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A^n+B^n=sum_(j=0)^(|_n/2_|)(-1)^jn/(n-j)(n-j; j)(AB)^j(A+B)^(n-2j), where |_x_| is the floor function and (n; k) is a binomial coefficient.

An equation representing a locus L in the n-dimensional Euclidean space. It has the form L:f(x_1,...,x_n)=0, (1) where the left-hand side is some expression of the Cartesian ...

The probability P(a,n) that n random arcs of angular size a cover the circumference of a circle completely (for a circle with unit circumference) is ...

A conical frustum is a frustum created by slicing the top off a cone (with the cut made parallel to the base). For a right circular cone, let s be the slant height and R_1 ...

The EKG sequence is the integer sequence having 1 as its first term, 2 as its second, and with each succeeding term being the smallest number not already used that shares a ...

An evolute is the locus of centers of curvature (the envelope) of a plane curve's normals. The original curve is then said to be the involute of its evolute. Given a plane ...

The plane figure formed by a sequence of circles C_1, C_2, C_3, ... that are all tangent to each other at the same point and such that the sequence of radii converges to ...

The first example discovered of a map from a higher-dimensional sphere to a lower-dimensional sphere which is not null-homotopic. Its discovery was a shock to the ...

In general, the internal similitude center of two circles C_1=C(x_1,r_1) and C_2=C(x_2,r_2) with centers given in Cartesian coordinates is given by ...

The Mercator projection is a map projection that was widely used for navigation since loxodromes are straight lines (although great circles are curved). The following ...