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An idealized coin consists of a circular disk of zero thickness which, when thrown in the air and allowed to fall, will rest with either side face up ("heads" H or "tails" T) ...

The graph distance matrix, sometimes also called the all-pairs shortest path matrix, is the square matrix (d_(ij)) consisting of all graph distances from vertex v_i to vertex ...

A roulette is a curve traced by a fixed point on a closed convex curve as that curve rolls without slipping along a second curve. The roulettes described by the foci of ...

Starting with a triangle, draw a circle touching two sides. Then draw a circle tangent to this circle and two other sides. Continue in the same direction. The result is a ...

The Lemoine axis is the perspectrix of a reference triangle and its tangential triangle, and also the trilinear polar of the symmedian point K of the reference triangle. It ...

The term "vesica piscis," meaning "fish bladder" in Latin, is used for the particular symmetric lens formed by the intersection of two equal circles whose centers are offset ...

A vector field on a circle in which the directions of the vectors are all at the same angle to the circle.

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 ...

The Atzema spiral, also known as the Pritch-Atzema spiral, is the curve whose catacaustic for a radiant point at the origin is a circle, as illustrated above. It has ...

The bend of a circle C mutually tangent to three other circles is defined as the signed curvature of C. If the contacts are all external, the signs of the bends of all four ...