The purpose of this study was to develop and establish the validity and reliability of an instrument to measure students' attitudes toward geometry. Participants consisted of 264 undergraduate students from two universities, one in the Midwest and one in the Southwest. The instrument is a 5-point Likert-scaled survey consisting of 32 statements…

This article tells the story of an elementary school principal, a former high school mathematics teacher, who uses the geoboard in her work with a group of fifth-grade students. As the investigation of polygons progresses from symmetry to area to perimeter, hands-on applications of advanced mathematics topics such as the Pythagorean theorem and…

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…

Paper-folding activities demonstrate properties of the conic sections and equilateral triangles. (SD)

This is part three of a three-part School Mathematics Study Group (SMSG) textbook. It contains eight chapters of supplements. Four of these are designed to be supplements to the specific chapters 2, 3, 7, and 10. The other four supplements cover the topics: Determinants; Flow Chart for Two Linear Equations in x and y; Graphs with Non-uniform…

The last 13 of 32 exercises of a course designed to give a wide range of skills in deductive, inductive, and indirect methods of proof in geometry are presented. (MP)

It is shown that, by taking as the basis unit vectors along the sides of an equilateral triangle, certain isometric transformations can easily be determined in matrix form. (MN)

The material examines areas generated by combinations of: (1) Circles and Triangles; (2) Closely Packed Circles; and (3) Overlapping Circles. The presentation looks at examples of certain areas and at logical ways to generate the necessary algebra to clarify the problems and solve general cases. Ideas for extension are provided. (MP)

People are noted as intrigued for centuries by interplay between algebra and geometry with many important advances viewed to have come down through some sort of linking of the two. Examples are given of advantages to learning and discovery that can be found in an investigative approach combining them. (Author/MP)

The lesson described combines mathematics, science, and literature, and is easily adaptable for use with classes in basic mathematics, geometry, analytic geometry, or calculus. (MP)

The author explores relationships among the lengths of sides of a triangle, one of whose angles measures 60 degrees. A computer program designed to search for special triangles is included. (SD)

Three worksheets are provided to help secondary students explore relationships among the areas of a variety of similar figures constructed on the sides of right triangles. The activity is extended to include the relationship among the lengths of the sides of the right triangle. Included are several student worksheets. (DC)