The activity uses an area model to analyze probabilities associated with games of chance. Three activity sheets are included, with teaching suggestions. (MNS)

Discusses flexible polyhedrons, called flexors, that can be bent so that the faces stay rigid while the angles between them seem to change. Presents models representing flexors and directions on how examples can be constructed. (MDH)

Discusses the mathematical model presented by Vito Volterra to describe the dynamics of population density. Discusses the predator prey relationship, presents an computer simulated model from marine life involving sharks and mackerels, and discusses ecological chaos. (MDH)

Presents a proof of Euler's Theorem on polyhedra by relating the theorem to the field of modern topology, specifically to the topology of relief maps. An analogous theorem involving the features of mountain summits, basins, and passes on a terrain is proved and related to the faces, vertices, and edges on a convex polyhedron. (MDH)

Presents the origin and mathematics of Hubble's Law of the expanding universe. Discusses limitations to this law and the related concepts of standard candles, elliptical galaxies, and streaming motions, which are conspicuous deviations from the law. The third of three models proposed as explanations for streaming motions is designated: The Great…

This guide is support material for geometry teachers in middle schools or high schools in South Carolina. The guide describes the content of each program in the television series and suggests further learning activities for the students. The geometry that underlies the world around us is presented through applications. Contents of the series…