Symmetry in mathematics

✍ Scribed by Peter Hilton; Jean Pedersen

• Book ID: 103930201
• Publisher: Elsevier Science
• Year: 1986
• Tongue: English
• Weight: 813 KB
• Volume: 12
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/0898-1221(86)90157-4

✦ Synopsis

The role of symmetry in geometry is universally recognized. The principal purpose of this article, on the other hand, is to show how it plays many significant, hut varied, roles throughout the whole of mathematics. We illustrate this fact through characteristic examples; in most of these examples the mathematics is well known, but the symmetry aspects of the arguments have not been rendered explicit as a guiding principle. In one example, however, we do look at an unfamiliar geometrical construction of regular star polygons, which we relate to number-theoretical properties. In this example we draw attention to the presence of symmetry of an unexpected and untraditional nature, not obviously related to the regularity of the polygons.

We have attempted to identify specific principles illustrated by our examples of symmetry in mathematics. We draw attention to the Halfway Principle (Sec. 3) and the principle of the symmetric definition of symmetric concepts (Sec. 4).