Jem glossed over a bit of the curve design. The chain method gave him "a" curve of the right height and period, but it also very elegantly gave him "the" curve - the right shape - as well. A chain hangs in a catenary curve (y = cosh x) and that's just the shape needed for a square wheel. I haven't seen a really elegant proof of that yet - can anyone come up with something short and convincing?
The skateboard makes a good small scale demonstration, and we'll see next week how the square-wheeled motorbike turned out (I've seen Jem since and he still has all his teeth), but is there any scope for using this in real life? Maybe for traffic control in towns? A suitably shaped roller could put the ridges in the road and then only buses would be allowed tyres of the right shape. Rumble strips on a grand scale!
Any other ideas? Could mean fitting the road to the wheel, or the wheel to the road - are there any regular and bumpy shaped things that need moving around? Square wheels look so daft that I really hope there's a use for them!
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