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1215:, a compilation of Hispano-Arabic inspiration which Millas Vallicrosa relates to the Arabised scientific corpus of the Monastery of Ripoli. Roman methods existed side by side, in Spain, with triangulation surveying. Simplified Roman procedures seem to have been used by individual farmers, while triangulation was carried out by professional surveyors -- Christian and Muslim -- employed by large landowners. In the later Middle Ages, triangulation must have become a more common procedure.
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1342:"Important developments in cartography occurred in the 16th century in the Netherlands, Germany and Austria, where triangulation began to be applied to the measurement of land distances. (Bagrow 1964, Tooley & Bricker 1968, Crone 1978 )" -- Michael Jones, "Tycho Brahe, Cartography and Landscape in 16th Century Scandinavia", in Hannes Palang (ed), European Rural Landscapes: Persistence and Change in a Globalising Environment (2004), p.210
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1374:"Tycho Brahe was familiar with the principles of trigonometry and triangulation (Dreyer 1963 ; Christianson 2000), and had visited cartographers in Germany who were amongst the first to apply such principles to making maps (Thoren 1990; cf Tooley & Bricker 1965:35, Crone 1978 ):60-61). In 1579 he had undertaken triangulations between the main landmarks of Hven and the surrounding landscape on both sides of the Øresund..."
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and was confused as to what units of angle were being used in the calculations in this
Triangulation article. I assume the calcs here use radians, but after reading that grad or gon is used "mainly in triangulation" I'm now unsure. I think this article needs to explain the units of angle used here as
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If there is other fair use media, consider checking that you have specified the fair use rationale on the other images used on this page. Note that any fair use images uploaded after 4 May, 2006, and lacking such an explanation will be deleted one week after they have been uploaded, as described on
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Yes this needs far more explanation. The Wiki page 'Solution of triangles' has the answer, or much of it. In essence if you know the length of one side of a triangle and two of the angles of the triangle you can work out all the missing data using geometry. Thus proceeding from just one establishing
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A source is needed for the assertion that Roman surveyors didn't use trigonometry. The latter introduction of trig into medieval Europe in no way indicates whether it was used prior to the collapse of the Empire. As chordal equivalents were already in existence in Greek it seems plausible that the
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Determining your location is more difficult if you are not at ground level - so if you happened to be in a hot air balloon (or on a mountain), you would either need a third reference point, or some measure of altitude to accurately determine your location along the line between C and C' (where the
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in about the middle of the first century AD, there is a description of a dioptra that is very similar to a modern theodolote apart from the absence of a telescope... Although this is a very ingenious instrument with obvious relevance in the history of surveying, it was probably not very robust, and
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Given an observer can see two points (A and B) a known distance (D) apart (in a known direction that is not on the same line as the observer). The observer can narrow down their own location on a map to one of two points (C or C') if they can determine which way they are facing (using a compass or
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I notice at present the article is very focused on determining the location of a ship, given two observers on the shore. Triangulation works just as well for one observer on the ship, observing two objects (say perhaps the lights from two ports), if he knows how far apart the objects are (perhaps
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You could be using degrees, radians, grads. It doesn't matter. So long as you've told your calculator which units of angle you're using (or in olden days got out the appropriate book of trigonometry tables), the formulas are the same and you will get the same answer, whatever units you choose.
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You are right – however that is NOT a triangulation. Tri–angulation means using three angles (in fact two angles suffice, as the third one can be easily calculated). Of course one length is also necessary, because angles alone give us an information about the shape but not a scale of a
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I vote not. They are related in a way that the topological notion is a natural generalization of the geometrical one. So, IMO the better idea is to change their order in the article and mention the fact of generalization.... I am doing it right now... Will not be worse anyway :-)
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The page could use a section laying out some history of how triangulation became adopted in surveying. Who first used or described the method? What equipment did they use? How did this understanding spread, and who took it up? Were there initial practical difficulties?
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The observer on a ship can not determine his position by triangulation, because he can measure only one angle – at the triangle's vertex where his ship is. That gives him a position line in a form of circular arc (that follows from the inscribed angle theorem, see
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Should have gone to the wiki. The de.wiki article on triangulation in geodesy is nice, with some history; while fr.wiki also has some nice articles including
Triangulation, Resolution of a Triangle, and History of the Triangulation of France.
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is described as 'Triangulation point signed by iron rod' - but in my opinion the rod's head indicates it's not a triangulation point, but rather a benchmark, i.e. an elevation reference point. Any sources to resolve this ambiguity?
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well, I don't know if it is a proper TP, that were used for triangulation , but it is an high altitude mountain, that can be seen by other mountains. I searched a little and I found that in Israel, a nailed top is truly a TP.
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In mathematics, a triangulation is not a process, but perhaps the final result of the process. I'm not sure I can quote a good definition at the moment, but the definition on this page is unduly narrow and needs work.
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Process or not, this page is obtuse to the point of being an obstruction to learning. How on earth this would qualify as an encyclopaedic entry is beyond me. It makes a hash of a simple concept and its application.
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Right, I've now added something, as a start anyway, based mostly on the sources above. No doubt it could be improved, perhaps based on the "Further reading" sources, which I haven't had a chance to look through.
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reviews the state of play in
England in the 1570s. Systematic triangulation (rare) should be distinguished from a quick compass sketch from a single point; and from a more traditional open or closed traverse.
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Using "angular size" (how large an object looks from a point) and distance to determine size of object, or using "angular size" (how large an object looks from a point) and size of object to determine distance,
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I added above question because if we derive this factor 'd' then it requires assumption of existence of right triangles(as shown in the original figure also) which will not hold when alpha(or beta): -->
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Still very confusing: The sentence "Specifically in surveying, triangulation involves only angle measurements" is plainly wrong, you need to know one distance, angles only is not enough.
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is an easy way to insure that your image is in compliance with
Knowledge policy, but remember that you must complete the template. Do not simply insert a blank template on an image page.
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I don't want to argue, but I think that for most non-mathematician triangulation is a process, the end result beeing the lenght, height or area just determinated by ... triangulation. --
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Or using three points on a map, etc, to form a triangle, making smaller triangles within it by drawing points on the centres of the sides, and repeating the process to find the centre?
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I really don't understand triangulation after reading this article. I think it needs some clarification, and I think that an example would really help in the explanation.
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In surveying/geodesy, triangulation is also the process of covering an area with triangles and computing the co-ordinates of the nodal points. This could be made clearer.
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would soon have gone out of alignment if subjected to the wear-and-tear of use on construction sites. For everyday use in measuring angles, a simple rotateable
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I know that. I just think that given that the text refers to it often, it would be nice to have an image that actually has that angle. It's just a suggestion.
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as using triangulations to fix points in his survey of
Norfolk, circa 1570; and it was surely used much earlier than this, eg in the creation of medieval
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It will still all work fine. You'll just find that tan(α) is negative, because the perpendicular lands to the left of A rather than between A and B.
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It tells that the nailed point, is the correct point which you need to aim your instruments in order to make a correct triangulation . TNX !
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similar). If these points are along a coastline - then one of the two points C or C' will (usually) be in the sea and the other on the land.
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The text refers to the angle θ, but the image on the right does not show where this angle is. Can someone create a new image with that angle?
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90 degree,i found it to give same expression for 'd'(i should have done this earlier,i admit),also i convinced myself for the fact that d: -->
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Methods of triangulation were unknown to the Roman agromensores, and were introduced to Spain by astrolabic treatises such as that of
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See the quote from the book by Donald
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triangle you can work your way across a whole terrain measuring from one trig point and triangle to the next.
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More: according to a page at NOAA, "In the 16th and 17th centuries, triangulation started to be used widely"
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of the
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Can anyone provide more detailed information on the history of the uptake of triangulation in surveying?
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90 degrees(because then no perpendicular can be drawn between baseline & the object to be viewed)?
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Pardon my ignorance of math, etc. but when trying to understand the topic I referred to the article on
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I removed it because triangulation is usually not taught in elementary. That's why I removed the word.
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The triangulation in topology and geometry are highly related, who can merge the two parts together?
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who "described for the first time the method of triangulation still used today in surveying" (1533).
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is being used on this article. I notice the image page specifies that the image is being used under
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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Knowledge. If you would like to participate, please visit the project page, where you can join
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on Knowledge. If you would like to participate, please visit the project page, where you can join
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in Greek means any instrument for taking a line of sight. In a treatise on surveying written by
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in China (224-271) appears not to include triangulation in his "six principles of map-making".
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well as angle unit conventions and their context in triangulation, and/or add a link to the
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Doh! Thanks for not mentioning my ignorance. I was tired & have math-o-phobia?? (
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Out of curiosity, could we put a section about triangulation in chess endgames ?
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On second thoughts, while this may be the first use of a triangulation
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provided with a scale of angles was probably the normal instrument...
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Maps and their Makers: An Introduction to the History of Cartography
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Ambiguous Units of Angle in Calculations? (or explaination needed.)
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in effect used triangulation to estimate the radius of the earth.
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1399:; revised and enlarged by R.A. Skelton. Harvard University Press.
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Thanks,i convinced myself by deriving the relation when alpha: -->
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earth's surface cuts the circle of possible locations in 3D)
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Whether 'd' will have physical meaning if alpha(or beta): -->
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Is accuracy of the triangulation is better than that of the
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A History of Cartography: 2500 Years of Maps and Mapmakers
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A number of Arabic writers, including the great scientist
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A History of Engineering in Classical and Medieval Times
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Hi. Would either of these be considered triangulation:
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Google books found me this, in Donald Routledge Hill,
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Geography articles with topics of unclear notability
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1757:. Can some one comment on this? --
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1699:—Preceding
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1255:Jean Picard
1128:Seigneur101
1109:Seigneur101
601:Cartography
526:CE articles
112:Mathematics
103:mathematics
59:Mathematics
30:Start-class
1870:Categories
1776:The image
1705:EdwardLane
1300:portrayed
858:Malangthon
669:photograph
396:Notability
345:Listed at
1822:see also
1780:added by
1406:(5th ed).
1194:al-Biruni
1172:The word
1142:History ?
1017:enderminh
982:enderminh
217:Geography
208:geography
164:Geography
1851:Eliran t
1810:Eliran t
1713:contribs
1701:unsigned
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1306:portolan
1152:Resolved
1062:fair use
1046:fair use
930:Thanks.
894:unsigned
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740:Mikkalai
673:included
1725:figure.
1298:Map Man
1294:network
1228:Pei Xiu
1185:alidade
1175:dioptra
938:stroHur
842:www.doc
637:on the
544:on the
368:Infobox
326:Cleanup
244:on the
139:on the
1791:CiaPan
1759:உமாபதி
1735:CiaPan
1652:Jheald
1607:Jheald
1570:Jheald
1550:Jheald
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1314:Jheald
1270:Jheald
1235:Jheald
1008:CiaPan
968:N734LQ
943:ricane
793:Jheald
722:looxix
697:Upload
688:Flickr
299:Assess
36:scale.
1636:Jd4x4
1632:Angle
1627:Angle
1266:WP:RS
731:wshun
424:Stubs
410:Photo
1855:talk
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1054:this
998:and
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629:High
610:Maps
599:and
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569:Maps
536:High
429:See
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401:See
387:See
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359:See
331:See
316:and
290:and
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236:High
131:High
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