# Geometric Illustration of Machin-Like Formulas

Geometric Illustration of Machin-Like Formulas

This Demonstration illustrates geometrically some Machin-like formulas for computing the number . A Gregory number is =arcccot(x), where is a rational number. Since =π/4, Gregory numbers arise in the determination of Machin-like formulas for computing the number .

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Størmer's numbers =3,7,8,13,17,18,21,30,… are the positive whole numbers for which the largest prime factor of +1 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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