Embedded Files
Here's that pi video they watched.
Geogebra is a great way to play around with geometry.
A proof of the Pythagorean theorem is below, in the excerpt from the book. Here's an algebraic proof, using the same diagram.
Mom mentioned the conventional proof for the perpendicular bisector. Here it is.
How to construct the circumscribing polygons (and do the algebra)
From the (first draft of the) manuscript:
“Let’s prove it together. Can you each draw a square? It’s ok if your drawings aren’t perfect. They’re just to help us see relationships.
“Now put a point on one side, off center. And put it on each side in the same place, like this.
“Now connect them. What do you see?”
Sofia. “A tilted square inside.”
Aiden. “And 4 triangles around it.”
Althea. “Right triangles.”
Kiara. “And all the triangles are the same as each other.”
Mom. “All useful observations. Let’s label the outside with a’s on our short triangle legs and b’s on our longer legs.”
Althea. “And then we could put the c’s on the hypotenuses of the triangles. And so the area of the tilted square would be c2.”
Mom. “Lovely. You could all probably do this without me. There are two ways to proceed now. One is algebraic, and the other is more visual. I’ve come to love the visual way. If you can draw the same picture a 2nd time, we’re going to modify it. So be sure to use pencil on the inside this time.”
She waits.
“Now move the two top triangles next to the two on the bottom. You might want to add a line or two. The square that had area c2 is gone, and in its place are two smaller squares.”
It's quiet for a minute while we all draw.
Kiara. “And the small one is a2 and the big one is b2! Woo hoo! And I guess it didn’t matter where we put our point when we started.”
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