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A spherical cap is the region of a sphere which lies above (or below) a given plane. If the plane passes through the center of the sphere, the cap is a called a hemisphere, ...

The median of a statistical distribution with distribution function D(x) is the value x such D(x)=1/2. For a symmetric distribution, it is therefore equal to the mean. Given ...

Any triangle that has two equal angle bisectors (each measured from a polygon vertex to the opposite sides) is an isosceles triangle. This theorem is also called the ...

The tetrahedral group T_d is the point group of symmetries of the tetrahedron including the inversion operation. It is one of the 12 non-Abelian groups of order 24. The ...

The number of colors sufficient for map coloring on a surface of genus g is given by the Heawood conjecture, chi(g)=|_1/2(7+sqrt(48g+1))_|, where |_x_| is the floor function. ...

The distribution for the sum X_1+X_2+...+X_n of n uniform variates on the interval [0,1] can be found directly as (1) where delta(x) is a delta function. A more elegant ...

A sequence {x_1,x_2,...} is equidistributed iff lim_(N->infty)1/Nsum_(n<N)e^(2piimx_n)=0 for each m=1, 2, .... A consequence of this result is that the sequence {frac(nx)} is ...

Let V be a real symmetric matrix of large order N having random elements v_(ij) that for i<=j are independently distributed with equal densities, equal second moments m^2, ...

The shortest circular sequence of length sigma^n such that every string of length n on the alphabet a of size sigma occurs as a contiguous subrange of the sequence described ...

A 4-cusped hypocycloid which is sometimes also called a tetracuspid, cubocycloid, or paracycle. The parametric equations of the astroid can be obtained by plugging in n=a/b=4 ...