal:Geometry 1731:I will try to present the same in few lines soon. 1680:The sources mention references too. For example, 1215:. The common feature in their work is the use of 2909:links to a dab page and must be replaced by ]. 2289:Just a sandbox attempt to make the references. 220:Algebraic Geometry for Scientists and Engineers 2593:This message was posted before February 2018. 2463:This message was posted before February 2018. 1407:axiomatization trying to complete the work of 1329:thereby becomes an aspect of geometry. Their 1242:Much of this theory relates to the theory of 182:The article now includes a suspect sentence: 8: 2148:On the hypotheses on which geometry is based 1980:We need a more complete history of the word. 1392:, and to extend geometry into the domain of 1277:, a connected development of geometry as an 3103:Semi-protected edit request on 30 June 2020 2681:A discussion is taking place as to whether 2380:Importance in fields outside of mathematics 487:20:40:21 Wednesday February 14, 2007 (UTC) 3745:(5). Taylor & Francis, Ltd.: 291–314. 3618:In any case, this is already discussed in 3352: 3064: 2433:I have just modified one external link on 2405: 3783: 2883:may be modelled by Calabi-Yau manifolds. 2543:I have just modified 3 external links on 2208:where they could see it and discuss it. — 2019:The Grassmanns Justus, Hermann and Robert 1353:, intensively studied in relation to the 873:: Models and their analytical treatments. 3816:Shmuel (Seymour J.) Metz Username:Chatul 3659:Shmuel (Seymour J.) Metz Username:Chatul 3590:Shmuel (Seymour J.) Metz Username:Chatul 3481:Shmuel (Seymour J.) Metz Username:Chatul 3449:Shmuel (Seymour J.) Metz Username:Chatul 3254:Shmuel (Seymour J.) Metz Username:Chatul 3224:Shmuel (Seymour J.) Metz Username:Chatul 1781:You might find it helpful to read about 2929: 2905:the addition of this section. However, 1787:http://www-history.mcs.st-andrews.ac.uk 1411:, is to create winners and losers. The 861:There seems to be some agreement here: 3802: 3791: 3312: 3249: 2110:, geometry, which is known to be true 2060:Which article are you talking about? — 1441:became popular, helped by a 1957 book 1364:An example from recent decades is the 44:Do not edit the contents of this page. 3248:reverted my changes with the summary 993:Picture not representative of Geology 7: 3494:Before answering a previous post of 3475:, without giving your objections in 2837:Italian school of algebraic geometry 1349:, the classical groups give rise to 1235:theory in theoretical physics. (See 605:This question is more suited to the 3477:Talk:Geometry#Flaws in The Elements 2689:Knowledge's policies and guidelines 1168:Moved two sections from the article 1125:how many lines can pass through A? 3192:Geometry is more general than that 2126:(who never published his theory), 1400:of multiplication is not assumed. 346:A new topic just popped up called 24: 2547:. Please take a moment to review 2437:. Please take a moment to review 2142:in his 1867 inauguration lecture 2134:, who demonstrated that ordinary 476:16:15:12 February 14, 2007 (UTC) 3712:. American Mathematical Society. 3167: 3110: 2843:, who introduced the concept of 2816:, and has found applications to 2739: 2674: 1303:Computational synthetic geometry 1258:in pursuing ideas introduced by 1237:Category:Structures on manifolds 1121:pls help me with my assignment.. 255:Suggestions on further expansion 29: 2940:of non-Euclidean geometry, see 2106:argued that there is only one, 2102:remained essentially the same. 1808: 1805: 1771: 1768: 1747:keeping a neutral point of view 1735: 1732: 1688: 1685: 1621: 1618: 1580: 1577: 1471:synthetic differential geometry 1289:. There were many champions of 751: 744: 3309:Geometry#Contemporary geometry 2795:Here is what I would suggest: 2698:The page will be discussed at 2354:. Also elementary terms like " 2094:to study problems in geometry. 1783:secondary and tertiary sources 1716:that's not too controversial. 1560:22:47, 24 September 2010 (UTC) 1269:Axiomatic and open development 625:01:23, 19 September 2007 (UTC) 599:23:01, 18 September 2007 (UTC) 1: 3824:23:55, 9 September 2020 (UTC) 3681:15:37, 9 September 2020 (UTC) 3667:14:58, 9 September 2020 (UTC) 3632:09:07, 9 September 2020 (UTC) 3540:08:36, 9 September 2020 (UTC) 3508:08:36, 9 September 2020 (UTC) 3489:04:36, 9 September 2020 (UTC) 3457:04:36, 9 September 2020 (UTC) 3424:22:56, 8 September 2020 (UTC) 3405:22:54, 8 September 2020 (UTC) 3371:17:58, 7 September 2020 (UTC) 3347:, which is central to modern 3330:mentioned Algebraic Geometry, 3307:, and conflicts with much of 3291:14:48, 7 September 2020 (UTC) 3262:13:48, 7 September 2020 (UTC) 3232:22:10, 4 September 2020 (UTC) 2757:15:35, 5 September 2019 (UTC) 2733:14:24, 5 September 2019 (UTC) 2334:" get oversimplified to mean 1933:18:28, 20 November 2012 (UTC) 1916:08:25, 20 November 2012 (UTC) 1867:22:32, 15 February 2007 (UTC) 1849:19:40, 15 February 2007 (UTC) 1838:19:20, 15 February 2007 (UTC) 987:22:05, 22 December 2008 (UTC) 940:21:00, 10 November 2008 (UTC) 881:Axioms of projective geometry 109:For previous discussions see 3648:are themselves anachronisms. 3311:. Would you accept deleting 2420:00:18, 23 January 2015 (UTC) 1115:05:16, 30 January 2010 (UTC) 1090:03:26, 18 January 2010 (UTC) 1063:02:46, 18 January 2010 (UTC) 1045:20:05, 5 February 2008 (UTC) 968:15:50, 6 November 2008 (UTC) 336:15:53, 23 October 2006 (UTC) 324:15:26, 23 October 2006 (UTC) 294:14:16, 19 October 2006 (UTC) 3620:Euclid's elements#Criticism 3303:The existing lead violates 3137:to reactivate your request. 3125:has been answered. Set the 3058:Origin of the word Geometry 2919:18:32, 8 January 2020 (UTC) 2896:18:05, 8 January 2020 (UTC) 2853:complex algebraic varieties 2531:15:07, 9 January 2017 (UTC) 1959:22:57, 3 January 2013 (UTC) 1425:such as those derived from 1417:(calculus of extension) of 924:17:53, 5 October 2006 (UTC) 915:Re: references and examples 481:different forms of geometry 467:Different forms of geometry 280:13:53, 3 October 2006 (UTC) 249:07:56, 9 October 2006 (UTC) 238:00:39, 9 October 2006 (UTC) 173:01:32, 9 October 2006 (UTC) 155:16:12, 3 October 2006 (UTC) 139:08:18, 3 October 2006 (UTC) 123:01:52, 3 October 2006 (UTC) 105:01:41, 3 October 2006 (UTC) 100:Good luck, and have fun. -- 3846: 3097:17:00, 16 April 2020 (UTC) 2861:holomorphic vector bundles 2857:complex analytic varieties 2798: 2778:complex analytic varieties 2624:(last update: 5 June 2024) 2540:Hello fellow Wikipedians, 2494:(last update: 5 June 2024) 2430:Hello fellow Wikipedians, 2372:06:19, 1 August 2013 (UTC) 2322:18:27, 29 April 2010 (UTC) 2075:This section in Geometry. 1711:. The history section of 1507:19:35, 13 April 2010 (UTC) 1429:. In the shape of general 1182:03:45, 25 March 2010 (UTC) 1095:Remark - equiform geometry 885:associated discussion page 548:Knowledge:Uploading images 368:02:59, 16 April 2007 (UTC) 355:19:08, 15 April 2007 (UTC) 3186:20:56, 30 June 2020 (UTC) 3161:20:39, 30 June 2020 (UTC) 2814:several complex variables 2661:23:48, 12 June 2017 (UTC) 2299:07:01, 14 June 2013 (UTC) 2168:general relativity theory 2014:08:33, 11 June 2013 (UTC) 1889:22:17, 13 July 2012 (UTC) 1231:that lies at the root of 1162:13:45, 3 March 2010 (UTC) 1075:template:general geometry 975:Geometry (disambiguation) 946:redirect from "geometric" 657:Well, you can read about 579:17:28, 31 July 2007 (UTC) 566:16:30, 31 July 2007 (UTC) 537:16:27, 31 July 2007 (UTC) 522:21:00, 27 July 2007 (UTC) 495:20:31, 27 July 2007 (UTC) 453:01:56, 11 June 2007 (UTC) 416:21:29, 10 June 2007 (UTC) 94:articles on the subject. 3598:02:07, 8 July 2020 (UTC) 3586:Grundlagen der Geometrie 2767:to Contemporary geometry 2713:23:24, 2 June 2019 (UTC) 2691:or whether it should be 2395:13:15, 3 June 2014 (UTC) 2282:11:50, 31 May 2013 (UTC) 2264:08:12, 31 May 2013 (UTC) 2248:10:43, 27 May 2013 (UTC) 2233:08:57, 27 May 2013 (UTC) 2218:04:22, 27 May 2013 (UTC) 2195:00:17, 27 May 2013 (UTC) 2070:00:02, 27 May 2013 (UTC) 2053:00:00, 27 May 2013 (UTC) 1995:09:12, 1 June 2013 (UTC) 1814:06:00, 12 May 2011 (UTC) 1800:04:28, 12 May 2011 (UTC) 1777:07:10, 11 May 2011 (UTC) 1763:06:24, 11 May 2011 (UTC) 1741:06:12, 11 May 2011 (UTC) 1726:05:05, 11 May 2011 (UTC) 1694:06:12, 11 May 2011 (UTC) 1676:04:10, 11 May 2011 (UTC) 1650:19:21, 10 May 2011 (UTC) 1627:19:12, 10 May 2011 (UTC) 1602:17:44, 10 May 2011 (UTC) 1586:17:36, 10 May 2011 (UTC) 1493:Hi, I posted a question 1382:non-commutative geometry 1024:20:21, 6 July 2009 (UTC) 1008:18:08, 6 July 2009 (UTC) 909:11:45, 19 May 2008 (UTC) 892:20:41, 18 May 2008 (UTC) 845:02:15, 18 May 2008 (UTC) 790:07:07, 28 May 2008 (UTC) 758:13:31, 17 May 2008 (UTC) 713:13:22, 17 May 2008 (UTC) 699:05:09, 17 May 2008 (UTC) 652:10:24, 12 May 2008 (UTC) 342:Variable shape geometry? 111:Talk:History of geometry 3719:The Mathematics Teacher 3445:Noncommutative Geometry 2763:Addition of section on 2718:Sentence needs deletion 2536:External links modified 2426:External links modified 2400:Geometry scavenger hunt 1965:Etymology of "geometry" 1522:10:01, 9 May 2010 (UTC) 1489:Axiomatic vs. synthetic 1281:, is in a tension with 1229:principle of covariance 348:Variable shape geometry 3801:Cite journal requires 2885: 2793: 2274:Stigmatella aurantiaca 2240:Stigmatella aurantiaca 2120:non-Euclidean geometry 2095: 2079:Geometry beyond Euclid 1987:Stigmatella aurantiaca 1751:using reliable sources 1452:infinitely near points 1273:The model of Euclid's 1254:, defined formally by 1200: 1187:Contemporary geometers 956:geometric distribution 269:Non-Euclidean geometry 244:a genuine topic here. 189:infinitely near points 3218:has no lines or even 2797: 2786: 2088:Differential geometry 2086: 1479:non-standard analysis 1467:differential calculus 1458:Principia Mathematica 1335:representation theory 1219:as the basic idea of 1194: 631:Geometries vs. Spaces 401:) 18:52, 2007 June 10 310:comment was added by 199:Principia Mathematica 113:. Founded by Greeks. 42:of past discussions. 3767:"Survey of Geometry" 3739:Mathematics Magazine 3349:Quantum Field Theory 2869:Calabi-Yau manifolds 2776:(there are singular 2605:regular verification 2475:regular verification 2358:" get redirected to 1785:. The web pages at 1745:Please keep in mind 1534:WP:Jagged 85 cleanup 1423:mathematical physics 1390:von Neumann algebras 1355:finite simple groups 1246:, or in other words 671:topological geometry 663:probability geometry 3527:History of geometry 3202:Projective Geometry 2782:algebraic varieties 2595:After February 2018 2465:After February 2018 2310:Elementary geometry 2304:Elementary geometry 2172:Riemannian geometry 1809:Humour Thisthat2011 1772:Humour Thisthat2011 1736:Humour Thisthat2011 1709:History of geometry 1689:Humour Thisthat2011 1622:Humour Thisthat2011 1581:Humour Thisthat2011 1565:The reverted edits 1435:multilinear algebra 1380:. In contrast, the 1305:is now a branch of 1244:continuous symmetry 973:I redirected it to 865:Projective geometry 777:hyperbolic manifold 740:Hyperbolic geometry 732:Hyperbolic geometry 645:Projective geometry 590:geometry beginnings 503:User:Rktect/degrees 265:projective geometry 218:'s 1990 monograph, 202:, is yet unwritten. 77:History of geometry 3523:Euclidean geometry 3441:Algebraic Geometry 2877:superstring theory 2649:InternetArchiveBot 2600:InternetArchiveBot 2519:InternetArchiveBot 2470:InternetArchiveBot 2116:synthetic a priori 2096: 1291:synthetic geometry 1233:general relativity 1201: 667:topological spaces 659:probability spaces 641:Euclidean geometry 446:Special relativity 275:should be added. ( 3704:(February 2011). 3605:Euclid's Elements 3574:Euclid's Elements 3510: 3473:Euclid's Elements 3373: 3357:comment added by 3141: 3140: 3082: 3069:comment added by 2849:complex manifolds 2841:Jean-Pierre Serre 2625: 2495: 2422: 2410:comment added by 2176:Hermann Grassmann 2160:Hermann Grassmann 2156:Robert Grassmann 2152:Justus Grassmann 2056: 2039:comment added by 1949:comment added by 1906:comment added by 1879:comment added by 1682:about Sulbasutras 1528:Misuse of sources 1475:categorical logic 1443:Geometric Algebra 1419:Hermann Grassmann 1378:complex manifolds 1357:; and associated 1287:coordinate system 1256:Shiing-shen Chern 1199:Petrie Projection 1152:comment added by 1105:comment added by 1088: 1061: 1030:Picture selection 615: 572:Wikimedia Commons 556: 528:Butterfly Theorem 512: 442:Quantum mechanics 403: 389:comment added by 374:Kant and Geometry 327: 261:analytic geometry 227:978-0-8218-1535-9 102:The Transhumanist 72: 71: 54: 53: 48:current talk page 3837: 3810: 3804: 3799: 3797: 3789: 3787: 3774: 3761: 3733: 3713: 3706:"Why Only Five?" 3613:axiomatic method 3558:I've called for 3557: 3493: 3244: 3178:Bill Cherowitzo 3176:- good catch. -- 3175: 3171: 3170: 3132: 3128: 3114: 3113: 3107: 3050: 3047: 3041: 3038: 3032: 3029: 3023: 3020: 3014: 3011: 3005: 3002: 2996: 2993: 2987: 2984: 2978: 2975: 2969: 2966: 2960: 2955: 2949: 2934: 2865:coherent sheaves 2833:Riemann surfaces 2831:in his study of 2829:Bernhard Riemann 2806:Complex geometry 2801:Complex geometry 2773:complex geometry 2765:complex geometry 2747: 2743: 2742: 2711: 2678: 2677: 2659: 2650: 2623: 2622: 2601: 2529: 2520: 2493: 2492: 2471: 2340:geometric shapes 2122:in the works of 2090:uses tools from 2055: 2033: 1961: 1925:Bill Cherowitzo 1918: 1891: 1846:Charles Matthews 1812: 1810: 1775: 1773: 1739: 1737: 1692: 1690: 1625: 1623: 1584: 1582: 1439:Clifford algebra 1431:exterior algebra 1414:Ausdehnungslehre 1339:algebraic groups 1331:invariant theory 1327:classical groups 1315:pure mathematics 1307:computer algebra 1299:Hilbert's axioms 1279:axiomatic system 1239:for a survey.) 1217:smooth manifolds 1213:William Thurston 1164: 1117: 1087: 1085: 1078: 1060: 1058: 1051: 950:For some reason 921:Charles Matthews 871:Projective space 754: 753: 746: 736:Hyperbolic space 728:Hyperbolic space 623: 613: 564: 554: 544:Knowledge:Upload 520: 510: 402: 383: 305: 246:Charles Matthews 152:Charles Matthews 75:Separation from 63: 56: 55: 33: 32: 26: 3845: 3844: 3840: 3839: 3838: 3836: 3835: 3834: 3800: 3790: 3777: 3771:web.mnstate.edu 3764: 3751:10.2307/2690647 3736: 3716: 3700: 3570: 3551: 3238: 3194: 3168: 3166: 3130: 3126: 3111: 3105: 3060: 3055: 3054: 3053: 3048: 3044: 3039: 3035: 3030: 3026: 3021: 3017: 3012: 3008: 3003: 2999: 2994: 2990: 2985: 2981: 2976: 2972: 2967: 2963: 2956: 2952: 2935: 2931: 2822:mirror symmetry 2803: 2769: 2740: 2738: 2720: 2707: 2684:Portal:Geometry 2679: 2675: 2672: 2668:Portal:Geometry 2653: 2648: 2616: 2609:have permission 2599: 2553:this simple FaQ 2538: 2523: 2518: 2486: 2479:have permission 2469: 2443:this simple FaQ 2428: 2402: 2382: 2360:geometric shape 2332:geometric solid 2306: 2136:Euclidean space 2081: 2034: 2021: 1967: 1944: 1941: 1901: 1897: 1874: 1830: 1613:The picture is 1569: 1530: 1491: 1481:is by means of 1398:commutative law 1359:finite geometry 1323:affine geometry 1271: 1189: 1170: 1147: 1138: 1135: 1129: 1123: 1100: 1097: 1081: 1079: 1071: 1054: 1052: 1032: 995: 948: 917: 750: 679:vector geometry 637:Euclidean space 633: 610: 592: 551: 530: 507: 469: 433:inherent truths 384: 376: 344: 306:—The preceding 301: 287:finite geometry 273:affine geometry 257: 208:Procrustean bed 180: 162: 81: 59: 30: 22: 21: 20: 12: 11: 5: 3843: 3841: 3833: 3832: 3831: 3830: 3829: 3828: 3827: 3826: 3813: 3812: 3811: 3775: 3765:Timothy Peil. 3762: 3734: 3725:(8): 578–584. 3714: 3710:Feature column 3702:Bill Casselman 3688: 3687: 3686: 3685: 3684: 3683: 3652: 3651: 3650: 3649: 3635: 3634: 3616: 3609:axiomatic form 3569: 3563: 3549: 3548: 3547: 3546: 3545: 3544: 3543: 3542: 3511: 3464: 3463: 3462: 3461: 3460: 3459: 3429: 3428: 3427: 3426: 3408: 3407: 3391: 3390: 3385: 3384: 3379: 3378: 3377: 3376: 3375: 3374: 3336: 3335: 3334: 3333: 3332: 3331: 3322: 3321: 3320: 3319: 3318: 3317: 3296: 3295: 3294: 3293: 3279: 3272: 3235: 3234: 3208: 3193: 3190: 3189: 3188: 3151:of an object" 3139: 3138: 3115: 3104: 3101: 3100: 3099: 3089:David Eppstein 3059: 3056: 3052: 3051: 3042: 3033: 3024: 3015: 3006: 2997: 2988: 2979: 2970: 2961: 2950: 2928: 2927: 2923: 2922: 2921: 2799:Main article: 2768: 2761: 2760: 2759: 2725:40.142.185.108 2719: 2716: 2673: 2671: 2666:Nomination of 2664: 2643: 2642: 2635: 2588: 2587: 2579:Added archive 2577: 2569:Added archive 2567: 2559:Added archive 2537: 2534: 2513: 2512: 2505: 2458: 2457: 2449:Added archive 2427: 2424: 2401: 2398: 2381: 2378: 2377: 2376: 2375: 2374: 2364:Oicumayberight 2305: 2302: 2287: 2286: 2285: 2284: 2251: 2250: 2221: 2220: 2210:David Eppstein 2080: 2077: 2073: 2072: 2062:David Eppstein 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762: 761: 760: 718: 717: 716: 715: 702: 701: 687:Stone geometry 685:but not about 677:but not about 669:but not about 661:but not about 632: 629: 628: 627: 607:reference desk 591: 588: 586: 584: 583: 582: 581: 576:David Eppstein 529: 526: 525: 524: 468: 465: 456: 455: 437: 436: 419: 418: 409:Kant was wrong 391:137.205.26.170 375: 372: 371: 370: 365:David Eppstein 343: 340: 339: 338: 333:David Eppstein 300: 297: 259:Section(s) on 256: 253: 252: 251: 204: 203: 179: 176: 161: 158: 142: 141: 126: 125: 120:David Eppstein 118:the article? — 80: 73: 70: 69: 64: 52: 51: 34: 23: 15: 14: 13: 10: 9: 6: 4: 3: 2: 3842: 3825: 3821: 3817: 3814: 3808: 3795: 3786: 3781: 3776: 3772: 3768: 3763: 3759: 3756: 3752: 3748: 3744: 3740: 3735: 3731: 3728: 3724: 3720: 3715: 3711: 3707: 3703: 3699: 3698: 3696: 3695: 3694: 3693: 3692: 3691: 3690: 3689: 3682: 3678: 3674: 3670: 3669: 3668: 3664: 3660: 3656: 3655: 3654: 3653: 3647: 3643: 3639: 3638: 3637: 3636: 3633: 3629: 3625: 3621: 3617: 3614: 3610: 3606: 3602: 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703: 700: 696: 692: 691:Michael Hardy 688: 684: 680: 676: 675:vector spaces 672: 668: 664: 660: 656: 655: 654: 653: 650: 646: 642: 638: 630: 626: 621: 617: 608: 604: 603: 602: 600: 597: 596:65.33.196.220 589: 587: 580: 577: 573: 569: 568: 567: 562: 558: 549: 545: 541: 540: 539: 538: 535: 527: 523: 518: 514: 505: 504: 499: 498: 497: 496: 493: 488: 486: 482: 477: 475: 466: 464: 460: 454: 451: 447: 443: 439: 438: 434: 430: 425: 424: 423: 417: 414: 410: 406: 405: 404: 400: 396: 392: 388: 380: 373: 369: 366: 362: 359: 358: 357: 356: 353: 349: 341: 337: 334: 330: 329: 328: 325: 321: 317: 313: 309: 298: 296: 295: 292: 288: 283: 281: 278: 274: 270: 266: 262: 254: 250: 247: 242: 241: 240: 239: 236: 232: 228: 225: 221: 217: 213: 209: 201: 200: 195: 191: 190: 185: 184: 183: 177: 175: 174: 171: 168: 159: 157: 156: 153: 148: 140: 136: 132: 128: 127: 124: 121: 116: 115: 114: 112: 107: 106: 103: 98: 95: 91: 87: 84: 78: 74: 68: 65: 62: 58: 57: 49: 45: 41: 40: 35: 28: 27: 19: 18:Talk:Geometry 3794:cite 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