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The general sextic equation x^6+a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0=0 can be solved in terms of Kampé de Fériet functions, and a restricted class of sextics can be solved in ...

Measurements of a centered convex body in Euclidean n-space (for n>=3) show that its brightness function (the volume of each projection) is smaller than that of another such ...

The square antiprism is the antiprism with square bases whose dual is the tetragonal trapezohedron. The square antiprism has 10 faces. The square antiprism with unit edge ...

A string of length n on an alphabet l of m characters is an arrangement of n not necessarily distinct symbols from l. There are m^n such distinct strings. For example, the ...

Every closed three-manifold with finite fundamental group has a metric of constant positive scalar curvature, and hence is homeomorphic to a quotient S^3/Gamma, where Gamma ...

The cubic curve defined by ax^3+bx^2+cx+d=xy with a!=0. The curve cuts the axis in either one or three points. It was the 66th curve in Newton's classification of cubics. ...

The polyhedron compound of the truncated cube and its dual, the small triakis octahedron. The compound can be constructed from a truncated cube of unit edge length by ...

The distribution of the product X_1X_2...X_n of n uniform variates on the interval [0,1] can be found directly as P_(X_1...X_n)(u) = ...

A compact set W_infty with area mu(W_infty)=8/9(24)/(25)(48)/(49)...=pi/4 created by punching a square hole of length 1/3 in the center of a square. In each of the eight ...

Let the values of a function f(x) be tabulated at points x_i equally spaced by h=x_(i+1)-x_i, so f_1=f(x_1), f_2=f(x_2), .... Then Weddle's rule approximating the integral of ...