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The Lebombo bone is the oldest known mathematical artifact. It dates from 35000 BC and consists of 29 distinct notches that were deliberately cut into a baboon's fibula. It ...

Let K be a finite complex, let h:|K|->|K| be a continuous map. If Lambda(h)!=0, then h has a fixed point.

Let H be a subgroup of G. A subset T of elements of G is called a left transversal of H if T contains exactly one element of each left coset of H.

A quantity a is said to be less than b if a is smaller than b, written a<b. If a is less than or equal to b, the relationship is written a<=b. In the Wolfram Language, this ...

L=sigma/(sigma_B), where sigma is the variance in a set of s Lexis trials and sigma_B is the variance assuming Bernoulli trials. If L<1, the trials are said to be subnormal, ...

Second and higher derivatives of the metric tensor g_(ab) need not be continuous across a surface of discontinuity, but g_(ab) and g_(ab,c) must be continuous across it.

A Lie groupoid over B is a groupoid G for which G and B are differentiable manifolds and alpha,beta and multiplication are differentiable maps. Furthermore, the derivatives ...

A sphere is rigid.

Let f(s) defined and analytic in a half-strip D={s:sigma_1<=R[s]<=sigma_2,I[s]>=t_0 0}. If |f|<=M on the boundary partialD of D and there is a constant A such that ...

Also known as the first fundamental form, ds^2=g_(ab)dx^adx^b. In the principal axis frame for three dimensions, ds^2=g_(11)(dx^1)^2+g_(22)(dx^2)^2+g_(33)(dx^3)^2. At ...