Discussed are the idea, examples, problems, and applications of convexity. Topics include historical examples, definitions, the John-Loewner ellipsoid, convex functions, polytopes, the algebraic operation of duality and addition, and topology of convex bodies. (KR)

Presented is a game using different types of dominoes that represents growth of seeds from the beginning of the universe. Included are diagrams of the types of seeds, instructions, and examples of the game play. (KR)

Describes an activity to create squares by placing different numbers of tangram pieces together. Discusses why the combination of six tangram pieces can not create a square. Presents diagrams of the tangram pieces and the squares made. (YP)

Illustrated are three proofs of the Pythagorean theorem. Information for instruction is provided. (YP)

Discusses how various children's books can be used to introduce and explain geometric topics through a problem-solving approach. Selected are five books with words and five books without words. (YP)

Reviews three computer software packages: "Mystery Objects," a science inquiry series for grades one-four; "Physics," covering physics content for high school and introductory college level; and a tutorial program "Sensei Geometry." Required hardware, price, and addresses for each software package are listed. (YP)

Five geometry experiments with 127 Australian high school students found that guidance provided in a format requiring attention to two sources of information resulted in performance no better than that on conventional problems. A format not requiring split attention resulted in the superiority of worked examples over conventional problems. (SLD)

Illustrates some learning encounters for facilitating first graders' understanding of geometry. Describes some of children's approaches using Cuisenaire rods and teacher's intervening. Presents six problems involving various combinations of Cuisenaire rods and cubes. (YP)

Presented are three cases for intuitive understanding in secondary and college level geometry. Four ways to develop the intuition (physical experience, mutable manipulatives, visualization, and looking back) step are discussed. (YP)

Offers three practical tips for teaching of topics in the secondary school curriculum: (1) methods for identifying problem areas; (2) a device for teaching slopes; and (3) methods for teaching the property of collinearity in geometry. (YP)

Patterns and relationships are shown between the Pythagorean theorem, Fibonacci sequences, and the golden ratio. Historical references also include the works of Euclid and Euler. These unexpected relationships can be used to motivate secondary students. (DC)

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…