For questions about the mathematical study of shapes and space based on the works of Euclid.
Questions tagged [euclidean-geometry]
97 questions
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Why did Euclid Avoid Using the 5th Postulate?
In Euclid's elements, some of the theorems (e.g. SAA congruence) can be proven using the parallel postulate, much easier than without it. But it seems that Euclid has intentionally avoided using it, when possible.
Am I right?
What is the reason…
user2321323
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4
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1 answer
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 Euclid, but also that it was a mistake made by…
user157860
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What is the earliest attested mention of the fact that a parallelepiped in Euclidean 3-space can be decomposed into six tetrahedra?
The question is in the title.
A pictorial representation of what this is about is the following:
(created with GeoGebra and GIMP)
The orthoschemes named after Ludwig Schläfli are very relevant but more special, and I suspect that the above…
Peter Heinig
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4
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Inscribing equilateral triangle in square — mistake in historical work by Abu'l-Wafa Al-Buzjani?
(I asked this question in the general Mathematics forum, but I have been advised to post it here instead -- or as well.)
In David Wells's "Curious and Interesting Puzzles", Penguin, 1992, his Puzzle 38 is taken from a work (unspecified) by…
Prime Mover
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3
votes
1 answer
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?
Dom Turner
- 139
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2
votes
3 answers
History of the quadrature of curvelinear figures prior to the middle ages
Hippocrates was able to construct the quadrature of three different lunes. Euler found two more squarable lunes. Tschebatorew and Durodnow showed that these five are the only squarable lunes.
Although Archimedes quadrature of the parabolic segment…
nwr
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vote
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Were there impossibility proofs for constructions in Greek geometry?
Greek geometry was confronted with problems such as squaring the circle. Straightedge and compass constructions were unable to provide a solution, but other mechanical curves, such as the quadratix, were introduced to deal with these difficult…
elias1952
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vote
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Question about Euclid Elements book 1, definition 1
While I was reading translated into Korean version of Thomas Heath Euclid Elements, I found something weird. And I am doubting whether that translation is wrong. I will retranslate it so you guys can rate it. Before, please read the original text of…
Vito
- 37
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0
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1 answer
No distance in Euclid
The mathematical concept of distance is fundamental in all mathematics and, since Bernard Riemann’s definition of manifolds, is also foundational in geometry and geometry of physics.
Contrary to a widespread belief, probably encouraged by that…
massimo
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-1
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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 could be assigned to the octave 2, but what would be…
John Shanahan
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