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Questions tagged [euclidean-geometry]

For questions about the mathematical study of shapes and space based on the works of Euclid.

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9 votes
1 answer
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When do we see for the first time the use of the Cartesian coordinates?

I want to see an exact image of the first use of the Cartesian plane. I guess it came the first time with Descartes.
copper's user avatar
  • 993
12 votes
1 answer
3k views

The origin of quadratic equation in actual practice

I read that in ancient times the quadratic equation of this kind $$x^2+10x=39$$ had been solved long ago. I read that this kind of equation originated in the geometric question of "Given an area of 39,...
user2921's user avatar
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9 votes
4 answers
4k views

Why is calculus missing from Newton's Principia?

I'm not suggesting that Newton did not discover calculus - the question is written this way to express my surprise that the Principia does not use the methods of calculus (or 'fluxions'). He instead ...
Mozibur Ullah's user avatar
33 votes
3 answers
4k views

Why did the ancient Greeks originally become interested in conic sections?

How much is known, or can be conjectured, about why the Greeks originally became interested in the somewhat arbitrary construction of intersecting a plane with a cone? The folklore that I've heard is ...
Jack M's user avatar
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24 votes
1 answer
1k views

Why were geometers dissatisfied with the parallel postulate?

Euclid himself already treats it with gloves, it has an unusually precise formulation, and is not used in the first 28 propositions of the Elements. Why? Did he doubt it? It's not like Euclid was a ...
Conifold's user avatar
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17 votes
4 answers
5k 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 ...
Anthony Pham's user avatar
10 votes
2 answers
921 views

What caused or contributed to Euclid's Elements and Synthetic Geometry falling into disfavor?

Euclid's Elements could tout to have the longest and most famed publishing history of any book ever written. First written in 300 B.C., Euclid's Elements became the standard text from which ...
user avatar
2 votes
2 answers
930 views

What made Euclid/Heron define line as a length without breadth and point as that which has no part?

A point is that of which there is no part. And a line is a length without breadth.$^1$ If above definition on point, expresses on point as to be indivisible length, as seems to be expressed in ...
Sensebe's user avatar
  • 675
18 votes
2 answers
10k views

Who calculated for the first time the volume (and surface area) of the sphere exactly?

As we know, even Archimedes did soon some experimental calculations. My question were, who calculated first time the exact formulas ($V=\frac{4\pi}{3}r^3$, $A=4\pi r^2$)? As I know, these formulas ...
peterh's user avatar
  • 919
12 votes
1 answer
714 views

Concerning the measurement of the Earth's circumference by Eratosthenes

I. In an episode of his Cosmos series, Carl Sagan discussed the brilliant argument whereby Eratosthenes purportedly estimated the circumference of our planet. At one point of the episode, Carl Sagan ...
José Hdz. Stgo.'s user avatar
10 votes
1 answer
208 views

History of greater-than symbol used in reverse?

I was surprised to find that Oliver Byrne's 1847 marvelous The Elements of Euclid (color version)1 uses $\sqsubset$ to mean "greater than" and $\sqsupset$ to mean "less than," in ...
Joseph O'Rourke's user avatar
10 votes
1 answer
299 views

What theorem of Sophus Lie on the number of geometries is H. Poincaré referring to?

In this quotation from Henri Poincaré's essay "Non-Euclidean Geometry" published in Nature in 1892 (No. 1165, Vol 45, p. 406), he refers to a theorem of Sophus Lie. Does anyone know a source for this ...
harpersferry's user avatar
9 votes
2 answers
7k views

On Einstein's proof of the so-called Pythagorean theorem

Part I In E. Maor's book [2, p. 117] we read that, somewhere in his Autobiographical Notes, Einstein wrote this: An uncle told me about the Pythagorean theorem before the holy geometry booklet had ...
José Hdz. Stgo.'s user avatar
7 votes
2 answers
2k views

Discovery and Development of Coordinate Systems

I'm very interested to know how coordinate systems were discovered and why mathematicians discovered them? Actually I want to know what things motivated mathematicians to discover and develop ...
Shahed al mamun's user avatar
7 votes
2 answers
887 views

Who discovered integer triangles with one angle trisecting another?

When & who was the first mathematician to discover the following simple triangle with a unique property that it has one angle is equal to one third of another angle in the same triangle? The ...
Bassam Karzeddin's user avatar
6 votes
3 answers
1k views

What did the ratio of two magnitudes mean to ancient Greek mathematicians?

My understanding is that magnitudes to ancient Greeks meant the actual line segments and plane regions (not the size of the line segment or the area of the plane region), the concept of ratio was then ...
abk's user avatar
  • 163
4 votes
1 answer
825 views

How did Saint Vincent prove the logarithmic property of areas under hyperbolas?

How did Saint Vincent prove that if $\frac{a}{b} = \frac{c}{d}$, then the area of a hyperbola $y = \frac{1}{x}$ from $a$ to $b$ equals the area from $c$ to $d$? What references (pdfs, links, books) ...
Cicero's user avatar
  • 561
4 votes
2 answers
405 views

What were the applications of ellipses before elliptical orbits were discovered?

I'm interested in the history of ellipses. When were they discovered, what uses (if any) did they have before the true shape of orbits were found (by Kepler I think)? There are some interesting ways ...
DrZ214's user avatar
  • 861
4 votes
1 answer
328 views

Who originated the concept of making the point dimensionless?

Over the years I read different versions of how the point in geometry (and subsequently in maths) came to be defined as an abstract, dimensionless entity. I read that it was Architas who influenced ...
user157860's user avatar