Question

Prove the existence of a CONTINUOUS rigid motion

score 76 · Answer 1 · 2021-12-27 18:26:14

76

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Prove the existence of a CONTINUOUS rigid motion

Published on 27 Dec 2021 - 18:26

score 96 · Answer 2 · 2026-03-28 05:22:45

96

Views

proof that the instantaneous center of rotation has to have zero speed

Published on 28 Mar 2026 - 5:22

score 203 · Answer 3 · 2022-01-02 16:12:27

203

Views

Prove that isometries of the hyperbolic plane map horocycles to horocycles

Published on 02 Jan 2022 - 16:12

score 85 · Answer 4 · 2022-01-03 14:04:07

85

Views

Why the isometry $h(v)=Av+w$ is a rotation around $P$ when $\det A=1$

Published on 03 Jan 2022 - 14:04

score 54 · Answer 5 · 2022-01-05 16:46:43

54

Views

Which two straight lines satisfy the following condition?

Published on 05 Jan 2022 - 16:46

score 175 · Answer 6 · 2022-01-06 18:33:44

175

Views

Isometry group of connected manifold has finite component group

Published on 06 Jan 2022 - 18:33

score 78 · Answer 7 · 2022-01-07 18:44:15

78

Views

Is the continuous part of the symmetry group of a compact subset $\mathbb{R}^3$ isomorphic to $SO(k)$?

Published on 07 Jan 2022 - 18:44

score 126 · Answer 8 · 2022-01-20 09:13:27

126

Views

Which rotation groups of compact subsets of $\mathbb{R}^n$ are symmetry groups of compact subsets of $\mathbb{R}^n$?

Published on 20 Jan 2022 - 9:13

score 127 · Answer 9 · 2022-01-26 08:47:06

127

Views

Show that there is an isometry $f:\mathbb{R}^n\to \mathbb{R}^n$ such that $f|_X$ is $g$ where $g :X \to X$ is isometric on subset $X$.

Published on 26 Jan 2022 - 8:47

score 217 · Answer 10 · 2022-01-27 12:17:45

217

Views

The set of all translations is a normal subgroup of $\text{I}(\mathbb{R}^n)$.

Published on 27 Jan 2022 - 12:17

score 91 · Answer 11 · 2022-01-29 01:51:06

91

Views

Existence of isometrical isomorphism between isomorphic finite dimensional vector spaces

Published on 29 Jan 2022 - 1:51

score 132 · Answer 12 · 2026-03-28 10:55:43

132

Views

Oriented Orthonormal Frame Bundle and Orientation-Preserving Isometry Group

Published on 28 Mar 2026 - 10:55

score 58 · Answer 13 · 2022-01-31 00:11:22

58

Views

Why the isometry $f$ must be a translation when it satisfies $\text{d}(f(x),x) < K$ for some $K > 0$?

Published on 31 Jan 2022 - 0:11

score 198 · Answer 14 · 2022-02-01 10:45:49

198

Views

Any translations can be written in a composition of two half-turns. But, how do we show this?

Published on 01 Feb 2022 - 10:45

score 79 · Answer 15 · 2022-02-02 06:18:15

79

Views

Composition of two rotations with angle $\alpha$ and $-\alpha$, but with different centers is a translation.

Published on 02 Feb 2022 - 6:18

List Question

Prove the existence of a CONTINUOUS rigid motion

proof that the instantaneous center of rotation has to have zero speed

Prove that isometries of the hyperbolic plane map horocycles to horocycles

Why the isometry $h(v)=Av+w$ is a rotation around $P$ when $\det A=1$

Which two straight lines satisfy the following condition?

Isometry group of connected manifold has finite component group

Is the continuous part of the symmetry group of a compact subset $\mathbb{R}^3$ isomorphic to $SO(k)$?

Which rotation groups of compact subsets of $\mathbb{R}^n$ are symmetry groups of compact subsets of $\mathbb{R}^n$?

Show that there is an isometry $f:\mathbb{R}^n\to \mathbb{R}^n$ such that $f|_X$ is $g$ where $g :X \to X$ is isometric on subset $X$.

The set of all translations is a normal subgroup of $\text{I}(\mathbb{R}^n)$.

Existence of isometrical isomorphism between isomorphic finite dimensional vector spaces

Oriented Orthonormal Frame Bundle and Orientation-Preserving Isometry Group

Why the isometry $f$ must be a translation when it satisfies $\text{d}(f(x),x) < K$ for some $K > 0$?

Any translations can be written in a composition of two half-turns. But, how do we show this?

Composition of two rotations with angle $\alpha$ and $-\alpha$, but with different centers is a translation.

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