Examined are the roles of several historical figures in the development of the field of geometry. Discussed are Thales, Pythagoras, Plato, Euclid, and Apollonius. (CW)

Developed is a condition, expressed in terms of an index, that ensures that a quasinormal subgroup is normal. The arguments suggest a variety of exercises for a course in group theory or Galois theory. Included are the definitions, lemmas, and proofs. (KR)

Provided are 20 ideas for learning activities in mathematics suitable for individual independent use by gifted elementary and middle school students. Typical ideas include making models of various triangles, scale drawings, exploring prime numbers, and drawing graphs. (DB)

Presented are several applications of geometric concepts and measurement skills that are used daily by surveyors, real estate attorneys, and paralegal assistants. Described are the objectives and directions for this lesson. Activity sheets for students are included. (CW)

Several activities involving area and volume using empty paper rolls are presented. The relationships of parallelograms to cylinders are illustrated. Teaching suggestions are provided. (CW)

Discusses the use of flexible straws for teaching properties of figures and families of shapes. Describes a way to make various two- or three-dimensional geometric shapes. Lists eight advantages of the method. (YP)

The focus of this article is on the verification processes children use when assessing the equality of parts produced by them when partitioning geometric shapes. Different processes and children's verbal proofs of equality are presented. Activities for mathematics instruction are suggested. (YP)

Discussed is the benefit of the inclusion of historical material in a student's text. Several geometry problems are used as examples. A suggested list of problem sources is provided in the appendix. (YP)

Discusses the use of computer graphics in the teaching of geometry. Describes five types of geometry: Euclidean geometry, transformation geometry, coordinate geometry, three-dimensional geometry, and geometry of convex sets. (YP)

Describes the stages of a process of reflective thinking. Investigates how geometrical models can be used in learning and teaching mathematics in connection with the process. Identifies two models for children of age four to eight: constant path in the space of shapes and continuous path of varied polygonal shapes. (Author/YP)

Summarizes a reanalysis of the data from an investigation of a test designed to measure a learning sequence in geometry based on the work of van Hiele (1986). Discusses the test based on the Rasch model. (YP)

Provided are activities for creating tangrams. Illustrates how to make tangrams and use them. (YP)

Analyzes fifth graders' approaches for solving the problem of the distance to the horizon. Describes determining the area bounded by the horizon. (YP)

Illustrates how to draw a regular pentagon. Shows the sequence of a succession of regular pentagons formed by extending the sides. Calculates the general formula of the Lucas and Fibonacci sequences. Presents a regular icosahedron as an example of the golden ratio. (YP)

Presents 10 space-related ideas, thoughts, and questions represented on the Australian Association of Mathematics Teachers (AAMT) calendar. The ideas are on impossible shapes, fractals, space itself, galaxy, tesselated pigs, spirals, helices, black holes and three-dimensional surfaces, tesseracts, and mobius bands. (YP)