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Pentagram map
In mathematics, the pentagram map is a discrete dynamical system on the moduli space of polygons in the projective plane. The pentagram map takes a given polygon, finds the intersections of the shortest diagonals of the polygon, and constructs a new polygon from these intersections.
Richard Schwartz introduced the pentagram map for a general polygon in a 1992 paper
though it seems that the special case, in which
the map is defined for pentagons only, goes back to an 1871 paper of Alfred Clebsch and a 1945 paper of Theodore Motzkin.
The pentagram map is similar in spirit to the constructions underlying Desargues' Theorem and Poncelet's porism. It echoes the rationale and construction underlying a conjecture of Branko Grünbaum concerning
the diagonals of a polygon.
==Definition of the map==
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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