Thingiverse
Pythagorean Theorem Ornaments by paulblankenbaker
by Thingiverse
Last crawled date: 4 years, 11 months ago
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.
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.