# Questions tagged [geometry]

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

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### An unpublished calculation of Gauss and the icosahedral group

According to p.68 of Paul Stackel's essay "Gauss as geometer" (which deals with "complex quantities with more than two units") , Gauss calculated the coordinates of the vertices of ...
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### Where does the term "reflection" come from?

Earlier today, I was asked why a motion of the plane that fixes a line of points is called a reflection and I was stumped for an answer. The best explanation I can think of is that the image of a ...
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### What is the origin of "two straight lines cannot enclose a space" axiom in Euclid's Elements?

This post is prompted by a recent question on MSE asking about "Axiom 10" of Euclid's Elements, as found in editions by Byrne and Conway: "Two right lines cannot enclose a space". ...
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### What is the history of vector bundles and their characteristic classes?

The theory of vector bundles (and their characteristic classes) appears to have been standardized in the 20th century by all of the familiar names. Considering its substantial importance throughout ...
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### Ancient drawing board in mathematics

According to Van Der Waerden's "Science Awakening", it was common for Ancient Greek mathematicians to use a board filled with sand to draw their figures, ie : But the ancients made their ...
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### What is Laguerre's definition of the angle via the cross ratio?

I recently read an article which said Cayley showed that affine geometry could be developed from projective geometry after he learnt of Laguerre's definition of the angle using the cross ratio. This ...
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### Ancient Egyptian geometry

When reading on the topic of Ancient Egyptian geometry by Ancient Greek philosophers, there is a certain sense that this is quite a thriving discipline that seems comparable to the type of geometry ...
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### Which geometer first compared a length (one dimensional) to an area (two dimensional)?

What are sources placing a length (one dimensional) in proportion to an area (two dimensional)? The Greek geometers compared quantities of the same dimension: e.g. the area of a circle is in ...
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### DeMorgan's commentary on Euclid's Elements

Augustus DeMorgan wrote comments on Euclid's Elements, which capture many of the most important points. Heath quotes them extensively. I cannot find any source for the original: Where can I see ...
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### Who first considered signed area?

Who first suggested that the area enclosed by a closed path and that enclosed by that path traversed in reverse could be regarded as equal in magnitude but opposite in sign? Cauchy must have noticed ...
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### How did the Ancient Greeks conceive of the Platonic solids?

Now we generally think of the Platonic solids as being the regular convex polyhedra. And while the Ancient Greeks were aware of this solids as being particularly special, I don't believe that it is ...
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### Negative coefficients in the barycentric calculus

The barycentric calculus of Möbius involves formal sums of expressions of the form $mP$ where $m$ is a real number and $P$ is a point, where $mP$ is to be thought of as $m$ units of mass located at $P$...
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### First occurrence of hyperboloid paraboloid

The ancient greeks considered surfaces such as cones, but did they study the hyperbolic paraboloid? What is the first occurrence of such surface in history?
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### The role of the Elements in the development of mathematics

The Elements are often regarded as the cornerstone of the axiomatic approach to mathematics. However, mathematical textbooks have served as the foundational pillars upon which writing style, language, ...
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### Is there any book dealing with the history of both astronomy and geometry?

I am preparing an introductory course on the history of astronomy and geometry for intermediate students. The intention is to teach Copernican heliocentrism, Kepler's laws of planetary motion & ...
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### What was the pre-Renaissance proto-perspective scaling technique for painting square tiled floors?

I read once (I don't remember where exactly) about an early technique (Early Renaissance) to draw a square tiling floor in perspective. The next row in the drawing is done multiplying the previous one ...
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### When did we first know the $11$ ways of opening up a cube?

Take a box in the shape of a cube and cut $7$ of its edges so that all the faces stay connected and flatten it out onto a table. It turns out, there are $11$ distinct meshes that emerge: https://math....
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### Origin of the term "affixe"/"affix" in the geometric treatment of complex numbers

In current French mathematical tradition, when introducing complex numbers, it is common to hear about "complex plane of Argand-Cauchy". What is particular in French treatment, it is the ...
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### Explanation request for the terminology and notation employed by Gauss in his major 1843/6 treatise on Geodesy

Background: In his 1827 treatise on differential geometry, Gauss in his "theorema egregium" proved that the curvature of a surface is an intrinsic invariant; it doesn't change under ...
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### How was longitude determined in the 1700s?

I'm going through the journals of Alexander Mackenzie (ca 1790) and I came across this passage: I gather that he's determining his latitude and longitude but I'm not clear on what units he's using, ...
1 vote
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### 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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### Why did Columbus think the Earth was much smaller than it is?

Columbus set off on his westward journey to Asia, believing the Earth was much smaller than it is. There was some apparent disagreement about the size, and Columbus was staking his life on it. Why ...
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### Why 360° is assigned to circle full turn ? Not any other number? [duplicate]

Please look at this question https://math.stackexchange.com/posts/comments/9011243?noredirect=1 A user comment this so I thought of asking here You mean why did we decide on using 360 degrees? I don'...
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### What is the origin of the "problem of Brahmagupta" of constructing inscribed quadrangle with given sides?

I am looking for a source of the following construction problem: Construct an inscribed quadrangle with given sides. I know it under the name problem of Brahmagupta, but I do not know any evidence ...
1 vote
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### 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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### Historicity of Euclid. Looking for the references of Euclid in ancient texts that has survived [duplicate]

The general consensus is that Euclid was a real historical figure. Wikipedia https://en.wikipedia.org/wiki/Euclid concludes on the hypothesis that Euclid was not a real person, "This hypothesis ...
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### What is the History of Coordinates?

Can someone give a history of coordinates? When did coordinates first appear, which was the first ever coordinate system? In which field were they used?
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