Pythagorean Theorem Ornaments

thingiverse

# Pythagorean Theorem Pieces One of my favorite Pythagorean proofs involves a square having sides that are "a+b" long. This is a physical example of that proof with two different sizes of "a" and "b". * Print four of the right triangles and one of the corresponding squares * The four triangles and square will assemble into a single square having a total area of (a + b)^2 * You can also assemble the four triangles into two rectangles and leave the square separate showing an area of (2 * a * b) + c^2 * Since the same pieces were used, both are equal in area: (a + b)^2 = (2 * a * b) + c^2 * This equation simplifies to: a^2 + b^2 = c^2 Each piece has a 3 mm hole in a corner. This allows the pieces to be converted into ornaments that can serve as annual reminder of the proof each year over the holidays.