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On an oriented n-dimensional Riemannian manifold, the Hodge star is a linear function which converts alternating differential k-forms to alternating (n-k)-forms. If w is an ...

The mathematical study of a nonlinear equation f(phi)=y, where f maps from a Hilbert space X to a Hilbert space Y and y in Y which abstracts the construction of optical ...

On the class of topological spaces, a homeomorphism class is an equivalence class under the relation of being homeomorphic. For example, the open interval (-pi/2,pi/2) and ...

Nonconcurrent triangles with parallel sides are always homothetic. Homothetic triangles are always perspective triangles. Their perspector is called their homothetic center.

A sextic surface given by the implicit equation 4(x^2+y^2+z^2-13)^3+27(3x^2+y^2-4z^2-12)^2=0.

The radius used in performing an inversion with respect to an inversion circle.

If p divides the numerator of the Bernoulli number B_(2k) for 0<2k<p-1, then (p,2k) is called an irregular pair. For p<30000, the irregular pairs of various forms are p=16843 ...

The security of a cryptosystem must not depend on keeping the cryptographic algorithm secret.

The statistical index P_L=(sump_nq_0)/(sump_0q_0), where p_n is the price per unit in period n and q_0 is the quantity produced in the initial period.

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 ...