Difference between revisions of "Spiral similarity"
Archimedes1 (talk | contribs) (New page: A '''spiral similarity''' is the composition of a homothety with a rotation.) |
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| + | A spiral similarity is a plane transformation composed of a rotation of the plane and a dilation of the plane having the common center. The order in which the composition is taken is not important. | ||
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| + | The transformation is linear and transforms any given object into an object homothetic to given. | ||
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| + | On the complex plane, any spiral similarity can be expressed in the form <math>T(x) = x_0+k (x-x_0),</math> where <math>k</math> is a complex number. The magnitude <math>|k|</math> is the dilation factor of the spiral similarity, and the argument <math>\arg(k)</math> is the angle of rotation. | ||
Revision as of 02:05, 10 June 2023
A spiral similarity is a plane transformation composed of a rotation of the plane and a dilation of the plane having the common center. The order in which the composition is taken is not important.
The transformation is linear and transforms any given object into an object homothetic to given.
On the complex plane, any spiral similarity can be expressed in the form 
where 
is a complex number. The magnitude 
is the dilation factor of the spiral similarity, and the argument 
is the angle of rotation.
