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Given three noncollinear points, construct three tangent circles such that one is centered at each point and the circles are pairwise tangent to one another. Then there exist ...

To pick a random point on the surface of a unit sphere, it is incorrect to select spherical coordinates theta and phi from uniform distributions theta in [0,2pi) and phi in ...

Let a spherical triangle be drawn on the surface of a sphere of radius R, centered at a point O=(0,0,0), with vertices A, B, and C. The vectors from the center of the sphere ...

The Steiner circumellipse is the circumellipse that is the isotomic conjugate of the line at infinity and the isogonal conjugate of the Lemoine axis. It has circumconic ...

There are (at least) three different types of points known as Steiner points. The point S of concurrence of the three lines drawn through the vertices of a triangle parallel ...

A statistical distribution published by William Gosset in 1908. His employer, Guinness Breweries, required him to publish under a pseudonym, so he chose "Student." Given N ...

The symmetric group S_n of degree n is the group of all permutations on n symbols. S_n is therefore a permutation group of order n! and contains as subgroups every group of ...

Two circles with centers at (x_i,y_i) with radii r_i for i=1,2 are mutually tangent if (x_1-x_2)^2+(y_1-y_2)^2=(r_1+/-r_2)^2. (1) If the center of the second circle is inside ...

A Taylor series is a series expansion of a function about a point. A one-dimensional Taylor series is an expansion of a real function f(x) about a point x=a is given by (1) ...

Thurston's conjecture proposed a complete characterization of geometric structures on three-dimensional manifolds. Before stating Thurston's geometrization conjecture in ...