Greek temples, French department stores, Islamic domes, church windows, Egyptian tombs, Assyrian vessels, Chinese porcelains … The examples of symmetry in Chapter 3 give evidence of the multitude of its forms and of its ubiquitousness. They were meant only to illustrate different forms of symmetry and neither attempted to focus on specific contexts nor to discuss particular artists.

Such expositions are the goal of this chapter. In its first section we witness early occurrences of symmetry through archaeological findings. We then proceed with a short discussion on Oriental rugs, which are doubtless a colourful source of symmetric patterns. In Section 4.3 the focus is on Chinese lattices. Both Oriental rugs and Chinese lattices spread over a period of more than two millennia (even though most of our examples will be relatively recent). Section 4.4, in contrast, brings the focus to the twentieth century and discusses some of the work of M.C. Escher.

Origins

A paper by Thomas Wynn (2002) provides an unusual application of the notion of symmetry. A declared goal of the paper is the “reconstruction of aspects of early hominid spatial cognition based on an analysis of artifactual symmetries”. Spatial cognition aside, Wynn's paper is of interest to us because of its tracing of early instances of intentional symmetry in human artefacts.

The earliest examples of such artefacts are stone tools approximately 2.5 million years old (from the preceding period of 1.5 million years separating the split between hominids and other African apes and the production of these stone tools there are no archaeological records).