A Reuleaux triangle is an example of a curve of constant width; the distance between parallel tangents is the same no matter which direction is used. A consideration of a particular set of Reuleaux triangles is offered which leads to a good example of problem-solving in geometry. (JN)

With a standard geoboard, five pegs by five pegs, how many different triangles can be formed using a single rubber band with the pegs serving as vertices? Discusses ways to solve this problem and offers related problems and some pedagogical considerations (particularly for the teaching of geometry and problem solving). (JN)

Describes the most enduring link between Napoleon and mathematics as the geometric result known as Napoleon's Theorem, which states that if equilateral triangles are drawn on the three sides of any triangle, the line segments joining the centers of these equilateral triangles will themselves form an equilateral triangle. (ASK)

Gives definitions of taxicab geometry and the MacDraw format for graphing. In the world of taxicab geometry, movement through the plane is along horizontal and vertical paths. Describes specific application to conic sections, including circle, ellipse, parabola, and hyperbola. Lists five references. (YP)

Focuses on improving geometry teaching by: (1) identifying the meaning of "transforming spatial operations into logical ones;" (2) embodying this meaning in several exemplary experiences; and (3) commenting and reflecting on the significance of the geometrical operations underlying the experiences. (JN)

Describes some general techniques for making collapsible models, including spiral models, for all the Platonic solids except the cube. Discusses the nature of the dissections of the faces necessary for the construction of the spiral cube. (ASK)

Advantages of representing ternary and quaternary composition diagrams by means of rectangular coordinates were pointed out in a previous paper (EJ 288 693). A further advantage of that approach is that analytic geometry, based on rectangular coordinates, is directly applicable as demonstrated by the examples presented. (JN)

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)

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)

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)

Illustrated is the use of isometric graph paper in the discovery of nonstandard area formulas. The use of definitions, geometric construction, record keeping, and conjectures about triangles, rhombuses, hexagons, parallelograms, isosceles trapezoids, rectangles, and trapezoids are described. (YP)

Presented is a four-part program for teaching geometric concepts related to the shape of a football. The program includes activities in which students examine footballs, construct a football using isometric paper, examine the "football" versus a regular icosahedron, and investigate planes of geometry. (JN)

The process of investigating some of the properties of diagonals and other geometric concepts with a group of 11-year-old girls is presented. Possible changes that could have been made in the lesson are discussed, and examples of individual student work are provided. (MP)