Mathematics
... Mathematics
Grade Seven – Pre-Algebra - Unit 9
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13.2 Angles of Rotation
... • In geometry, an angle is defined by two rays that
have a common endpoint.
• In trig, an angle is defined by a ray that is rotated
around the endpoint…this is called ANGLE OF
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section 1.1-1.3 - Fulton County Schools
... • A line is perfectly straight, contains an infinite
number of points, extend infinitely in two directions,
and have no thickness.
• A plane is a flat surface that extends infinitely in all
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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.