# Questions tagged [euclidean-geometry]

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

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### When and who was the first mathematicians to prove rigorously that $\sqrt{2}$ was impossible number? [closed]

The purpose of the question is to understand why the number $\sqrt{2}$, that was proven rigorously by ancient Greek is an impossible number (even at infinity), by their three famous impossibility ...
770 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 ...
4k 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 ...
571 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 ...
465 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) ...
2k 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,...
275 views

### Classical source for theorem on three parallel lines cut by two transversals

I am trying to find a classical source for the following theorem about parallel lines and transversals: If three parallel lines are cut by two transversals, then the segments between the ...
852 views

### Did Dieudonné say “Euclid must go!” or “Down with Euclid! Death to triangles!”?

In his famous address at the Royaumont Seminar in 1959, Jean Dieudonné famously called for the elimination of Euclidean geometry from the secondary school curriculum. In the published (English-...
394 views

### 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.
2k 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 ...
3k 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 ...
193 views

### Five perfect solids

Has anyone ever considered the connection between the five perfect solids and the three most important music intervals of 2, 1.5, 1.25 and their two counterparts, 1.33333 and 1.6? The tetrahedron ...
635 views

### Who discovered the duality between platonic solids?

As it is well known, every platonic solid has a dual (obtained by interchanging vertices and faces), which also happens to be a platonic solid. I would like to know who was the first person to ...
1k 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 ...
2k 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 ...
8k 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 ...
757 views

### Who came up with the “proof” that all triangles are isosceles?

"All triangles are isosceles" is a famous geometric fallacy (see below). Unlike many other fallacies its flaw is subtle and hard to spot, so it is often used as a cautionary example against ...
118 views

### About Archimedes methods in the discovered palimpsest

I think Archimedes had some great non-infinitesimal methods for discovering the area and volume of shapes. Some very visual methods involving his method of exhaustion for the volume of a sphere for ...
795 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 ...
2k views

### Why is the Pythagorean Theorem so ubiquitous?

We all know the Pythagorean Theorem is one of the most fundamental formulas in mathematics, but it is very interesting to me that this ratio shows up as often as it does. It seems to have been ...
215 views

### Do we have any in depth material on Baudhayana?

I know he wasn't strictly a mathematician, but as I understand, Baudhayana recorded information on (what we know as) the Pythagorean Theorem and other geometrical properties like $\sqrt{2}$, in the ...
The cross-ratio of four collinear points $A,B,C,D$ in the Euclidean Plane is defined by $$(A,B,C,D) = \frac{AC}{AD}\frac{BD}{BC}$$ And the wikipedia article states it already appeared in the works ...