Every object we think of or encounter, whether a natural or human-made, has a regular or irregular shape. In its own intrinsic conceptual design, it has elements of mathematics, science, engineering, and arts, etc., which are part of the object's geometric shape, form and structure. Geometry is not only an important part of mathematics, but it is…

Examines how constraint-based 3D modeling can be used as a vehicle for rethinking instructional approaches to engineering design graphics. Focuses on moving from a mode of instruction based on the crafting by students and assessment by instructors of static 2D drawings and 3D models. Suggests that the new approach is better aligned with…

Curve stitching activities can be used to motivate calculus students. The problem described here involves showing that a given envelope of a curve is parabolic. (SD)

Preservice elementary teachers were given the task of showing a special case of the Pythagorean theorem by paper cutting. In the process they developed approximations to the square root of two. (SD)

These materials, used in a self-paced course in engineering descriptive geometry for freshman and sophomore college-level students, cover three modules: basic spatial relationships; intersections, parallelism, and perpendicularity; and graphic analysis and development. Each module contains five instructional units. Each unit includes a rationale,…

Computers can be programmed to produce increasingly complex line drawings. Through programming activities students can learn the geometric principles involved. (SD)

A description is given of a geometry unit for preservice elementary teachers in which professionalized subject matter is coupled with field-based teaching experiences. Details of an inservice course in measurement also are given. (DT)

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)

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)

Described is a way to illustrate cyclic and dihedral groups through symmetry using corporate logos and hubcaps. Examples of the different kinds of symmetry groups are explained in terms of Leonardo's Theorem. (KR)

Presented is a way of extending the list of rotation groups to include all finite subgroups of symmetries of the sphere, up to conjugation in its full group. Included is Klein's method for enumeration of the finite subgroups. (KR)

Presented is L'Hopital's rule for the evaluation of limits in the case when x goes to infinity using geometric concepts. Included are the rule, extensions, counterexamples, and a rule for sequences. (KR)

Discussed are the idea, examples, problems, and applications of convexity. Topics include historical examples, definitions, the John-Loewner ellipsoid, convex functions, polytopes, the algebraic operation of duality and addition, and topology of convex bodies. (KR)

Presented is a proof where special attention is accorded to rigor and detail in proving the lemma that relates ruler-and-compass constructions to arithmetical operations. The idea that some angles cannot be trisected by a ruler and compass is proved using three different cases. (KR)

Presented is an annotated list of 24 references on the LOGO programing language. The information provided is intended for classroom teachers and for researchers. Topics include use of the language in classroom situations, evaluation of a LOGO training program, the educational utility of LOGO, and others. (JN)