[math-fun] Newton's cradle
Veit>Here's a fun application of the pairwise model that you can try at home. Hold a basketball while resting a tennis ball on top of it. Now drop the basketball (the tennis ball should be co-moving and nearly in contact). You'll find that after all the collisions (pairwise!) have finished the tennis ball is shot up to a surprising height. It took this to remind me of the short-lived AstroBlaster toy, an unopened copy of which I may still own. It was a tapered sequence of (very) bouncy balls on a stem firmly embedded in the bottom one. The middle ones could slide on the stem, but were trapped by a thickening near the top. The topmost, tiny ball had a large enough hole to slide off. Dangle it by the stem, drop it, and instantly lose the tiny ball, or your eye if it was above the impact point. I wonder if Tim Rowett owns one. --rwg
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Bill Gosper