The Rotation Group

Karol Pąk

Formalized Mathematics (2012)

  • Volume: 20, Issue: 1, page 23-29
  • ISSN: 1426-2630

Abstract

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We introduce length-preserving linear transformations of Euclidean topological spaces. We also introduce rotation which preserves orientation (proper rotation) and reverses orientation (improper rotation). We show that every rotation that preserves orientation can be represented as a composition of base proper rotations. And finally, we show that every rotation that reverses orientation can be represented as a composition of proper rotations and one improper rotation.

How to cite

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Karol Pąk. "The Rotation Group." Formalized Mathematics 20.1 (2012): 23-29. <http://eudml.org/doc/267776>.

@article{KarolPąk2012,
abstract = {We introduce length-preserving linear transformations of Euclidean topological spaces. We also introduce rotation which preserves orientation (proper rotation) and reverses orientation (improper rotation). We show that every rotation that preserves orientation can be represented as a composition of base proper rotations. And finally, we show that every rotation that reverses orientation can be represented as a composition of proper rotations and one improper rotation.},
author = {Karol Pąk},
journal = {Formalized Mathematics},
language = {eng},
number = {1},
pages = {23-29},
title = {The Rotation Group},
url = {http://eudml.org/doc/267776},
volume = {20},
year = {2012},
}

TY - JOUR
AU - Karol Pąk
TI - The Rotation Group
JO - Formalized Mathematics
PY - 2012
VL - 20
IS - 1
SP - 23
EP - 29
AB - We introduce length-preserving linear transformations of Euclidean topological spaces. We also introduce rotation which preserves orientation (proper rotation) and reverses orientation (improper rotation). We show that every rotation that preserves orientation can be represented as a composition of base proper rotations. And finally, we show that every rotation that reverses orientation can be represented as a composition of proper rotations and one improper rotation.
LA - eng
UR - http://eudml.org/doc/267776
ER -

References

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