Examines the cause of confusion arising from ambiguity of units and semantics in length, area, and volume concept formation. Introduces the mimik, a standard area of one thousand square millimeters, and advocates its use as an interim symbol system. (JM)

Provides examples of proofs of the Pythagorean result. These proofs fall into three categories: using ratios, using dissection, and using other forms of transformation. Shows that polygons of equal area are equidecomposable and that the approach taken (via squares) is a new approach. (JN)

This article discusses two of the reasons for the decline of formal Euclidean geometry in recent syllabi: (1) Traditional approach; and (2) Inherent difficulties. Suggested are some reasons and examples as to why the decline should be reversed. (YP)

Compared is the use of Euclidean and synthetic geometry in American and European schools. Included is the history of the major developments in the teaching of geometry. Discussed is the demise of formal geometry since World War II. (KR)

As a part of the investigation into children's understanding of mathematics undertaken by the Concepts in Secondary Mathematics and Science (CSMS) project, students in English secondary schools were given a class test on transformation geometry. This is a discussion of the results of the third-year sample, who were about 14 years old. (Author/MK)

Includes patterns for and a brief discussion of the polyhedra: octahedron, tetrahedron, dodecahedron, cuboid, prism, and star. (PK)

Describes an enrichment activity based on the problem "Given a 2x2 square, and three colors, how many different ways can we shade the square?" (PK)

Examines the study of transformations which result from cross-sections of a prism. The study involves some model-making, which in turn introduces some new problems of drawing and construction. The material is presented with the practicalities of classroom teaching in mind. (Author/JN)

Analyzes fifth graders' approaches for solving the problem of the distance to the horizon. Describes determining the area bounded by the horizon. (YP)

Illustrates how to draw a regular pentagon. Shows the sequence of a succession of regular pentagons formed by extending the sides. Calculates the general formula of the Lucas and Fibonacci sequences. Presents a regular icosahedron as an example of the golden ratio. (YP)

A general historical background for the development of some common formulas concerning length, area, and volume is given through a discussion of various written records. (MN)

Sets forth the history of the Fibonacci Sequence and details its occurrence in nature and its potential for project work in schools. Ideas and activities include the rabbit problem, investigations of the sequence itself, its relationship to plants, music, snail shells, and the golden section. Computer generation of spirals is also discussed. (PK)

Provides two examples of the "regular falsi" method using geometry and a computer program. (YP)

Explores the close relationship between pattern formation and traditional geometry using the LOGO programing language with the specific example of joining squares, corner to corner, to form a closed ring. Includes the LOGO programs utilized, as well as color illustrations of the interesting and eye-catching patterns generated. (JJK)