Questions tagged [euclidean-geometry]
For questions about the mathematical study of shapes and space based on the works of Euclid.
20
questions
9
votes
1
answer
1k
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.
- 983
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,...
- 121
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 ...
- 3,119
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 ...
- 76k
8
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 ...
- 3,708
17
votes
4
answers
4k
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 ...
- 407
10
votes
2
answers
907
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 ...
user6918
2
votes
2
answers
919
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 ...
- 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 ...
- 919
12
votes
1
answer
709
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 ...
- 1,862
10
votes
1
answer
296
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 ...
- 103
10
votes
1
answer
198
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 ...
- 1,417
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 ...
- 1,862
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 ...
- 191
7
votes
2
answers
884
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 ...
- 177
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 ...
- 163
4
votes
2
answers
404
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 ...
- 861
4
votes
1
answer
813
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) ...
- 551
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 ...
- 703
3
votes
1
answer
1k
views
When did mathematicians invent the unit circle to extend the trig functions?
Is there any evidence showing that a unit circle approach was used by early mathematicians?
- 139