Yesterday we did a fun project on these two questions:
(1) Given a square with area one, find a way to make a square with area 2,
(2) Given a square with area one, find a way to make a square with area 3.
That project is here (where you can see that part 2 gave both kids a lot of trouble):
A neat and easy to state geometry problem
I decided to revisit a piece of that project today to show them that both of their solutions to part 2 were essentially proofs of the Pythagorean theorem.
We started by reviewing yesterday’s project:
Next we talked about how my younger son’s way of constructing the square with area three can be used to prove the Pythagorean theorem:
Finally, we looked at the slightly different way that my older son constructed the square with are 3. This approach proves the Pythagorean theorem in a different way:
This was a fun couple of projects that came from a really innocuous sounding question.