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An unpublished calculation of Gauss and the icosahedral group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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First appearance of the "four triangles and a square" proof of the Pythagorean Theorem
A well-known proof of the Pythagorean Theorem is illustrated in the figure below:
This figure shows a square with side lengths $a + b$, dissected into four right triangles (each with area $\frac 12 ...
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