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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the pentagram map is a kind of iteration on polygons. The pentagram map takes a given convex pentagon, finds the intersections of the diagonals of the pentagon and constructs a new pentagon from these intersections. Pentagram maps were studied by John Conway and Richard Schwartz among others. They possess a cross ratio and are an example of an integrable system and have applications in computer vision.