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The envelope of a one-parameter family of curves given implicitly by U(x,y,c)=0, (1) or in parametric form by (f(t,c),g(t,c)), is a curve that touches every member of the ...

There are infinitely many primes m which divide some value of the partition function P.

A point related to the construction and properties of conic sections. Hyperbolas and noncircular ellipses have two distinct foci and two associated conic section directrices, ...

The forward difference is a finite difference defined by Deltaa_n=a_(n+1)-a_n. (1) Higher order differences are obtained by repeated operations of the forward difference ...

For a Galois extension field K of a field F, the fundamental theorem of Galois theory states that the subgroups of the Galois group G=Gal(K/F) correspond with the subfields ...

Let a spherical triangle have sides a, b, and c with A, B, and C the corresponding opposite angles. Then (sin[1/2(a-b)])/(sin(1/2c)) = (sin[1/2(A-B)])/(cos(1/2C)) (1) ...

The gnomonic projection is a nonconformal map projection obtained by projecting points P_1 (or P_2) on the surface of sphere from a sphere's center O to point P in a plane ...

The great retrosnub icosidodecahedron, also called the great inverted retrosnub icosidodecahedron is the uniform polyhedron with Maeder index 74 (Maeder 1997), Wenninger ...

The group direct sum of a sequence {G_n}_(n=0)^infty of groups G_n is the set of all sequences {g_n}_(n=0)^infty, where each g_n is an element of G_n, and g_n is equal to the ...

Let a set of vertices A in a connected graph G be called convex if for every two vertices x,y in A, the vertex set of every (x,y) graph geodesic lies completely in A. Also ...