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Handbook of the Mathematics of the Arts and Sciences pp 1–26Cite as

Homeomorphisms Between the Circular Disc and the Square

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Abstract

The circle and the square are among the most common shapes used by mankind. Consequently, it is worthwhile to study the mathematical correspondence between the two. This chapter discusses three different ways of mapping a circular region to a square region and vice versa. Each of these mappings has nice closed-form invertible equations and different interesting properties. In addition, this chapter will present artistic applications of these mappings such as converting the Poincaré disk to a square as well as molding rectangular artworks into oval-shaped ones.

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Authors and Affiliations

  1. exile.org, San Francisco, CA, USA

    Chamberlain Fong

Authors
  1. Chamberlain Fong
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Correspondence to Chamberlain Fong .

Editor information

Editors and Affiliations

  1. Dept of Mathematical Sciences, The University of Montana Dept of Mathematical Sciences, Missoula, MT, USA

    Bharath Sriraman

Section Editor information

  1. Department of Mathematical Sciences, The University of Montana, Missoula, MT, USA

    Bharath Sriraman

  2. Department of Mathematics Education, College of Education, Seoul National University, Seoul, South Korea

    Kyeong-Hwa Lee

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Fong, C. (2019). Homeomorphisms Between the Circular Disc and the Square. In: Sriraman, B. (eds) Handbook of the Mathematics of the Arts and Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-70658-0_27-1

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  • DOI: https://doi.org/10.1007/978-3-319-70658-0_27-1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-70658-0

  • Online ISBN: 978-3-319-70658-0

  • eBook Packages: Springer Reference MathematicsReference Module Computer Science and Engineering

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