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A two-dimensional map also called the Taylor-Greene-Chirikov map in some of the older literature and defined by I_(n+1) = I_n+Ksintheta_n (1) theta_(n+1) = theta_n+I_(n+1) ...

The term "vesica piscis," meaning "fish bladder" in Latin, is used for the particular symmetric lens formed by the intersection of two equal circles whose centers are offset ...

Count the number of lattice points N(r) inside the boundary of a circle of radius r with center at the origin. The exact solution is given by the sum N(r) = ...

A Pisot number is a positive algebraic integer greater than 1 all of whose conjugate elements have absolute value less than 1. A real quadratic algebraic integer greater than ...

The prime number theorem gives an asymptotic form for the prime counting function pi(n), which counts the number of primes less than some integer n. Legendre (1808) suggested ...

The alternating factorial is defined as the sum of consecutive factorials with alternating signs, a(n)=sum_(k=1)^n(-1)^(n-k)k!. (1) They can be given in closed form as ...

The term analysis is used in two ways in mathematics. It describes both the discipline of which calculus is a part and one form of abstract logic theory. Analysis is the ...

Consider three mutually tangent circles, and draw their inner Soddy circle. Then draw the inner Soddy circles of this circle with each pair of the original three, and ...

An asymptotic series is a series expansion of a function in a variable x which may converge or diverge (Erdélyi 1987, p. 1), but whose partial sums can be made an arbitrarily ...

The confluent hypergeometric function of the second kind gives the second linearly independent solution to the confluent hypergeometric differential equation. It is also ...