Patterns on a surface: the reconciliation of the circle and the square

Chris J K Williams

Research output: Contribution to journalArticle

4 Citations (Scopus)
121 Downloads (Pure)

Abstract

The theory of heat flow on a surface shows that any curvilinear quadrilateral can be ‘tiled’ with curvilinear squares of varying size. This paper demonstrates a simple numerical technique for doing this that can also be applied to shapes other than quadrilaterals. In particular, any curvilinear triangle can be tiled with curvilinear equilateral triangles.
Original languageEnglish
Pages (from-to)281-295
Number of pages15
JournalNexus Network Journal
Volume13
Issue number2
Early online date7 Jun 2011
DOIs
Publication statusPublished - 1 Jul 2011

Keywords

  • isothermal coordinates
  • tension coefficient
  • dynamic relaxation
  • tiling
  • differential geometry
  • harmonic coordinates

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