There has been a lot of material written about logarithmic spirals of golden proportion but this author states that he has never come across an article that states the exact equation of the spiral which ultimately spirals tangentially to the sides of the rectangles. In this article, the author intends to develop such an equation. (Contains 5…

This article describes how research on children's geometric thinking was used in conjunction with the picture book "The Greedy Triangle" to gain valuable insights into children's prior geometric knowledge of polygons. Exercises focused on the names, visual appearance, and properties of polygons, as well as real-world connections for each, are…

Each ellipse and hyperbola has a circle associated with it called the director circle. In this article, the author derives the equations of the circle for the ellipse and hyperbola through a different approach. Then the author concentrates on the director circle of the central conic given by the general quadratic equation. The content of this…

Three- to six-year-old children (n=28) and adults (n=46) participated in a two-dimensional search task that included geometry and feature conditions. During each of 24 trials, participants watched as a cartoon character hid behind one of three landmarks arranged in a triangle on a computer screen. The landmarks and character then disappeared and…

The incenter, orthocenter, and centroid of a triangle are discussed in a sequence which students knowing ratio and proportion can understand. (SD)

This is one in a series of SMSG supplementary and enrichment pamphlets for high school students. This series is designed to make material for the study of topics of special interest to students readily accessible in classroom quantity. Topics covered include graphs, slope, distance, mid-point, proof, equations, and circles. (MP)

This is part three of a three-part manual for teachers using SMSG junior high school text materials. Each chapter contains an introduction and a collection of sample test questions. Each section contains a discussion related to the topic at hand and answers to all the exercises. Chapter topics include: (1) non-metric geometry; (2) volumes and…

Construction of colorful braided polyhedra can provide upper elementary students with enjoyable geometric experiences. (SD)

A method of bisecting an angle by construction of an isosceles triangle and its axis of symmetry is described. (SD)

The third session of IT@EDU98 consisted of five papers on educational software and was chaired by Tran Van Hao (University of Education, Ho Chi Minh City, Vietnam). "Courseware Engineering" (Nguyen Thanh Son, Ngo Ngoc Bao Tran, Quan Thanh Tho, Nguyen Hong Lam) briefly describes the use of courseware. "Machine Discovery Theorems in Geometry: A…

This column contains brief notes on graphing in three dimensions; patterns in Pascal's triangle; plotting graphs by computer; and an application of the hypocycloid. (MM)

Presents a reexamination of an intuitively geometric view of the nonrelativistic Pauli spinor in a simplified discussion of the connection between the rotation group and special transformations in the plane of projection. This view of the spinor is related to those based on the existence of an istropic or null vector. (SK)

Children's perception and understanding of three-dimensional figures and of operations on them is discussed. Piaget's findings are reviewed and more current research is described. Classroom implications are explored. (SD)

The concept of trigonometric ratios in a right triangle can be clearly presented through the use of interactive-geometry software. Investigation in this manner allows students to see the crucial features of the concepts before they are formalized and to gain ownership of these ideas through discovery. Many examples of the mathematical…