Homeomorphisms Between the Circular Disc and the Square

Chamberlain Fong ()
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Chamberlain Fong: exile.org

Chapter 6 in Handbook of the Mathematics of the Arts and Sciences, 2021, pp 123-148 from Springer

Abstract: 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.

Keywords: Conformal square; Escheresque artworks; Invertible mappings; Non-Euclidean geometry; Poincaré disk; squircles (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/978-3-319-57072-3_27

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