![]() ![]() “They are joined together, so much so that if we isolate pi or pi to the nth power, we have a formula with the nth Bernoulli number, it is so precise that if we truncate at the nth position, we obtain enough precision to affirm that it is the nth decimal.” “The formula which joins them… I would think that it must go back to Euler.” “It is possible because these Bernoulli numbers are very close to pi and powers of pi,” he tells IFLScience. There are no long calculations or abstract proofs here instead, Plouffe’s result relies on the ability to just look at something old in a new way. It’s why the most striking thing about the new paper – other than the result itself – is just how short it is: only six pages in total, not counting a short reference section. Like that 1995 result, the new formula is based on results which “ known for centuries,” he tells IFLScience, and yet rarely returned to by working mathematicians. “It can be done in any base if we want, for that I can adjust the formula quite simply.” Now, he says, his result can be extended to any base at all: “By adjusting for base 10 or base 2 it is valid for all n,” he notes. Pi in base two is something of a specialty for Plouffe, in fact: he’s the P in the BBP algorithm, a method of calculating the nth digit of the binary expansion of pi which he discovered all the way back in 1995.
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