Question

What does the primitive relations "betweenness" defined in Cayley–Klein model? What's the difference to the Euclidean geometry?

score 98 · Answer 1 · 2026-05-10 21:11:32

98

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What does the primitive relations "betweenness" defined in Cayley–Klein model? What's the difference to the Euclidean geometry?

Published on 10 May 2026 - 21:11

score 48 · Answer 2 · 2026-03-25 14:39:17

48

Views

showing a non-Euclidean property in Geometry

Published on 25 Mar 2026 - 14:39

score 227 · Answer 3 · 2026-03-25 14:39:17

227

Views

Can a "biangle" on a sphere be considered a "regular polygon" on the sphere?

Published on 25 Mar 2026 - 14:39

score 877 · Answer 4 · 2026-03-25 14:47:01

877

Views

In non-euclidean geometry, can hypotenus of rightangle triangle be shorter than sides?

Published on 25 Mar 2026 - 14:47

score 73 · Answer 5 · 2026-03-25 14:39:53

73

Views

generalizing linear separability and the perceptron algorithm

Published on 25 Mar 2026 - 14:39

score 39 · Answer 6 · 2026-03-25 14:46:54

39

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Conjecture: $\pi\le\sum_{cyc}\operatorname{arcsec}(f(a,b,c))\le3\pi/2$, where $f(a,b,c)=\frac{a^2+b^2-c^2-a^2b^2c^2}{2ab(1-c^2)}$ and $a,b,c>\sqrt{3}$

Published on 25 Mar 2026 - 14:46

score 695 · Answer 7 · 2026-03-25 14:47:03

695

Views

Why is the fourth angle of a Lambert quadrilateral obtuse in elliptic geometry?

Published on 25 Mar 2026 - 14:47

score 137 · Answer 8 · 2026-03-25 14:39:40

137

Views

distance in nonEuclidean geometries

Published on 25 Mar 2026 - 14:39

score 208 · Answer 9 · 2026-03-25 14:39:17

208

Views

Does Minkowski space have anything to do with Minkowski geometry?

Published on 25 Mar 2026 - 14:39

score 104 · Answer 10 · 2026-03-25 14:39:08

104

Views

Is there an explanation/theorem which explains why the triangle is so fundamental in euclidean space?

Published on 25 Mar 2026 - 14:39

score 263 · Answer 11 · 2026-03-25 14:39:50

263

Views

Hyperbolic Geometry - Triangle Bisectors Proof

Published on 25 Mar 2026 - 14:39

score 49 · Answer 12 · 2026-03-25 14:39:14

49

Views

Are there geometries in which points have finitely many parallel lines?

Published on 25 Mar 2026 - 14:39

score 526 · Answer 13 · 2026-03-25 14:39:18

526

Views

How is Euclid's 5th Postulate wrong exactly? Why do we think that parallel lines and geodesics are the same?

Published on 25 Mar 2026 - 14:39

score 76 · Answer 14 · 2026-03-25 14:39:18

76

Views

Is there any proof that Euclid's fifth postulate cannot be proven?

Published on 25 Mar 2026 - 14:39

score 807 · Answer 15 · 2026-03-25 14:39:46

807

Views

How does spherical geometry contradict Euclid's parallel postulate?

Published on 25 Mar 2026 - 14:39

List Question

What does the primitive relations "betweenness" defined in Cayley–Klein model? What's the difference to the Euclidean geometry?

showing a non-Euclidean property in Geometry

Can a "biangle" on a sphere be considered a "regular polygon" on the sphere?

In non-euclidean geometry, can hypotenus of rightangle triangle be shorter than sides?

generalizing linear separability and the perceptron algorithm

Conjecture: $\pi\le\sum_{cyc}\operatorname{arcsec}(f(a,b,c))\le3\pi/2$, where $f(a,b,c)=\frac{a^2+b^2-c^2-a^2b^2c^2}{2ab(1-c^2)}$ and $a,b,c>\sqrt{3}$

Why is the fourth angle of a Lambert quadrilateral obtuse in elliptic geometry?

distance in nonEuclidean geometries

Does Minkowski space have anything to do with Minkowski geometry?

Is there an explanation/theorem which explains why the triangle is so fundamental in euclidean space?

Hyperbolic Geometry - Triangle Bisectors Proof

Are there geometries in which points have finitely many parallel lines?

How is Euclid's 5th Postulate wrong exactly? Why do we think that parallel lines and geodesics are the same?

Is there any proof that Euclid's fifth postulate cannot be proven?

How does spherical geometry contradict Euclid's parallel postulate?

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