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・ Plane curve
・ Plane Daffy
・ Plane Dippy
・ Plane Driven PD-1
・ Plane Dumb
・ Plane geometry (disambiguation)
・ Plane guard
・ Plane joint
・ Plane Mad
・ Plane Martin
・ Plane mirror
・ Plane Nuts
・ Plane of immanence
・ Plane of incidence
・ Plane of reference
Plane of rotation
・ Plane of Shadow
・ Plane of the solar system
・ Plane partition
・ Plane sailing
・ Plane Saver Credit Union
・ Plane Space
・ Plane strain compression test
・ Plane stress
・ Plane Stupid
・ Plane symmetry
・ Plane Table
・ Plane table
・ Plane wave
・ Plane wave expansion


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Plane of rotation : ウィキペディア英語版
Plane of rotation
In geometry, a plane of rotation is an abstract object used to describe or visualise rotations in space. In three dimensions it is an alternative to the axis of rotation, but unlike the axis of rotation it can be used in other dimensions, such as two, four or more dimensions.
Mathematically such planes can be described in a number of ways. They can be described in terms of planes and angles of rotation. They can be associated with bivectors from geometric algebra. They are related to the eigenvalues and eigenvectors of a rotation matrix. And in particular dimensions they are related to other algebraic and geometric properties, which can then be generalised to other dimensions.
Planes of rotation are not used much in two and three dimensions, as in two dimensions there is only one plane so identifying the plane of rotation is trivial and rarely done, while in three dimensions the axis of rotation serves the same purpose and is the more established approach. The main use for them is in describing more complex rotations in higher dimensions, where they can be used to break down the rotations into simpler parts. This can be done using geometric algebra, with the planes of rotations associated with simple bivectors in the algebra.〔Lounesto (2001) pp. 222–223〕
==Definitions==


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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