Quotes About Torus

From apples to black holes, the shape of a torus is a recurring pattern of creation in nature.

Intersections of lines, for example, remain intersections, and the hole in a torus (doughnut) cannot be transformed away. Thus a doughnut may be transformed topologically into a coffee cup (the hole turning into a handle) but never into a pancake. Topology, then, is really a mathematics of relationships, of unchangeable, or "invariant," patterns.

Such orbits are not completely regular, since they never exactly repeat themselves, but they are certainly predictable, and they are far from chaotic. Points never arrive inside the curve or outside it. Translated back to the full three-dimensional picture, the orbits were outlining a torus, or doughnut shape, and Hénon's mapping was a cross-section of the torus. So far, he was merely illustrating what all his predecessors had taken for granted. Orbits were periodic.