Homeomorphisms Between the Circular Disc and the Square

  • Chamberlain FongEmail author
Living reference work entry


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.


Conformal square Escheresque artworks Invertible mappings Non-Euclidean geometry Poincaré disk squircles 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.exile.orgSan FranciscoUSA

Section editors and affiliations

  • Bharath Sriraman
    • 1
  • Kyeong-Hwa Lee
    • 2
  1. 1.Department of Mathematical SciencesThe University of MontanaMissoulaUSA
  2. 2.Department of Mathematics Education, College of EducationSeoul National UniversitySeoulSouth Korea

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