How do we know that the circumference of every circle has the same ratio π to its diameter? The following theorem assures us. Circles are to one another as their circumscribed squares - Euclid, XII, 2

Remarkably enough, as we will see, the theorem applies both to the boundaries and the areas.

• point on a circle rolling inside an other of twice the size draw a straight line - Secrets of the NOTHING GRINDER
  • if greater it will the outside will be triangle, square and pentagon