Fagnano Orbits of Polygonal Dual Billiards

Serge Tabachnikov

doi:10.1023/A:1005199315944

Fagnano Orbits of Polygonal Dual Billiards

Serge Tabachnikov

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Given a convex n-gon P, a Fagnano periodic orbit of the respective dual billiard map is an n-gon Q whose sides are bisected by the vertices of P. For which polygons P does the ratio Area Q/Area P have the minimal value? The answer is shown to be: for affine-regular polygons.

Original language	English (US)
Pages (from-to)	279-286
Number of pages	8
Journal	Geometriae Dedicata
Volume	77
Issue number	3
DOIs	https://doi.org/10.1023/A:1005199315944
State	Published - 1999

All Science Journal Classification (ASJC) codes

Geometry and Topology

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10.1023/A:1005199315944

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title = "Fagnano Orbits of Polygonal Dual Billiards",

abstract = "Given a convex n-gon P, a Fagnano periodic orbit of the respective dual billiard map is an n-gon Q whose sides are bisected by the vertices of P. For which polygons P does the ratio Area Q/Area P have the minimal value? The answer is shown to be: for affine-regular polygons.",

author = "Serge Tabachnikov",

note = "Funding Information: I am grateful to E. Gutkin for his interest and stimulating questions. The work was supported in part by an NSF grant. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.",

year = "1999",

doi = "10.1023/A:1005199315944",

language = "English (US)",

volume = "77",

pages = "279--286",

journal = "Geometriae Dedicata",

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publisher = "Springer Netherlands",

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T1 - Fagnano Orbits of Polygonal Dual Billiards

AU - Tabachnikov, Serge

N1 - Funding Information: I am grateful to E. Gutkin for his interest and stimulating questions. The work was supported in part by an NSF grant. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.

PY - 1999

Y1 - 1999

N2 - Given a convex n-gon P, a Fagnano periodic orbit of the respective dual billiard map is an n-gon Q whose sides are bisected by the vertices of P. For which polygons P does the ratio Area Q/Area P have the minimal value? The answer is shown to be: for affine-regular polygons.

AB - Given a convex n-gon P, a Fagnano periodic orbit of the respective dual billiard map is an n-gon Q whose sides are bisected by the vertices of P. For which polygons P does the ratio Area Q/Area P have the minimal value? The answer is shown to be: for affine-regular polygons.

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UR - https://www.scopus.com/pages/publications/0042638249#tab=citedBy

U2 - 10.1023/A:1005199315944

DO - 10.1023/A:1005199315944

M3 - Article

AN - SCOPUS:0042638249

SN - 0046-5755

VL - 77

SP - 279

EP - 286

JO - Geometriae Dedicata

JF - Geometriae Dedicata

IS - 3

ER -

Fagnano Orbits of Polygonal Dual Billiards

Abstract

All Science Journal Classification (ASJC) codes

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