The author outlines a possible approach to the discovery of Euler's Theorem that results from a search for a classification of polyhedra. (MN)

The author investigates the construction of angles (using Euclidean tools) through a numerical approach. He calls attention to the surprising impossibility of constructing the conventional units of angle measure--the degree, minute, second, radian, and mil. (MN)

An application of the formula for finding the sum of an infinite geometric series is described through the use of Pierre Fermat's method for finding the area under a curve. (JT)

Ploynomials which can be used to calculate the number of ways of coloring hexagonal patterns are presented. (SD)

Presented are examples from geometry that are designed to investigate whether situations fit Euclidean geometry. Diagrams and activities are provided for examples. (RH)

Discusses the need to include symmetry as an important topic in the mathematics curriculum. Describes how symmetry might be developed conceptually and its relation to geometry, algebra, group theory, and physics. (JM)

Presents a problem, modified from a familiar situation, that would be suitable for high school students to investigate. The problem involves the properties of an array known as the odd triangle, which is made up of the odd counting numbers. (JN)

The Fibonacci sequence of Pascal's triangle is considered in pyramids and in the fourth and n dimensions. Four theorems are presented. (MNS)

Presents six mathematical problems (with answers) which focus on: (1) chess moves; (2) patterned numbers; (3) quadratics with rational roots; (4) number puzzles; (5) Euclidean geometry; and (6) Carrollian word puzzles. (JN)

Provides examples of proofs of the Pythagorean result. These proofs fall into three categories: using ratios, using dissection, and using other forms of transformation. Shows that polygons of equal area are equidecomposable and that the approach taken (via squares) is a new approach. (JN)

The study and use of "Venn diagrams" can lead to many interesting problems of a geometric, topological, or combinatorial character. The general nature of these diagrams is discussed and two new results are formulated. (JN)

Shows how to construct a cube using Origami techniques. Also shows how, by identifying analogous features, to construct an octahedron. (JN)

Presents a sequence of activities which serve to unravel the mystery of pi. In addition, the activities give meaning to circle relationships that formerly have been, at best, rotely learned. (JN)

Discusses the derivation of Pick's theorem. However, this derivation is beyond the grasp of most high school students. Therefore, a sequence of simple exploratory activities is provided which will enable students to discover and apply Pick's theorem for finding the area of a polygon whose vertices are lattice points. (JN)

Discussed for use with learning disabled children are the geometric materials and teaching methods developed by M. Montessori. (DB)