Presents interesting investigations and activities for inscribed and escribed circles of right-angled triangles. (ASK)

Previous work has identified four areas of difficulty that students seem to have with the topic of similarity: (1) understanding the definition of similarity; (2) proportional reasoning; (3) dimensional growth relationships; and (4) correspondences in right triangle similarity. This paper reports the results of an investigation into high school…

The concept of trigonometric ratios in a right triangle can be clearly presented through the use of interactive-geometry software. Investigation in this manner allows students to see the crucial features of the concepts before they are formalized and to gain ownership of these ideas through discovery. Many examples of the mathematical…

Examines secondary school students' ability to interpret representations of three-dimensional objects including prototypes of component, perspective drawings, orthogonal views, descriptions by coordinates, verbal descriptions, and verbal quasi-descriptions. Students were given four identical wooden cubes and asked to construct the objects. Reports…

This instructor's guide consists of materials for use in teaching a course in geometry designed for students enrolled in postsecondary vocational or technical education programs. Covered in the individual units of the guide are the following topics: basic terms, straight line combinations, angular conversion, circles, polygons, and geometric…

Provides an activity to develop students' (grade 5 through 10) spatial understanding and problem solving ability. Describes materials, prerequisites, directions, extensions, and technology using Geometric Supposer software. Presents worksheets and answers. Four references are listed. (YP)

This book examines everything having to do with the triangle. It begins with a basic definition of the triangle and continues with discussions on tetrahedrons, triangular prisms, and pyramid shapes. Some ideas addressed include how triangles are used to measure heights and distances, the importance of triangles to builders, Alexander Graham Bell's…

Gives definitions of taxicab geometry and the MacDraw format for graphing. In the world of taxicab geometry, movement through the plane is along horizontal and vertical paths. Describes specific application to conic sections, including circle, ellipse, parabola, and hyperbola. Lists five references. (YP)

This updated reprint of a classic work presents design analysis of geometric patterns and information helpful to constructing mathematical drawings of industrial and achitectural features. Both simple and complex designs are given. Problems combine both algebra and geometry. The work is divided into six chapters which are further divided into…

This book contains a set of versatile enrichment exercises that cover a very broad range of mathematical topics and applications in geometry including Euclidean, post-Euclidean, and non-Euclidean geometry. Several criteria have been used in developing the activities and selecting the topics that are included. All of them bear heavily and equally…

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)

Considers the problem of how to go from three coordinates to two. States that it is not a problem that mathematics students ordinarily encounter. Presents four methods of graphing three-dimensional figures on a two-dimensional computer screen. (PK)

Presented is an informal technique for counting the number of different-sized equilateral triangles on an isometric grid. Five activities that relate to this topic are included. (KR)

Reports evidence of construction and coordination of units in a measurement setting using data gathered from four students during individual problem-solving sessions near the end of their fourth-grade year. Proposes the task of measuring two-dimensional regions becomes possible when a student can construct two-dimensional units and coordinate…

Presents a unit to review geometric concepts and problem solving by having students work cooperatively to discover geometric shapes constructed from two congruent right triangles obtained from cutting a rectangle along its diagonal. Students report their findings both orally and in writing. (MDH)