Set of Rotations in Space about Fixed Point forms Infinite Group
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Theorem
Let $\SS$ be a rigid body in space.
Let $O$ be a fixed point in space.
The set of all rotations of $\SS$ through some straight line through $O$ forms an infinite group.
Proof
This theorem requires a proof. In particular: Needs the mathematical definition of a rotation in space to be defined before we start. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |
Sources
- 1964: Walter Ledermann: Introduction to the Theory of Finite Groups (5th ed.) ... (previous) ... (next): Chapter $\text {I}$: The Group Concept: $\S 3$: Examples of Infinite Groups: $\text{(iii)}$