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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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 ...
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 ...
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 ...
11
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1answer
291 views

A knot cannot be tied in 4-dimensions, but when was this conjectured and proven?

Today it has been shown that a 1-dimensional object in 4-dimensional space cannot be tied into a knot. But I would like to know who first conjectured this and when? And when was it proven? (P.S., is ...
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 ...
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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,....
9
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1answer
1k views

What was the best approximation of π known to ancient Babylonians?

Wikipedia's Babylonian mathematics says that the ancient Babylonians usually used a round value for $\pi$ (3). But they knew a more precise value: Babylonian texts usually approximated π≈3, ...
11
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2answers
893 views

Where was the word "pencil" first used in (projective) geometry and what is the reason behind this curious name?

The title is pretty self-explanatory: A pencil in projective (or algebraic) geometry is the family of all lines through a point. The above-linked website tells me that Cremona, on page x of Elements ...
18
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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?
8
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1answer
3k views

How was Newton's classification of cubic curves completed?

According to what I have read, using Newton’s methods there are 78 different families of cubic curves. Newton discovered 72 of them while “subsequent research identified another 6”. This paper ...
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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 ...
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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.
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3answers
2k views

What is Ptolemy holding in his picture on Wikipedia?

I would like to know the name of the device Ptolemy is holding in his picture
2
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1answer
314 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 ...
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: ...
8
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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
603 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 ...
9
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4answers
1k views

First proof that circumference/diameter $=\pi$

I am interested in this question: Who was the first to show that for every circle the fraction $$\frac{\text{circumference}}{\text{diameter}}$$ is always constant? I am not interested in $\pi$ ...
10
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2answers
277 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 ...
13
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4answers
347 views

Why did Newton want lines to be generated by continued motion of points rather than by apposition of parts?

The following passage has been extracted from the Newton's (John Stewart's English translated version) "Sir Issac Newton's two Treatises: Of the Quadrature of Curves, and Analysis by equations of an ...
8
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1answer
342 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 ...
17
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4answers
3k views

Who was the first to calculate $\pi$?

I am very interested in the history of $\pi$. I am first trying to find out who calculated it. Many sources have different answers, from the ancient Egyptians, to Archimedes, to the Babylonians. I ...

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