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 952 · Answer 1 · 2017-11-26 18:54:03

952

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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 26 Nov 2017 - 18:54

score 87 · Answer 2 · 2020-08-29 19:32:23

87

Views

Defining real numbers through geometry

Published on 29 Aug 2020 - 19:32

score 106 · Answer 3 · 2020-09-03 14:41:27

106

Views

Catergorical Axiomatic System

Published on 03 Sep 2020 - 14:41

score 1.3k · Answer 4 · 2020-09-20 04:51:08

1.3k

Views

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

Published on 20 Sep 2020 - 4:51

score 169 · Answer 5 · 2020-10-20 00:29:15

169

Views

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

Published on 20 Oct 2020 - 0:29

score 748 · Answer 6 · 2020-10-28 13:32:39

748

Views

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

Published on 28 Oct 2020 - 13:32

score 201 · Answer 7 · 2020-11-21 11:12:23

201

Views

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

Published on 21 Nov 2020 - 11:12

score 85 · Answer 8 · 2020-11-25 09:04:08

85

Views

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

Published on 25 Nov 2020 - 9:04

score 439 · Answer 9 · 2020-12-05 15:41:26

439

Views

Prove a certain quadrilateral is actually a Saccheri Quadrilateral

Published on 05 Dec 2020 - 15:41

score 67 · Answer 10 · 2021-02-28 15:53:01

67

Views

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

Published on 28 Feb 2021 - 15:53

score 45 · Answer 11 · 2021-03-17 03:17:14

45

Views

Existence of skew lines in 3D

Published on 17 Mar 2021 - 3:17

score 159 · Answer 12 · 2021-05-05 14:13:26

159

Views

Synthetic geometry theorems that relate lengths to areas

Published on 05 May 2021 - 14:13

score 434 · Answer 13 · 2021-05-25 20:55:29

434

Views

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

Published on 25 May 2021 - 20:55

score 118 · Answer 14 · 2026-02-23 10:04:44

118

Views

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

Published on 23 Feb 2026 - 10:04

score 101 · Answer 15 · 2021-06-12 14:18:15

101

Views

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

Published on 12 Jun 2021 - 14:18

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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