English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The pentagram map takes a planar polygon $P$ to a polygon $P'$ whose verticesare the intersection points of consecutive shortest diagonals of $P$. This mapis known to interact nicely with Poncelet polygons, i.e. polygons which aresimultaneously inscribed in a conic and circumscribed about a conic. A theoremof R. Schwartz says that if $P$ is a Poncelet polygon, then the image of $P$under the pentagram map is projectively equivalent to $P$. In the present paperwe show that in the convex case this property characterizes Poncelet polygons:if a convex polygon is projectively equivalent to its pentagram image, then itis Poncelet. The proof is based on the theory of commuting differenceoperators, as well as on properties of real elliptic curves and thetafunctions.

The pentagram map, Poncelet polygons, and commuting difference operators