# Dilation Exploration

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**Objective:**
Learn to recognize similarity transformations.

For each print, discuss the symmetries. Find any isometries (rotations, for example) as well as any similarity transformations.

- Path of Life II (Visions of Symmetry pg. 311)
- Path of Life III (Visions of Symmetry pg. 316)
- Butterflies (Color) (Visions of Symmetry pg. 305)
- Sketch #65 (Moths) (Visions of Symmetry pg. 167)

Look at Escher's Regular Division of the Plane by Similar Figures patterns. These patterns (and Sketch #65 (Moths)) are all based on the following pattern, which has a dilation-rotation by a factor of <math>\frac{1}{\sqrt{2}}</math> and angle of 45°:

- 5. Sketch this square "scaffolding" on top of each of Escher's geometric patterns.