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,…

This is part two of a two-part manual for teachers using SMSG high school text materials. The manual contains a chapter-by-chapter commentary on the text, solutions to the problems in the text, and a collection of essays on topics related to material in the text. Chapter topics include: (1) perpendicular lines and planes in space; (2) parallel…

This discussion of the accomplishments of Buckminster Fuller describes the geodesic dome, the Dymaxion principle and its applications, and the Octet-Truss principle. (MP)

Presented is a sequence of ruler and compass constructions which are connected with the triangle. (SD)

A Reuleaux triangle is an example of a curve of constant width; the distance between parallel tangents is the same no matter which direction is used. A consideration of a particular set of Reuleaux triangles is offered which leads to a good example of problem-solving in geometry. (JN)

This article shows how simple instruments may be used to construct angles of certain measures and applies this procedure to more detailed problems. A proof of the Pythagorean Theorem is given using these procedures. (CT)

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