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The derivative of a function represents an infinitesimal change in the function with respect to one of its variables. The "simple" derivative of a function f with respect to ...

Successive application of Archimedes' recurrence formula gives the Archimedes algorithm, which can be used to provide successive approximations to pi (pi). The algorithm is ...

Let a_n and b_n be the perimeters of the circumscribed and inscribed n-gon and a_(2n) and b_(2n) the perimeters of the circumscribed and inscribed 2n-gon. Then a_(2n) = ...

The Brent-Salamin formula, also called the Gauss-Salamin formula or Salamin formula, is a formula that uses the arithmetic-geometric mean to compute pi. It has quadratic ...

A cubefree word contains no cubed words as subwords. The number of binary cubefree words of length n=1, 2, ... are 2, 4, 6, 10, 16, 24, 36, 56, 80, 118, ... (OEIS A028445). ...

The Machin-like formula 1/4pi=cot^(-1)(2)+cot^(-1)(3). The other 2-term Machin-like formulas are Hermann's formula, hutton's formula, and Machin's formula.

In the course of searching for continued fraction identities, Raayoni (2021) and Elimelech et al. (2023) noticed that while the numerator and denominator of continued ...

The sequence of six 9s which begins at the 762nd decimal place of pi, pi=3.14159...134999999_()_(six 9s)837... (Wells 1986, p. 51). The positions of the first occurrences of ...

The golden angle is the angle that divides a full angle in a golden ratio (but measured in the opposite direction so that it measures less than 180 degrees), i.e., GA = ...

The golden gnomon is the obtuse isosceles triangle whose ratio of side to base lengths is given by 1/phi=phi-1, where phi is the golden ratio. Such a triangle has angles of ...