Hello everyone!

Welcome back to Pythagoras Week.  If you missed it, be sure to check it out from the beginning.  Our final proof doesn't rely on any sort of fancy results like the last few.  We just need a few copies of our triangle.

Take three copies of a right triangle with sides .  Scale one by , one by , and the third by .  Place them together as shown below.The angles work out nicely, and it turns out we get a rectangle.  The top edge has length and the bottom edge has length .  Opposite sides of a rectangle are the same length, so we get .

That's it for Pythagoras week.  I'll post a final wrap-up tomorrow.

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