Sunday, May 3, 2020

Neat trick

{\displaystyle \exp x:=\sum _{k=0}^{\infty }{\frac {x^{k}}{k!}}=1+x+{\frac {x^{2}}{2}}+{\frac {x^{3}}{6}}+{\frac {x^{4}}{24}}+\cdots }

Floor function selects the finite end of the series, if you know the resolution of the floor function you know the degree.

Lots of Newton and his ilk end up with this series. If I tried this trick with a triple counter, one can see the Poisson solutions should floor to a cubic. There is an innate connection to topology that I do not quite get. But the three coloring with no even odd should put a hole in the beach ball.

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