Retracing the Turns of the Archimedean Spiral

This article will consider some of the properties of Archimedean spirals and their history, by retracing appearances of the spirals in various eras of the development of mathematics in reverse chronological order. The starting point will be the observation that the spirals currently serve as a fertile source of interesting and accessible examples for secondary and college courses. Their history and their intriguing properties also give various understandings of the motivation and context for considering these curves. As a by-product, ideas for some historically-based projects drawing on original sources, and suitable for undergraduate courses, will be suggested. Finally, it will become clear that the spiral itself serves almost as a visual metaphor for this story.