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PRODUCTS OF ROTATIONS BY A GIVEN ANGLE IN THE ORTHOGONAL GROUP
Published online by Cambridge University Press: 02 November 2017
Abstract
For every rotation $\unicode[STIX]{x1D70C}$ of the Euclidean space
$\mathbb{R}^{n}$ (
$n\geq 3$), we find an upper bound for the number
$r$ such that
$\unicode[STIX]{x1D70C}$ is a product of
$r$ rotations by an angle
$\unicode[STIX]{x1D6FC}$ (
$0<\unicode[STIX]{x1D6FC}\leq \unicode[STIX]{x1D70B}$). We also find an upper bound for the number
$r$ such that
$\unicode[STIX]{x1D70C}$ can be written as a product of
$r$ full rotations by an angle
$\unicode[STIX]{x1D6FC}$.
Keywords
MSC classification
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- Research Article
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- © 2017 Australian Mathematical Publishing Association Inc.