Gregory number
Encyclopedia
In mathematics
, a Gregory number, named after James Gregory
, is a real number
of the form:
where x is any rational number greater or equal to 1. Considering the power series expansion for arctangent, we have
Setting x = 1 gives the well-known Leibniz formula for pi.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, a Gregory number, named after James Gregory
James Gregory (astronomer and mathematician)
James Gregory FRS was a Scottish mathematician and astronomer. He described an early practical design for the reflecting telescope – the Gregorian telescope – and made advances in trigonometry, discovering infinite series representations for several trigonometric functions.- Biography :The...
, is a real number
Real number
In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...
of the form:
where x is any rational number greater or equal to 1. Considering the power series expansion for arctangent, we have
Setting x = 1 gives the well-known Leibniz formula for pi.