Machinlike
Machinlike is a term used in mathematics to describe a class of formulas for computing the mathematical constant pi. These formulas express pi as a linear combination of arctangent terms with rational arguments, typically in the form pi = sum_i a_i arctan(1/x_i), where a_i are integers and x_i are positive integers greater than 1. The term honors John Machin, whose 1706 formula helped renew interest in arctangent-based computations and inspired a family of related identities.
Historically, Machin published pi/4 = 4 arctan(1/5) - arctan(1/239). Using the arctangent addition formulas, this identity yields rapidly
Computation and relevance: In the era of hand calculation, Machinlike formulas enabled high-precision digits with comparatively
Variants: Notable examples include the classic Machin formula pi = 16 arctan(1/5) - 4 arctan(1/239) and numerous others