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It's an example of something called aDiophantine equation, in which all the unknowns must be integers, or whole numbers. With some numbers, this sort of thing is pretty easy. As Massachusetts Institute of Technology professorBjorn Poonenexplained in this2008 paper, the number 29, for example,...
It is, for that reason, one of the worst cases of Lagrange's approximation theorem and it is an extremal case of the Hurwitz inequality for diophantine approximations. This may be why angles close to the golden ratio often show up in phyllotaxis. It is...
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