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A geodesic is a locally length-minimizing curve. Equivalently, it is a path that a particle which is not accelerating would follow. In the plane, the geodesics are straight ...

The centroid is center of mass of a two-dimensional planar lamina or a three-dimensional solid. The mass of a lamina with surface density function sigma(x,y) is ...

In continuum percolation theory, the so-called germ-grain model is an obvious generalization of both the Boolean and Boolean-Poisson models which is driven by an arbitrary ...

The Golomb graph is a unit-distance graph discovered around 1960-1965 by Golomb (Soifer 2008, p. 19). It is implemented in the Wolfram Language as GraphData["GolombGraph"]. A ...

A root-finding method which was among the most popular methods for finding roots of univariate polynomials in the 19th and 20th centuries. It was invented independently by ...

A 2-variable oriented knot polynomial P_L(a,z) motivated by the Jones polynomial (Freyd et al. 1985). Its name is an acronym for the last names of its co-discoverers: Hoste, ...

The volumes of any n n-dimensional solids can always be simultaneously bisected by a (n-1)-dimensional hyperplane. Proving the theorem for n=2 (where it is known as the ...

There are a number of mathematical curves that produced heart shapes, some of which are illustrated above. A "zeroth" curve is a rotated cardioid (whose name means ...

An elliptic partial differential equation given by del ^2psi+k^2psi=0, (1) where psi is a scalar function and del ^2 is the scalar Laplacian, or del ^2F+k^2F=0, (2) where F ...

A hex number, also called a centered hexagonal number, is given by H_n = 1+6T_n (1) = 3n^2+3n+1, (2) where T_n=n(n+1)/2 is the nth triangular number and the indexing with ...