The author re-enacted the "Meno's" discussion between Plato and the slave about doubling the size of the square, and found that a six-year-old's answers paralleled those of the slave; neither had formal knowledge of geometry. Plato stated that learning is recollection of knowledge held before birth. (CHK)

Discusses some theorems and properties of figures produced when circles are tangent to one another. (GA)

The first of three articles showing how inductively-obtained results in transformation geometry may be organized into a deductive system. This article discusses two approaches to enlargement (dilatation), one using coordinates and the other using synthetic methods. (MM)

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

Describes three activities in discrete mathematics that involve coloring geometric objects: counting colored regions of overlapping simple closed curves, counting colored triangulations of polygons, and determining the number of colors required to paint the plane so that no two points one inch apart are the same color. (MKR)

Includes lesson plans and worksheets that deal with transformational geometry, specifically reflections. The lesson for grades three to four focuses on angles of incidence and reflection and that for grades five to six involves mirror images. (MKR)

Investigates the idea of the center of mass of a polygon and illustrates centroids of polygons. Connects physics, mathematics, and technology to produces results that serve to generalize the notion of centroid to polygons other than triangles. (KHR)

Presents an activity in which students use geometric figures, rep-tiles, to design a tile floor. Rep-tiles are geometric figures of which copies can fit together to form a larger similar figure. Includes reproducible student worksheet. (MKR)

Presents a framework for differentiating between five levels of extension of knowledge: basic features, forms, rules, application, and elaboration. Comparison of the extent of knowledge use exhibited by (n=14) Year-11 Australian students on a range of plane geometry problems found that high-achieving students exhibited greater extension of…

This Missouri Vocational Instruction Management System instructor's drafting guide has been keyed to the drafting competency profile developed by state industry and education professionals. The guide contains a cross-reference table of instructional materials. Three units cover related views and descriptive geometry: (1) auxiliary views and…

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 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)