Patterns on a Surface: The Reconciliation of the Circle and the Square

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. © 2011 Kim Williams Books, Turin.