- Experiment. Math.
- Volume 1, Issue 1 (1992), 71-81.
The pentagram map
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the pentagram map on the space of plane convex pentagons obtained by drawing a pentagon's diagonals, recovering unpublished results of Conway and proving new ones.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.
Experiment. Math., Volume 1, Issue 1 (1992), 71-81.
First available in Project Euclid: 26 March 2003
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Schwartz, Richard. The pentagram map. Experiment. Math. 1 (1992), no. 1, 71--81. https://projecteuclid.org/euclid.em/1048709118