Geometric Illustration of Machin-Like Formulas

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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 .

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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 .

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Contributed by: Izidor Hafner (March 2011)
Based on work by : John H. Conway and Richard K. Guy
Open content licensed under CC BY-NC-SA


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Details

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



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