General Mathematics

    

Some Missed Opportunities for Archimedes and Early pi-Computors

Authors: Warren D. Smith

We point out some simple improvements to Archimedes' "regular polygon methods" for computing and bounding π , which all the workers before 1650 could have used, but did not. All methods employed before the 1970s to compute the first D decimals of π required order D or more arithmetic operations (±, ×, ÷, x1/2, x-1/2). But we shall show that if Archimedes or his followers had been a bit smarter, they could have sped that up to O(D2/3).

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[v1] 2024-07-11 20:19:54

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