Re: Cool math shortcuts
There's a segment in one of the Feynman books - I think it's the Los Alamos from Below section of Surely You're Joking - that talks about Feynman trying to compete with Hans Bethe at speedy mental arithmetic. A technique very similar to this is mentioned, I believe for squaring numbers near 50.
One thing that strikes me is that fast approximate multiplication might have been somewhat easier in the past when people actually used logarithm tables.
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