Illustrated is the mathematical analysis of a three-dimensional game using techniques from the calculus of finite differences. This game is an analog of the familiar two-dimensional game, Dots and Squares. (JP)

Criteria for a reasonable axiomatic system are discussed. A discussion of the historical attempts to prove the independence of Euclids parallel postulate introduces non-Euclidean geometries. Poincare's model for a non-Euclidean geometry is defined and analyzed. (LS)

Parts of this paper were presented at the annual meeting of the Modern Language Association, New York, N.Y., December 30, 1970, under the title Toward the Formalization of Rudeness in Conversation.'' (VM)

Described is a physical realization of the Klein four-group which shows the isomorphism of the symmetry group of the rectangle and Piaget's INRC group of logical implications. (MM)

Examples of items on a test used to measure mathematical understanding are given. This article concludes the series; for previous articles see Volume 1 Number 5 July 1972 and Volume 1 Number 6 September 1972. (DT)

Included are coordinate tic-tac-toe,'' cerebrathenics,'' polyhedron toss,'' and patterns and distortions.'' (Author)

Describes a device designed to shoot rubber bands. Children investigate and measure forces, angles, distances and differences in materials used. (JM)

Discussed are generalizations and problem solving, unsound uses of generalizations, generalization as data, and student discovery of generalizations. (CT)

Develops two-dimensional descriptions of degenerate transformations using elementary matrix algebra. (RS)