The theorems and proofs presented are designed to enhance student understanding of the theory of infinity as developed by Cantor and others. Three transfinite numbers are defined to express the cardinality of infinite algebraic sets, infinite sets of geometric points and infinite sets of functions. (DC)

Presents two proofs that only five regular polyhedra exist. The first is a geometric proof, and the second is based on graph theory, using the relationship between the vertices, edges, and regions of the graph model. (MDH)

Discusses the use of middle-school students' natural understanding of large numbers to introduce the concept of infinity. Presents activities that investigate infinite sets by demonstrating a one-to-one correspondence between the counting numbers and the given set. Examples include prime numbers, Fibonacci numbers, fractions, even and odd numbers,…

Explores the history of geometry at the secondary level and discusses criticisms, suggested revisions, and reasons for the lack of evolution in secondary geometry. Recommends that teachers develop a broader knowledge of geometry, use supplements to the textbook, advocate changes in textbooks and tests, utilize coordinate geometry, and rethink the…

Applies Pascal's Triangle to determine the number of ways in which a given team can win a playoff series of differing lengths. Presents the solutions for one-, three-, five-, seven-, and nine-game series, and extends the solution to the general case for any series. (MDH)

Presents the geometric, software-ergonomic, and educative standards for interactive graphics systems envisioned for planimetric constructions and calculations in secondary mathematics instruction. Describes the geometric-didactic potentials of the MS DOS-Version 1.6 of CABRI-Gomtre which is an Intelligent Tutoring System with the possibilities for…

Describes a transformational geometry project in which groups of students explore symmetry, reflections, translations, rotations, and dilations to design and create one hole of miniature golf large enough to play on. Includes unit plan for transformational geometry. (MKR)

Discussed are several different transformations based on the generation of fractals including self-similar designs, the chaos game, the koch curve, and the Sierpinski Triangle. Three computer programs which illustrate these concepts are provided. (CW)

Presented is a proof where special attention is accorded to rigor and detail in proving the lemma that relates ruler-and-compass constructions to arithmetical operations. The idea that some angles cannot be trisected by a ruler and compass is proved using three different cases. (KR)

Provided is a set of six activities demonstrating how mathematical connections can be made using the concept of rectangle. The activities relating rectangle to factoring whole numbers, prime numbers, and calculating the area of rectangles, triangles, parallelograms, and circles, are also connected to each other. (MDH)

Presents a model that relates Polya's ideas on problem solving to teaching practices that help create a mathematics learning environment in which students are actively involved in doing mathematics. Illustrates the model utilizing a high school geometry problem that asks students to measure the width of a river. (MDH)

Ritzville Pyramids are cone-shaped piles of wheat found near the community of Ritzville, Washington. Presents the practical problem of determining the volume and surface area of a Ritzville pyramid to help farmers solve cost-effectiveness questions related to selling the wheat. (MDH)

Provided are the activity sheets for students and the teaching guide for this middle school geometry activity. Materials, prerequisites, objectives, and procedures are listed. Extension activities are suggested. An answer key is included. (CW)

Discusses the use of mathematics in the works of German artist Albrecht Durer, including the Mathematical Renaissance, Durer the geometer, mathematical drawing instruments, perspective drawing, and polyhedrons and magic squares. (Contains 14 references.) (MKR)

Argues that teachers and lecturers need to identify essential skills which are technology-independent and need to determine the most effective use of new technology in the classroom. Examines prospects for change using the newer technology of graphing calculators for mathematics courses. Contains 15 references. (ASK)