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A triangle is a 3-sided polygon sometimes (but not very commonly) called the trigon. Every triangle has three sides and three angles, some of which may be the same. The sides ...

cos(20 degrees)cos(40 degrees)cos(80 degrees)=1/8. An identity communicated to Feynman as a child by a boy named Morrie Jacobs (Gleick 1992, p. 47). Feynman remembered this ...

The word residue is used in a number of different contexts in mathematics. Two of the most common uses are the complex residue of a pole, and the remainder of a congruence. ...

Construct a square equal in area to a circle using only a straightedge and compass. This was one of the three geometric problems of antiquity, and was perhaps first attempted ...

The Hochberg-O'Donnell fish graph is the unit-distance graph on 23 nodes and 42 edges illustrated above. It is triangle-free and is the smallest example of a unit-distance ...

Let 0<k^2<1. The incomplete elliptic integral of the third kind is then defined as Pi(n;phi,k) = int_0^phi(dtheta)/((1-nsin^2theta)sqrt(1-k^2sin^2theta)) (1) = ...

Given an integer sequence {a_n}_(n=1)^infty, a prime number p is said to be a primitive prime factor of the term a_n if p divides a_n but does not divide any a_m for m<n. It ...

A symmetric polynomial on n variables x_1, ..., x_n (also called a totally symmetric polynomial) is a function that is unchanged by any permutation of its variables. In other ...

The reciprocal of the arithmetic-geometric mean of 1 and sqrt(2), G = 2/piint_0^11/(sqrt(1-x^4))dx (1) = 2/piint_0^(pi/2)(dtheta)/(sqrt(1+sin^2theta)) (2) = L/pi (3) = ...

A right angle is an angle equal to half the angle from one end of a line segment to the other. A right angle is pi/2 radians or 90 degrees. A triangle containing a right ...