[math-fun] sqrt(binomial) = hexanomial?
I asked
Do I hear six? So far, only from trinomials: 1/3 sqrt(10 - sqrt(5) + 5) =
5/6 1/3 5 1/6 2/3 sqrt(5) 5 1/6 1/6 5 ---- - 2 5 + ------- - ---- + 2 2 5 + ------- 1/6 sqrt(2) 1/6 sqrt(2) 2 2 ---------------------------------------------------------, 3 2/3 1/6 1/3 sqrt(5 + 5 + 2 ) = 5/6 2/3 1/3 1/6 5 5 1/6 5 5 1/6 - ------- + ---- + 2 sqrt(5) + ------- + ---- + 2 2 sqrt(2) 1/6 sqrt(2) 1/6 2 2 ---------------------------------------------------------, 3 but I'll bet there are sqrt(binomials) = multinomials of any desired length, if you know how to look. Does anyone? --rwg neologisms <-> gloominess
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R. William Gosper