Circle and Square Spirals

The following spiral is created by continually multiplying the size of a square by four, then connecting the squares next to each other in a clockwise rotational pattern. The special property of this construction is not so much the spiral or the squares, but circles that circumscribe each square. Notice that all the circles share the same point of origin.

Do the following triangles look familiar? They should. The triangles are reduced in size to fit comfortably on the screen and to print on a single page. The actual large right triangles are 7.5:10:12.5 (all in inches). These measurements are exact larger proportions of the 3:4:5 right triangle. Thus, we have returned full circle to the 3:4:5 right triangle.