Experimental Mathematics

The pentagram map

Richard Schwartz

Abstract

We consider the pentagram map on the space of plane convex pentagons obtained by drawing a pentagon's diagonals, recovering unpublished results of Conway and proving new ones. We generalize this to a "pentagram map'' on convex polygons of more than five sides, showing that iterated images of any initial polygon converge exponentially fast to a point. We conjecture that the asymptotic behavior of this convergence is the same as under a projective transformation. Finally, we show a connection between the pentagram map and a certain flow defined on parametrized curves.

Article information

Source
Experiment. Math., Volume 1, Issue 1 (1992), 71-81.

Dates
First available in Project Euclid: 26 March 2003

Permanent link to this document
https://projecteuclid.org/euclid.em/1048709118

Mathematical Reviews number (MathSciNet)
MR93h:52002

Zentralblatt MATH identifier
0765.52004

Subjects
Primary: 52A10: Convex sets in 2 dimensions (including convex curves) [See also 53A04]

Citation

Schwartz, Richard. The pentagram map. Experiment. Math. 1 (1992), no. 1, 71--81. https://projecteuclid.org/euclid.em/1048709118


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