466-HW-7 - a 2 + b 2 = 1 show that the formula for f is the...

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Math 466 - Homework Set 7 (16.12.2011) 1. If f is an isometry of the plane then show that the general equations of f are ( x 0 = ax - by + c, y 0 = ± ( bx + ay + d ) with a 2 + b 2 = 1 . 2. If f is a transformation from R 2 to itself with equations of the form given in question 1 show that f is an isometry of the plane. 3. If f is a transformation given by f ( x,y ) = ( ax - by + c,bx + ay + d ) = ( x 0 ,y 0 ) with
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Unformatted text preview: a 2 + b 2 = 1 show that the formula for f is the general formula for an even isometry of the plane. 4. Find the Frieze groups of the following frieze patterns. Indicate the points A i and M i on the patterns. Show the shortest (or smallest) translation by an arrow. 1...
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