This article presents some easily stated but unsolved geometric problems. The three sections are entitled: Housemoving, Manholes and Fermi Surfaces" (convex figures of constant width), Angels, Pollen Grains and Misanthropes" (packing problems), and The Four-Color Conjecture and Organic Chemistry." (MM)

Examples are given of the usefulness of mathematics in several different fields. (MM)

Problems involving the use of diagrams to depict plangers'' (in which lines cross a specified number of times) are discussed. (LS)

In a series of activities involving map coloring, students can discover various combinatorial theorems including Euler's formula. (SD)

Discussed are some applications of Euler's Formula N plus F minus E equals Z, where N, F, and E are respectively the number of vertices, faces, and edges of a planar figure. In particular, the Four-Color Problem is proved for the special case of five countries. (CT)