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Geometric Construction 14

This configuration was found in the Japanese temple. Make a dynamic animation
out of it.

This configuration was found in the Japanese temple. Make a dynamic animation
out of it.

Construct the pentagon, given the midpoint of each of its sides.

The following question is taken from I.M. Yaglom, Geometric Transformation
III, p. 15. Is there anything wrong?

Construct a linkage to draw the lemniscate after this design:

Decompose an equilateral triangle into four pieces and reassemble them
into a square.

Given two acute triangles S and T, show that each can be decomposed into
three pieces
S = S_{1} U S_{2} U S_{3}

T = T_{1} U T_{2} U T_{3}
so that S_{i} is similar to T_{i} for i = 1,2,3.