by a geometric method, a one-to-one correspondence is set up between the set of real numbers and the set of all points, except one, on a circle of unit diameter. Then some interesting results relating the corresponding points and real numbers are derived. (Author/CT)

Elucidated is the relationship among three threads of mathematical investigations: Kirkman's schoolgirl problems, finite geometries, and Euler's n-square officer problems. (JP)

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

The process that Hippasus of Metapontum (ca. 470 B.C.) may have used to discover irrational numbers is reconstructed. (MP)

Lines in the coordinatized plane which do not go through the origin can be designated by the ordered pair of intercepts. The enrichment unit described illustrates duality in mathematics. (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)

It is extremely difficult to extend in a natural way the concepts developed in high school geometry to motivate the concepts of trigonometry. To solve this difficultry, the author defines "sensed angles" as ordered pairs of rays and makes appropriate definitions which yield the familiar angle properties of plane geometry. He then shows how this…

Number sequence patterns for counting boundaries of familiar figures are extended to higher dimensions. (JP)

Results are presented of an impromptu exploration of polar formulas for volumes of revolution for certain plane regions. The material is thought to be unique, and to offer room for student exploration. It is felt pupil investigation can lead to increased pupil interest in both polar coordinates and calculus. (MP)