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 .