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Geometric Illustration of Machin-Like Formulas

This Demonstration illustrates geometrically some Machin-like formulas for computing the number

. A Gregory number is

, where

is a rational number. Since

, Gregory numbers arise in  the determination of Machin-like formulas for computing the number

Størmer's numbers

are the positive whole numbers

for which the largest prime factor of

is at least

. Størmer showed that every Gregory number

, where

is a Störmer number, can be uniquely expressed as an integer linear combination of smaller

(47 lines omitted)

J. H. Conway and R. K. Guy, The Book of Numbers, New York: Copernicus Books, 2006 pp. 244–247.

Contributed by: Izidor Hafner

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