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The constant pi, denoted pi, is a real number defined as the ratio of a circle's circumference C to its diameter d=2r, pi = C/d (1) = C/(2r) (2) pi has decimal expansion ...

A theory is decidable iff there is an algorithm which can determine whether or not any sentence r is a member of the theory.

Inversion is the process of transforming points P to a corresponding set of points P^' known as their inverse points. Two points P and P^' are said to be inverses with ...

Given a ship with a known constant direction and speed v, what course should be taken by a chase ship in pursuit (traveling at speed V) in order to intercept the other ship ...

The line segment KO^_ joining the symmedian point K and circumcenter O of a given triangle. It is the diameter of the triangle's Brocard circle, and lies along the Brocard ...

The number of ways to arrange n distinct objects along a fixed (i.e., cannot be picked up out of the plane and turned over) circle is P_n=(n-1)!. The number is (n-1)! instead ...

The roulette traced by a point P attached to a circle of radius b rolling around the outside of a fixed circle of radius a. These curves were studied by Dürer (1525), ...

Given two topological spaces M and N, place an equivalence relationship on the continuous maps f:M->N using homotopies, and write f_1∼f_2 if f_1 is homotopic to f_2. Roughly ...

Let a circle C_1 lie inside another circle C_2. From any point on C_2, draw a tangent to C_1 and extend it to C_2. From the point, draw another tangent, etc. For n tangents, ...

The reciprocal curve of a given circle is the locus of a point which moves so that its distance from the center of reciprocation varies as its distance from the line which is ...