Tidbits of geography (and of cake)

Futility Closet has plenty of great trivia. I want to share some of my favorite geographical tidbits from there, since I have maps on the mind lately.

Source: Wikimedia Commons

While we’re talking about shapes and areas, here’s a more mathematical-geometrical question: What’s the most efficient way to carve up a circle to fit inside a square of slightly-larger surface area?

Round peg into a square hole, er, that is, cake into pan

Round peg into a square hole, er, that is, cake into pan

I baked a cake in a round 9″ pan, so the surface area is \pi*r^2 = \pi*4.5^2 = 63.6 \text{ in}^2.  I wanted to transport it in a pan with a lid, and I have such a 8″ square  pan with surface area 8^2 = 64 \text{ in}^2. What’s the best way to fit it in, with the fewest cuts and least wasted scraps? (Well, not really wasted, I’ll eat them gladly 🙂 )

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