The Poincare group, the group of transformations of the plane which preserve the Minkowski distance between points, is derived as compositions of suitably defined reflections in straight lines. It is shown that any such transformations must be one of four types. (Author/JN)

The effect of testing format on achievement was investigated. Statistical analysis indicated no significant differences between any of the four formats used. (MK)

As a part of the investigation into children's understanding of mathematics undertaken by the Concepts in Secondary Mathematics and Science (CSMS) project, students in English secondary schools were given a class test on transformation geometry. This is a discussion of the results of the third-year sample, who were about 14 years old. (Author/MK)

A method is presented for determining cube roots on a calculator with square root facility that has a rapid rate of convergence. (MP)

The intention of this investigation was to diagnose the retention of some basic skills in some topics in algebra and geometry and to reveal difficult steps in the learning processes in these topics. (MP)

A discussion is given of the technique used to create repeating patterns with interlocking congruent figures using reflection, rotation, translation, and glide reflection. (MP)

A method for solving certain types of problems is illustrated by problems related to Fibonacci's triangle. The method involves pattern recognition, generalizing, algebraic manipulation, and mathematical induction. (MP)

Described is an experiment that allows students to determine the distance to the moon by triangulation. Included is a description of parallax methods and photographic techniques. (CS)

After students learn that it is impossible to trisect an angle using compass and straight-edge, students are introduced to the trisectrix curve which accomplishes the trisection. (SD)

Discusses some aspects of the defining process in geometrical context in the reference frame of the theory of "figural concepts." Presents analysis of some examples taken from a teaching experiment at the sixth-grade level. Contains 30 references. (Author/ASK)

Defines and discusses anamorphic art and describes an anamorphic art activity using the reflection of mirrored cylinders through a grid system. Particularly suitable for algebra or geometry classes. Requires some minimal skills from coordinate geometry and spatial visualization. (AIM)

Describes an activity, designed to comply with the National Science Education Standards, that integrates science and mathematics concepts. Mathematical modeling of the moon's phases is employed to show students the role of mathematics in describing scientific phenomena. (DKM)

Presents the classroom activity of finding a Hamiltonian circuit that helps students understand the properties of geometric shapes and symmetry. (ASK)

Describes the solution to a geometric problem by two ninth-grade mathematicians using The Geometer's Sketchpad computer software program. The problem was to divide any line segment into a regular partition of any number of parts, a variation on a problem by Euclid. The solution yielded two constructions, one a GLaD construction and the other using…

Describes a lesson that uses the graphing calculator to prompt the proof of the mean-value theorem. Students, through guided questioning, proposed the idea of using a difference function to find where a tangent line is parallel to a secant line. Through the use of graphing technology, students conjectured the essential fact that the constructed…