Questions tagged [geometry]

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

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2
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2answers
841 views

What astronomical reason led to the creation of the trigonometric sine and cosine?

Sines and cosines are commonly introduced as ratios of sides of a triangle with its hypotenuse and attributed to ancient Indian scholars. However, I've never actually thought of the reason for ...
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3answers
4k views

How was geometry with 3 dimensions discovered/invented?

I wondered if back in the time of ancient Greeks mathematicians, 3D geometry was discovered as result of plane geometry? (Was there anything in the axioms of plane geometry that indicated existence of ...
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1answer
2k views

What is the origin of French/Burmester's curves?

French curves are a set of curvilinear rulers used in industrial design, before the advent of CAD, when everything still had to be drawn by hands. The most popular set of such rulers is made up of 3 ...
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1answer
124 views

Why is there some doubt whether or not Gauss saw the pseudosphere as the embodiment of hyperbolic geometry?

I read a lot of historical articles that doubt the possibility that Gauss saw in the pseudosphere the realization of hyperbolic geometry; that geodetic triangles on the pseudosphere obey the same ...
6
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2answers
611 views

What did Farcas Bolyai write to his son?

There are famous quotes about what Farcas Bolyai wrote to his son Janos to persuade him not to study the "theory of parallels " or what is now known as hyperbolic geometry But not all translation of ...
6
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3answers
330 views

What did Lobachevsky do?

It is often said that he discovered non-Euclidean geometry. But in which sense? I am reading the book 'geometry' by Brannan et al. They use the disk model as an example of hyperbolic geometry. Did ...
3
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1answer
187 views

Books or articles criticizing Benoit Mandelbrot? (fractals)

I'm researching about fractals history and one of its main contributor and promoter Benoit Mandelbrot. As far as I'm concerned, when he published his first book about this subject in 1975, he was ...
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2answers
153 views

Is there any evidence supporting this claim about Cassini and his ovals?

The Wikipedia article for Cassini ovals claims in the introduction that "Cassini believed that the Sun traveled around the Earth on one of these ovals, with the Earth at one focus of the oval." This ...
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0answers
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 ...
6
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2answers
252 views

What exactly did Poincaré mean by 'simply connected'?

I've been reading John Stillwell's translation of the famous Analysis Situs and have become confused about the exact meaning of 'simply connected' in Poincaré's language. On page 7 (in the ...
2
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1answer
178 views

How did the Arabs determine the longitudes of cities?

I am reading the book by Berggren, 'Episodes in the mathematics of medieval islam'. An important problem is determing the direction of Mecca with respect to a local city. The book introduced a method ...
2
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3answers
208 views

Who first had the idea to study surfaces via rings of functions, as in algebraic geometry?

This idea provides the foundations of algebraic geometry now; and they have certainly gone down the rabbit hole with it. As a student studying this subject, I have always found it such a great leap to ...
8
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1answer
139 views

Origin of the latitude 36 of Eratosthenes

How did Eratosthenes come up with the latitude 36 line, also called 36th parallel north, in the Mediterranean world? Rhodes was one of the navel points in his calculations and even today N36.00 goes ...
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2answers
198 views

When did mathematician start to draw figures from equation?

I know that when solving geometric problem, Descartes used variables $x,y$ and derived equation such as $y^2=cy-\frac{cxy}{b}+ay-ac$. Conversely, in algebraic geometry, an arbitrary polynomial $F(X_1,....
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2answers
8k views

What is the etymology behind sine, cosine, tangent, etc.?

I heard somewhere that it was actually a mistake in translation. What's the correct story?
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4answers
1k views

What are the origins of the study of symmetry as a subject in itself?

Symmetry has become a central concept in mathematics. The Euclidean concept of similarity is an example of symmetry, but similarity was not a subject of study in itself. Q: How did symmetry come to ...
2
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1answer
315 views

What is meant by higher order infinitesimals in the works of Galileo and Cavalieri

According to Boyer, Salviati introduces the idea of a higher order infinitesimal on the “third day” in Galileo’s Two Chief Systems of 1632. They are introduced in order to counter Simplicio’s ...
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1answer
114 views

Straight line is the shortest of curves, who proved?

I am curious, when and by whom it was proved that straight line is the shortest of measurable curves connecting two given points.
3
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1answer
82 views

Early discoveries combining groups and geometry?

More specifically: When were the symmetries of polygons/solids first presented as groups in Cayley tables? Textbooks often use the symmetries of polygons/solids to introduce group theory, however, I ...
5
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1answer
278 views

How did Ramanujan empirically obtain these errors?

In one of Srinivasa Ramanujan's writings, he discusses the perimeter of an ellipse, $p$. He finds two approximations (page 39): 16. The following approximations for $p$ were obtained empirically: ...
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5answers
1k views

What is the history of the meanings behind the word "Geometric"?

I am trying to understand the uses of the word "Geometric" throughout mathematics. I suspect that there may be some historical reasons which would tie things together and help my understanding. ...
3
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2answers
604 views

History of impact of non-Euclidean geometry on math, philosophy, and the public

I'm interested in the impact of the discovery of non-Euclidean geometry on math, philosophy, and the attitudes of the general public. I don't know anything about how things changed right after the ...
10
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2answers
278 views

On the notion of a chain (as for example in chain complex)

The thing with mathematics is that on one if you define something, you are completely free in choosing any name you want, and on the other hand you should find a meaningful name that evokes some ...
8
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1answer
345 views

What were Riemann's other two submissions for his habilitation?

In Stalking the Riemann Hypothesis, Rockmore discusses how Bernhard Riemann, as per custom, submitted three potential areas of research for his habilitation. Gauss was the chairman of the committee ...

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