Discusses a number of Theo van Doesburg's paintings concerning arithmetic composition. (KHR)

Explores trapezoidal numbers, which are the result of subtracting two triangular numbers. Includes classroom activities involving trapezoidal numbers to help students develop their problem-solving skills. Includes reproducible student worksheets. (MKR)

Describes features and uses of the Geometry Forum, a National Science Foundation funded Internet project which includes a set of electronic newsgroups for people interested in geometry. (MKR)

Discusses a method of graphing polar equations using information from the Cartesian graphs of trigonometric functions. (MKR)

Discusses area, perimeter, the Pythagorean Theorem, surface area, and volume with regard to the use or nonuse of units of linear measure. (MKR)

In the late 1950s Freudenthal published several articles on the history of geometry around 1900, in particular on Hilbert's innovative approach to the foundations of geometry. Discusses Freudenthal's contribution to our understanding of the development of geometry and his style in historical research. (Contains 17 references.) (Author/MDH)

Provides practical applications of elementary coordinate geometry while discussing how mathematics is used to assess the security of systems. (ASK)

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)

Examines the roles of experimental tasks in "Elementary Geometry" (1903) by Godfrey and Siddons, which is considered one of the most important geometry textbooks in the history of geometry teaching. Roles of experimental tasks included preparations for deductive geometry and, even though it is implicit, the verification of geometrical facts.…

Discusses the new Standards' vision for teaching geometry in the middle grades, specifically geometry connections in the middle grades across the Standards. Students learn geometry within an integrated mathematics program that prepares them to solve problems in school and in their personal lives. (ASK)

Spatial tests involving the comparison of diagrams of interlaced ropes or knots at varying orientations were given to (n=21) subjects, mostly English college undergraduates, to determine an ordering in terms of complexity of tasks involving the mental manipulation of the knots. Certain knot shapes were processed faster than others and greater…

Defines tessellations as closed geometric shapes that completely cover a surface without gaps or overlaps. Suggests how they can be used in technology class activities. (JOW)

Discusses some questions connected with Cauchy's theorem which states that two convex closed polyhedral surfaces whose corresponding faces are congruent and whose faces adjoin each other in the same way are congruent. Describes how to construct a flexible polyhedron. (ASK)

Examines why a flexible polyhedron must be convex. Discusses the theorems of Cauchy and Euler. (ASK)

Describes empirical research into the effectiveness of using concepts and principles of physics in the teaching of geometrical proofs. Demonstrates, tentatively, that proofs from physics could be a viable addition to the mathematics curriculum. (Author/MM)