Question

Show that any line through the origin of a circle has two point on the circle and that a circle has infinite points.

score 953 · Answer 1 · 2026-02-23 22:31:09

953

Views

Show that any line through the origin of a circle has two point on the circle and that a circle has infinite points.

Published on 23 Feb 2026 - 22:31

score 88 · Answer 2 · 2026-02-23 22:25:52

88

Views

Defining real numbers through geometry

Published on 23 Feb 2026 - 22:25

score 107 · Answer 3 · 2026-02-23 22:25:35

107

Views

Catergorical Axiomatic System

Published on 23 Feb 2026 - 22:25

score 1.3k · Answer 4 · 2026-02-23 22:30:48

1.3k

Views

Prove: "if three points are on a straight line, at least one point is between the other two."

Published on 23 Feb 2026 - 22:30

score 170 · Answer 5 · 2026-02-23 22:31:40

170

Views

Can one prove non-trivial congruences of triangles without SAS or other congruence axioms?

Published on 23 Feb 2026 - 22:31

score 749 · Answer 6 · 2026-02-23 22:30:48

749

Views

Proving (via Hilbert's axioms) that, when two parallel lines are cut by a third line, they make congruent angles.

Published on 23 Feb 2026 - 22:30

score 202 · Answer 7 · 2026-02-23 22:30:10

202

Views

What logic can be used express Hilbert's axiomatization of Euclidian geometry?

Published on 23 Feb 2026 - 22:30

score 86 · Answer 8 · 2026-02-23 22:32:10

86

Views

How first-order logic based ZFC can model mathematical theories formulated with higher order logic?

Published on 23 Feb 2026 - 22:32

score 440 · Answer 9 · 2026-02-23 22:28:49

440

Views

Prove a certain quadrilateral is actually a Saccheri Quadrilateral

Published on 23 Feb 2026 - 22:28

score 68 · Answer 10 · 2026-02-23 22:31:09

68

Views

Are the theories of betweenness the same in $\mathbb{R}^n$ for all $n\geq 2$?

Published on 23 Feb 2026 - 22:31

score 46 · Answer 11 · 2026-02-23 22:32:10

46

Views

Existence of skew lines in 3D

Published on 23 Feb 2026 - 22:32

score 160 · Answer 12 · 2026-02-23 22:32:10

160

Views

Synthetic geometry theorems that relate lengths to areas

Published on 23 Feb 2026 - 22:32

score 435 · Answer 13 · 2026-02-23 22:27:38

435

Views

Is "There exists a circle passing through any three noncollinear points" really equivalent to Euclid's parallel postulate?

Published on 23 Feb 2026 - 22:27

score 119 · Answer 14 · 2026-04-09 15:23:58

119

Views

For Desarguian projective planes, coordinatization is inverse to the $K \mapsto K\mathbf{P}^2$ construction

Published on 09 Apr 2026 - 15:23

score 102 · Answer 15 · 2026-02-23 22:31:40

102

Views

What does it mean for one geometrical axiom to be considered _equivalent_ to another geometrical axiom?

Published on 23 Feb 2026 - 22:31

List Question

Show that any line through the origin of a circle has two point on the circle and that a circle has infinite points.

Defining real numbers through geometry

Catergorical Axiomatic System

Prove: "if three points are on a straight line, at least one point is between the other two."

Can one prove non-trivial congruences of triangles without SAS or other congruence axioms?

Proving (via Hilbert's axioms) that, when two parallel lines are cut by a third line, they make congruent angles.

What logic can be used express Hilbert's axiomatization of Euclidian geometry?

How first-order logic based ZFC can model mathematical theories formulated with higher order logic?

Prove a certain quadrilateral is actually a Saccheri Quadrilateral

Are the theories of betweenness the same in $\mathbb{R}^n$ for all $n\geq 2$?

Existence of skew lines in 3D

Synthetic geometry theorems that relate lengths to areas

Is "There exists a circle passing through any three noncollinear points" really equivalent to Euclid's parallel postulate?

For Desarguian projective planes, coordinatization is inverse to the $K \mapsto K\mathbf{P}^2$ construction

What does it mean for one geometrical axiom to be considered _equivalent_ to another geometrical axiom?

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