Three activities that involve space perception, the concept of geometric equivalence, and Euler's formula regarding regular polyhedra are described. (JT)

This activity is designed to help students recognize and extend rectangular patterns and to use patterning to formulate rules for "nth" cases. Three worksheets are included. (MNS)

Introduces students to nonperiodic tiling and allows them to construct their own sets of kites and darts through a series of explorations, conjectures, and discoveries. (ASK)

Some mathematical patterns are explored by visualizing and counting line segments, squares, cubes, and relationships between them. (JT)

Three theorems for Pythagorean triples are presented, with discussion of how students can amend their ideas about such numbers. (MNS)

Some activities are provided to help students develop a conceptual understanding of perimeter, area, and volume, as well as developing skills in spatial visualization and formulating generalizations. (MNS)

Deriving all Pythagorean triples from simple patterns within an addition table is presented, with formulas included. (MNS)

Number sequence patterns for counting boundaries of familiar figures are extended to higher dimensions. (JP)

Students, using the materials provided, can determine the number of diagonals, number of triangles formed by the diagonals, and degree measures of interior and exterior angles of regular polygons. The activity is designed to lead them to general formulae for polygons with n sides. (SD)

Mathematical proofs often leave students unconvinced or without understanding of what has been proved, because they provide no visual-geometric representation. Presented are geometric models for the finite geometric series when r is a whole number, and the infinite geometric series when r is the reciprocal of a whole number. (MNS)

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)

The author explores relationships among the lengths of sides of a triangle, one of whose angles measures 60 degrees. A computer program designed to search for special triangles is included. (SD)

Details of an investigation into polygonal numbers are given. From a study of the tabled series, patterns are discovered both within and between the various polygonal series. From a study of these results and the corresponding figures, formulas are developed. (LS)

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)