lunes
Squaring the circle
1) Show that, given the small semicircle on the bottom of the figure, you can construct the rest of the figure (using Plato's 3 rules and the shortcuts you have demonstrated).
2) Prove that the area of the large semicircle circle is equal to the sum of the areas of the 4 small semicircles.
3) Use this to prove that the area of the blue hexagon is equal to the sum of the areas of the 3 lunes and the remaining small semicircle
Squaring Lunes
A) Prove that the area of the large circle is equal to the sum of the areas of the 4 small semicircles.
B) Use this to prove that the area of the large square is equal to the sum of the areas of the 4 lunes. In other words the area of each small square is equal to the area of a lune.