... because before long, I had a couple of messages in my inbox from fellow teachers who made the note for us! Saw you guys on the Wiggins blog! ... and ... Congrats to your kids on their project with Grant Wiggins!

What in the world?!

I am incredibly embarrassed to say at this point that I was not one of the over 6500 people already reading Dr. Wiggins' blog on a regular basis; this just became an even bigger deal than the big deal we already knew it was!

So the pressure was now on with our new challenge from Dr. Wiggins and the thousands of eyeballs on our work:

 We all know that the Pythagorean Theorem states that a^2 + b^2 = c^2 in right-angled triangles in Euclidean geometry.    But you may have forgotten that the "squared" is meant literally here: the square on side a (i.e. the area of that square) + the square on side b (i.e. the area of that square) = the square on side c, i.e. the area of that square.    QUESTION: can the theorem be generalized to shapes other than squares?    For example, what about rhombus on side a + rhombus on side b? Do the areas of the two rhombuses (rhombi?) equal the area of the rhombus on side c? Find out. Does anything follow?    Obviously a rectangle as a shape is problematic because the possibilities are unlimited. A key one is the special case of the square, of course, but messing around with other rectangles with proportional relationships of width vs. length is interesting.    Investigate other areas of other shapes and their areas, regular and irregular.    So, how general can we make the theorem?

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