Here’s another thing.

1. prove, or see a proof of, the irrationality of root(2)

2. What about root(3) ?

3. What about root(2) + root(3) ? This is decidedly not obvious !

It surely does not have to be only geometry.

]]>Also the dissection into 12 pyramids is beautiful. There’s also the cube contained in the dodecahedron, with the 6 “roof” shapes on the side. A model made of Zometool is one great way to see and understand this.

Speaking of dodecahedra, rather than the Platonic regular one we see so much, I’ve recently fallen in love with the rhombic dodecahedron. Added bonus is that its surface area and volume are a lot easier to understand (and compute exactly) with elementary techniques!

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