On Polygons and Injective Mappings of the Plane

Boaz A. Slomka

doi:10.1007/978-1-4614-6406-8_14

On Polygons and Injective Mappings of the Plane

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

We give an affirmative answer to a question asked by Gardner and Mauldin (Geom. Dedicata 26, 323-332, 1988) about bijections of the plane taking each polygon with n sides onto a polygon with n sides. We also state and prove more general results in this spirit. For example, we show that an injective mapping taking each convex n-gon onto a non-degenerate n-gon (not necessarily convex or even simple) must be affine.

Original language	English
Title of host publication	Asymptotic Geometric Analysis
Subtitle of host publication	Proceedings of the Fall 2010 Fields Institute Thematic Program
Editors	Monika Ludwig, Vladimir Pestov, Vitali Milman, Nicole Tomczak-Jaegermann
Pages	299-312
Number of pages	14
DOIs	https://doi.org/10.1007/978-1-4614-6406-8_14
State	Published - 2013
Externally published	Yes

Publication series

Name	Fields Institute Communications
Volume	68

Keywords

Fundamental theorem of affine geometry
Injective maps
Polygons

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.1007/978-1-4614-6406-8_14

Cite this

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abstract = "We give an affirmative answer to a question asked by Gardner and Mauldin (Geom. Dedicata 26, 323-332, 1988) about bijections of the plane taking each polygon with n sides onto a polygon with n sides. We also state and prove more general results in this spirit. For example, we show that an injective mapping taking each convex n-gon onto a non-degenerate n-gon (not necessarily convex or even simple) must be affine.",

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On Polygons and Injective Mappings of the Plane. / Slomka, Boaz A.
Asymptotic Geometric Analysis: Proceedings of the Fall 2010 Fields Institute Thematic Program. ed. / Monika Ludwig; Vladimir Pestov; Vitali Milman; Nicole Tomczak-Jaegermann. 2013. p. 299-312 (Fields Institute Communications; Vol. 68).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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On Polygons and Injective Mappings of the Plane

Abstract

Publication series

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

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