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An interval is a connected portion of the real line. If the endpoints a and b are finite and are included, the interval is called closed and is denoted [a,b]. If the ...

Let C be a curve, let O be a fixed point (the pole), and let O^' be a second fixed point. Let P and P^' be points on a line through O meeting C at Q such that P^'Q=QP=QO^'. ...

Every semisimple Lie algebra g is classified by its Dynkin diagram. A Dynkin diagram is a graph with a few different kinds of possible edges. The connected components of the ...

A sequence whose terms are integers. The most complete printed references for such sequences are Sloane (1973) and its update, Sloane and Plouffe (1995). Neil Sloane ...

A branch cut is a curve (with ends possibly open, closed, or half-open) in the complex plane across which an analytic multivalued function is discontinuous. For convenience, ...

The points of intersection of the adjacent angle trisectors of the angles of any triangle DeltaABC are the polygon vertices of an equilateral triangle DeltaDEF known as the ...

Consider any star of n line segments through one point in space such that no three lines are coplanar. Then there exists a polyhedron, known as a zonohedron, whose faces ...

A "beam detector" for a given curve C is defined as a curve (or set of curves) through which every line tangent to or intersecting C passes. The shortest 1-arc beam detector, ...

A bitangent is a line that is tangent to a curve at two distinct points. Aa general plane quartic curve has 28 bitangents in the complex projective plane. However, as shown ...

The dual of Pascal's theorem (Casey 1888, p. 146). It states that, given a hexagon circumscribed on a conic section, the lines joining opposite polygon vertices (polygon ...