Update of 11:30 AM ET April 1, 2022 — A simpler version:
The above picture may be used to to introduce the concept of a "shape constant"
in similar figures — like the shape constant pi in a circle or the square root of 2
in a square. In each of the three similar figures at right above, the ratio of the
triangular area to the area of the attached square is a shape constant …
the same, because of their similarity, for each of the three shapes. Since the
areas of the top two triangles at right sum to that of the enclosed triangle at left,
their attached square areas sum to the area of the bottom square, Q.E.D.
The source of the proof —
