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Consider a one-dimensional Hamiltonian map of the form H(p,q)=1/2p^2+V(q), (1) which satisfies Hamilton's equations q^. = (partialH)/(partialp) (2) p^. = ...

The hexyl circle is the circumcircle of the hexyl triangle. Amazingly, its center is at the incenter I and its radius is 2R, where R is the circumradius. Its circle function ...

100=10^2. Madachy (1979) gives a number of algebraic equations using the digits 1 to 9 which evaluate to 100, such as (7-5)^2+96+8-4-3-1 = 100 (1) 3^2+91+7+8-6-5-4 = 100 (2) ...

Given a hypergeometric series sum_(k)c_k, c_k is called a hypergeometric term (Koepf 1998, p. 12).

A ring that is commutative under multiplication, has a multiplicative identity element, and has no divisors of 0. The integers form an integral domain.

A double rhomboid linkage which gives rectilinear motion from circular without an inversion.

The pedal curve of a logarithmic spiral with parametric equation f = e^(at)cost (1) g = e^(at)sint (2) for a pedal point at the pole is an identical logarithmic spiral x = ...

If a sphere is covered by three closed sets, then one of them must contain a pair of antipodal points.

A random process whose future probabilities are determined by its most recent values. A stochastic process x(t) is called Markov if for every n and t_1<t_2...<t_n, we have ...

A group in which the elements are square matrices, the group multiplication law is matrix multiplication, and the group inverse is simply the matrix inverse. Every matrix ...