Several years ago, retired military officer Guan Baihua invented what may be the ultimate geometry geek bicycle. The front wheel is a pentagonal curve, and the back wheel is a reuleaux triangle (a triangular curve). It seems like it shouldn't work, but it does โ€” and beautifully!

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It's called the Reuleaux Bicycle. I'm not sure why it hasn't caught on yet, given the lust for artisanal bikes among urbanites.