This article examines the Pythagorean Theorem from a geometric point of view by suggesting some natural extensions of the theorem. The use of a more general theorem to prove a difficult one is suggested, where possible. The article includes figures and proofs. (Author/MA)

Geometric interpretations and derivations of the six trigonometric relationships are demonstrated. Selected for discussion are limiting values, geometric verification of trigonometric identities, a one-dimensional illustration of the Pythagorean relationships, and the geometric derivation of infinite-series relationships. (DE)

Finding the shortest route between two points can be approached by vector methods. Several types of matrices modelling a map of 6 cities are described. (SD)

Presents an activity that utilizes the mathematical models of forest fires and oil spills that were generated (in the first part of this activity, published in the November 1998 issue) by students using probability and cellular automata. (ASK)

Activities in which students make and prove conjectures and devise their own geometric axiom systems are discussed. (SD)

This article provides a manipulative demonstration of the relationship between the squares on the sides of a right triangle. Materials are listed and directions are given for the student. Illustrations are included. (Author/MA)

Directions are given for making a model of a three-dimensional coordinate graph. (DT)

The problem of finding all topological spaces is considered. Two characterizations are presented whose proofs involve only elementary notions and techniques. The problem is appropriate for students in a beginning topology course after they have been presented with the Embedding Lemma. (DC)

Geometric concepts and theorems can be discovered by high school students using the materials described. Among the topics explored are Platonic solids and Euler's formula. (SD)

Shows that the experiment of the ancient Greek mathematician and geographer, Eratosthenes, can be replicated and used to teach geographic concepts. Eratosthenes calculated the most accurate ancient measurement of earth based on fundamental mathematics concepts and earth-sun relations. Includes instructions, illustrations, graphs, and historical…

An activity designed as an introduction to High School geometry empowering students to see relationships and make geometric connections. A list of student generated relationships based on student constructed and manipulated diagrams is included. Discussion guidelines are suggested. (DE)

Discussed are various models proposed for the Moebius strip. Included are a discussion of a smooth flat model and two smooth flat algebraic models, some results concerning the shortest Moebius strip, the Moebius strip of least elastic energy, and some observations on real-world Moebius strips. (KR)

Uses manipulative materials to build and examine geometric models that simulate the self-similarity properties of fractals. Examples are discussed in two dimensions, three dimensions, and the fractal dimension. Discusses how models can be misleading. (Contains 10 references.) (MDH)

An introductory preservice teacher activity from a typical college geometry course is presented. This activity leads the preservice teachers to specific goals, including increased geometric awareness within the everyday environment, appreciation for mathematical modeling techniques, and awareness of methods for teaching geometric concepts to…

Proof-writing is probably one of the most difficult skills for students to master in geometry. This may be due to the fact that students are not being taught the critical thinking skills necessary for proof-writing. The purpose of this paper is to illustrate how the ReQuest method can be used in the geometry classroom to improve students' question…