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The points of tangency t_1 and t_2 for the four lines tangent to two circles with centers x_1 and x_2 and radii r_1 and r_2 are given by solving the simultaneous equations ...

Determining the maximum number of pieces in which it is possible to divide a circle for a given number of cuts is called the circle cutting or pancake cutting problem. The ...

Given a unit circle, pick two points at random on its circumference, forming a chord. Without loss of generality, the first point can be taken as (1,0), and the second by ...

Select three points at random on the circumference of a unit circle and find the distribution of areas of the resulting triangles determined by these three points. The first ...

Define S_n(x) = sum_(k=1)^(infty)(sin(kx))/(k^n) (1) C_n(x) = sum_(k=1)^(infty)(cos(kx))/(k^n), (2) then the Clausen functions are defined by ...

Coaxal circles are circles whose centers are collinear and that share a common radical line. The collection of all coaxal circles is called a pencil of coaxal circles ...

A colossally abundant number is a positive integer n for which there is a positive exponent epsilon such that (sigma(n))/(n^(1+epsilon))>=(sigma(k))/(k^(1+epsilon)) for all ...

The complete elliptic integral of the second kind, illustrated above as a function of k, is defined by E(k) = E(1/2pi,k) (1) = ...

The constant a_(-1) in the Laurent series f(z)=sum_(n=-infty)^inftya_n(z-z_0)^n (1) of f(z) about a point z_0 is called the residue of f(z). If f is analytic at z_0, its ...

A composite number n is a positive integer n>1 which is not prime (i.e., which has factors other than 1 and itself). The first few composite numbers (sometimes called ...