Presents Heron's original geometric proof to his formula to calculate the area of a triangle. Attempts to improve on this proof by supplying a chain of reasoning that leads quickly from premises to the conclusion. (MDH)

This instructor's guide consists of materials for use in teaching a course in geometry designed for students enrolled in postsecondary vocational or technical education programs. Covered in the individual units of the guide are the following topics: basic terms, straight line combinations, angular conversion, circles, polygons, and geometric…

Illustrates various methods to determine the perimeter and area of triangles and polygons formed on the geoboard. Methods utilize algebraic techniques, trigonometry, geometric theorems, and analytic geometry to solve problems and connect a variety of mathematical concepts. (MDH)

Presents three teaching ideas: (1) investigating patterns in the sum of four numbers in a square array, no two from the same column or row; (2) using three-dimensional coordinates to generate models of three tetrahedra; and (3) applying the K=rs area formula for a triangle to other polygons. (MDH)

From the equality of the ratios of the surface areas and volumes of a sphere and its circumscribed cylinder, the exploration of theorems relating the ratios of surface areas and volumes of a sphere and other circumscribed solids in three dimensions, and analogous questions relating two-dimensional concepts of perimeter and area is recounted. (MDH)

This updated reprint of a classic work presents design analysis of geometric patterns and information helpful to constructing mathematical drawings of industrial and achitectural features. Both simple and complex designs are given. Problems combine both algebra and geometry. The work is divided into six chapters which are further divided into…

Results of operations on the Pythagorean formula are interpreted pictorially to yield interesting art forms. (MP)

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)

Geometric and algebraic solutions to problems involving reflections of balls on a pool table are presented. The question of whether the ball must eventually enter a pocket is explored. A determination of the number of reflections is discussed. (CW)

Discussed are two Euclidean constructions (synthetic approach and coordinate method) to inscribe regular polygons of 5 and 17 sides in a circle. Each step of the constructions is described using diagrams and mathematical expressions. (YP)

Four algebra problems and their solutions are presented to illustrate the use of a mathematical theorem. (CW)

Presents some examples from geometry: area of a circle; centroid of a sector; Buffon's needle problem; and expression for pi. Describes several roles of the trigonometric function in mathematics and applications, including Fourier analysis, spectral theory, approximation theory, and numerical analysis. (YP)

Explores many forms of a circle using variations of the distance formula. Metric space is defined and examples of metrics are given, including a "circle" that is a square. Also shown are variations which are not metrics. (MKR)

Utilized is the technique of expanding circles to explore the truth of the statement that, if the sums of the lengths of the opposite sides of a quadrilateral are equal, then a circle can be inscribed within that quadrilateral. This statement is the converse of a well-known geometric theorem. (JJK)

Presents a calculator-type computer program, CLICAL, in conjunction with complex number, vector, and other geometric algebra computations. Compares the CLICAL with other symbolic programs for algebra. (Author/YP)