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Product of Rotations
The product, or the sum as its often called, of two rotations is either a rotation or a translation, both of which can be trivial. Depending on the context, one may treat the product of two rotations which is trivial as either a rotation or a translation. The product of two rotations through angles a and b is a rotation through angle 
Let there be given two rotations gP and gQ with centers P and Q. Assume gP is executed first, gQ second. gP leaves P in place. Denote Now prove that (The fact just established provides a powerful tool for solving geometric problems, see, for example, proofs of Bottem's theorem and an analogue.) 
Copyright © 1996-2008 Alexander Bogomolny |
POP' = 
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