Reviews graphical methods for representing ternary and quaternary systems, focusing on use of triangular composition diagrams. Examines some of the relevant geometry of triangles in general, showing that right isosceles triangles possess some very advantageous features for representing ternary systems. (JN)

Geometry is viewed as the most neglected area of the elementary school mathematics curriculum. Tangram activities provide numerous worthwhile mathematical experiences for children. A method of constructing tangrams through paper folding is followed by suggested spatial visualization, measurement, and additional activities. (MP)

Almost-Regular Polygons (ARPs) are viewed as interesting, but hardly ever noticed. The growing availability of computers means that such figures can be examined. A program written in BASIC which was developed to generate and test large blocks of cases is presented and described. (MP)

The nature of the corner reflector array left on the moon by the July 1969 Apollo astronauts is described. The array was used to reflect earth-originating laser beams back to earth, and yielded a more accurate determination (to within six inches) of distance from the earth to the moon. (MP)

The activities presented here focus on symmetry. The materials aim to provide experience in: (1) observing grid-drawn pictures and coloring in appropriate squares; (2) making symmetric designs about two lines of symmetry; (3) using a ruler and protractor; and (4) using a ruler, protractor, and compass. Worksheet masters are provided. (MP)

An approach to teaching problem solving to preservice and in-service middle school teachers is described. They examined an unsolved question as a class research project. The process of developing the solution is detailed, and difficulties contained within the process are noted. (MP)

The material examines aspects of Fibonacci and Lucas sequences, the generation of the Divine Ratio, and the nature of this ratio in golden rectangles, triangles, and figures made up of golden triangles. It is noted Lucas sequence is formed like Fibonacci but has one and three as the first elements. (Author/MP)

This game uses attribute blocks to encourage the formation of problem-solving strategies, provide drill in the addition of randomly generated numbers, and aid in pupil recognition of pictorial representations of geometric shapes. The material is based on the psychological principles common to other attribute games. (MP)

The first idea discusses the use of Pascal's triangle to discover the total number of gifts presented during the 12 days of Christmas. The second idea looks at an approach to viewing L'Hospital's rule that is geared toward helping beginning calculus students develop a feeling as to why it works. (MP)

The use of microcomputers to aid geometry instruction is emphasized through discussion of a program written in BASIC which provides for experimenting with polynomial curves. The program listing is included. (MP)

Several methods of numerical mappings other than the usual cartesian coordinate system are considered. Some examples using parallel axes representation, which are seen to lead to aesthetically pleasing or interesting configurations, are presented. Exercises with alternative representations can stimulate pupil imagination and exploration in…

Examples of some geometric illustrations of limits are presented. It is believed the limit concept is among the most important topics in mathematics, yet many students do not have good intuitive feelings for the concept, since it is often taught very abstractly. Geometric examples are suggested as meaningful tools. (MP)

A test of 1,366 high school students revealed no significant sex differences in the ability to perform geometrical proofs. Boys did outscore girls on overall achievement in geometry, but the results are believed to reflect differential exposure to mathematics outside the classroom. (MP)

Ideas and activities are presented which are designed to help students gain better understanding of area and area formulas. It is felt many pupils have developed extremely vague or false notions about the concepts, and fail to understand why areas of certain regions can be determined through linear measurement tools. (MP)

Geometry is revealed as one of the most universal and useful tools in all parts of mathematics, with the idea of a "pure" geometry divorced from algebra an historically recent idea. (MP)