MATERIALS ARE INTENDED FOR A UNIFIED AND ACCELERATED PLANE AND SOLID GEOMETRY COURSE AND FOR EASY MODIFICATION AND ADAPTATION BY EXPERIENCED OR INEXPERIENCED TEACHER. TEXTBOOKS TO WHICH THE GUIDE HAS BEEN KEYED ARE LISTED. UNITS ARE GIVEN FOR BOTH SEMESTERS WITH TIME ALLOTMENTS RECOMMENDED. EACH UNIT IS SUBDIVIDED INTO TOPICS AND OBJECTIVES,…

This article presents some easily stated but unsolved geometric problems. The three sections are entitled: Housemoving, Manholes and Fermi Surfaces" (convex figures of constant width), Angels, Pollen Grains and Misanthropes" (packing problems), and The Four-Color Conjecture and Organic Chemistry." (MM)

The derivation of a formula relating areas of triangles formed by cutting the corner of a cube is given. (MK)

A UNIFIED TWO-SEMESTER COURSE IN PLANE AND SOLID GEOMETRY FOR THE GIFTED IS PRESENTED IN 15 UNITS, EACH SPECIFYING THE NUMBER OF INSTRUCTIONAL SESSIONS REQUIRED. UNITS ARE SUBDIVIDED BY THE TOPIC AND ITS CONCEPTS, VOCABULARY, SYMBOLISM, REFERENCES (TO SEVEN TEXTBOOKS LISTED IN THE GUIDE), AND SUGGESTIONS. THE APPENDIX CONTAINS A FALLACIOUS PROOF,…

The basic ideas of the theory of manifolds is illustrated using elementary geometry. (MM)

A method is given for the analysis of geodesic domes involving plane geometry. The method shows how to calculate all necessary angles and chords, given the length of one side. (MP)

A question posed by Euler is considered: How can polyhedra be classified so that the results is in some way analogous to the simple classification of polygons according to the number of their sides? (MK)

PRESENTED IS A FUSED COURSE IN PLANE, SOLID, AND COORDINATE GEOMETRY. ELEMENTARY SET THEORY, LOGIC, AND THE PRINCIPLE OF SEPARATION PROVIDE UNIFYING THREADS THROUGHOUT THE TEXT. THE TWO CURRICULUM GUIDES HAVE BEEN PREPARED FOR USE WITH TWO DIFFERENT TEXTS. EITHER CURRICULUM GUIDE MAY BE USED DEPENDING UPON THE CHOICE OF THE TEACHER AND THE NEEDS…

This is the teacher's edition of a text for the first year of a two-year high school geometry course. The course bases plane and solid geometry and trigonometry on the fact that the translations of a Euclidean space constitute a vector space which has an inner product. Volume 1 deals largely with affine geometry, and the notion of dimension is…

This is the teacher's edition of a text for the second year of a two-year high school geometry course. The course bases plane and solid geometry and trigonometry on the fact that the translations of a Euclidean space constitute a vector space which has an inner product. Congruence is a geometric topic reserved for Volume 2. Volume 2 opens with an…

One of a series of pre-apprenticeship phase 1 training modules dealing with math skills, this self-paced student module covers computation of areas of plane figures and volumes of solid figures. Included in the module are the following: cover sheet listing module title, goals, and performance indicators; introduction; study guide/check list with…

This module, designed to help students find and identify various geometric shapes and solids, contains 26 worksheets. Topics covered by these worksheets include: identification and grouping of objects with particular patterns, work with pentagons, hexagons, spirals, and symmetry. Teaching suggestions are included. (MK)

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…

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…