Questions tagged [geometry]

Branch of Mathematics about the properties of the shapes, their similarities and transformations in the space.

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Where can I find the complete papers of abstracts published by P. G. Tait in Proc. Roy. Soc. Edinburgh in 1880?

I am interested in looking up P. G. Tait's flawed proof of the four-colour theorem, published in 1880. The citation that I have seen is: P. G. Tait, On the colouring of maps, Proc. Roy. Soc. ...
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Why couldn't Robert Peary use his theodolite at the North pole

Robert Peary writes in his book The North Pole: The instruments used in taking observations for latitude may be either a sextant and an artificial horizon, or a small theodolite. Both these ...
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I want to know the source of why Archimedes' broken chord theorem is Archimedes good

I found "The Arabian scholar Abu'l Raihan al'biruni" has attributed to Archimedes the theorem of the broken chord in web. But I couldn't find a book or papers that this Arabian scholar wrote.
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Earliest drawings of the plots of trigonometric functions

[Even though this question may seem as a duplicate of this question about the History of sine function, I'd like to ask it again - with a more specific title and a more specific focus (on specific ...
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118 views

Explanation of the main points in Gauss's resultant calculus

After he read Mobius's 1827 treatise on the "barycentric calculus" (according to Gauss's own testimony, he read this treatise only in 1843), Gauss wrote down several unpublished notes on ...
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How did Roger Cotes come up with logarithm form of Euler formula?

I have been trying to get my head around how Roger Cotes first discovered Euler Formula. I knew how Euler did it, but I wanted a new perspective, especially from someone who discovered it earlier. ...
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181 views

What was the content of Emmy Noether's 'two-line' note on Homology?

I was surprised to learn that the note published by Emmy Noether in 1925 that suggested that Homology was better thought through as actual groups rather than numerically as Betti numbers consisted of ...
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129 views

Lessons from apparent paradoxes in geometric limits

1) Zeno's oxymoronic fleet, stationary arrow: One of the earliest infinity paradoxes, of course, is the flying arrow of Zeno which can't possibly be moving since it takes a finite amount of time to ...
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87 views

Literature on Mayan mathematics

I asked this question on math.se and they sent me here. It is well known that Mayan people used vigesimal (base 20) numeral system, and had had an advanced calendar system. Except for these facts, I'...
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87 views

Who invented the push-pull construction?

I learned about the push-pull construction from a video lecture by Freedman in which it is explained starting around 39:08. It is somewhat long and technical to describe in detail, but the main idea ...
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144 views

Did Newton invent convex hulls?

The convex hull of a set of points appears recognizably in a 1676 letter from Newton to Henry Oldenburg describing Newton polygons. Is there an earlier precedent for convex hulls or is this their ...
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98 views

What are the context and motivation for Gauss's study of the "Pothenot problem"?

My question refers to p.307-335 of volume 8 of Gauss's werke, which are part of a section of volume 8 which deals with Gauss's applications of complex numbers for geometry. The pages mentioned are ...
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Old geometry terminology

I was reading Ramsey's 1927 paper "A Contribution to the Theory of Taxation" and came across the following paragraph: "We have $\lambda_1 = \mu_1,\ldots,\lambda_m = \mu_m$, $m$ hyperplanes ($n-1$ ...
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230 views

Priority on lemniscate of Gerono?

The Lemniscate of Gerono is a special case of the Lissajous curves. The dates for the two mathematicians are fairly close: Gerono (1799-1891) and Lissajous (1822-1880). Historically who has priority ...
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67 views

When was this projective property of an ellipse's directrix known?

I stumbled on this image from here: It's mentioned w.r.t. to the elliptical orbits of planets and how the focus-directrix property comes into play. It's an interesting POV but when was such a thing ...
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92 views

Were units of area/volume always in terms of squares/cubes?

Throughout our known history of geometry were the units representing areas and volumes always in terms of squares and cubes respectively? Take ancient Egyptian formulas as an example, the fact that ...
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190 views

Analysis of Moscow Mathematical Papyrus problem no. 10

This problem is giving me headaches for quite some time now I guess mainly because I am not a mathematician, but I would very much like to know if there is anyone here that has any deeper insight into ...
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Help understanding Egyptian circle

I was reading this Wikipedia page searching for the Egyptian area of circle and there is a following picture there: Trying to understand what is meant by this since it is under the "Area" ...
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101 views

Fourth powers and quartic equations before Descartes

How did mathematicians interpret quartic equations and fourth powers before Descartes propose to perform elementary arithmetic on line segments? I ask this because it seems strange to me that ...
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55 views

Earliest presentation of a 3-D permutahedron?

Below is a picture of a 3-D permutahedron sundial by Stefano Buonsignori (16th century) in the Medici collection presented by Museo Galileo. The permutahedra / permutohedra and the closely related ...
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71 views

Did the ancients have the concept of dimension?

Plainly, they knew what a circle and sphere were and also a square and cube; but did they discuss the idea that a sphere was analogous to a circle but in 3 dimensions or similarly the analogy between ...
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Which was the first coordinate system? And why was it used?

I've been researching the motivation behind the invention of the Cartesian Co-ordinate system. But I was wondering, which coordinate system was the first to be invented? Was it the Spherical Co-...
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83 views

Platonian geometry illustrated

I recently found out that a lot of Plato's work can be drawn geometrically. See the Cerritos College YouTube video "Platos Divided Line" with the description Cerritos College Professor ...
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Beltrami's Essay on the Interpretation of non-Euclidean Geometry

I am reading the Essay of the title written by Beltrami in Italian and I found a specific point of the essay which in my opinion could be fully clarified only if compared with its translations. At the ...
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What is the earliest article in which Leibniz used 'matrices'?

The Chinese were using matrices ( fengcheng in the Nine Chapters of the Mathematical Art), long before they were used in Europe which suggests that possibly they were introduced by way of them. For ...
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352 views

Does the story about Thales and the heights of pyramids illustrate that Thales did not know of AAA triangle similarity?

Thales understood similar triangles and right triangles, and what is more, used that knowledge in practical ways. The story is told in DL (loc. cit.) that he measured the height of the pyramids by ...