The representation of figures in mongean projection (double system planned orthographic projection used in the studies of Descriptive Geometry), specially when placed in a particular situation in relation to the projection plans, possesses the quality that, through them, the actual dimensions of represented spatial objects can be found directly…

The refraction problem, well-known in calculus and physics, continues to reveal new insights. This paper presents a geometric solution in which the trammel of Archimedes plays the prominent role. When properly configured, the trammel generates an ellipse and its family of normal lines. One normal line in particular intersects the boundary…

WebTOP is a three-dimensional, Web-based, interactive computer graphics system that helps instructors teach and students learn about waves and optics. Current subject areas include waves, geometrical optics, reflection and refraction, polarization, interference, diffraction, lasers, and scattering. Some of the topics covered are suited for…

Describes how to draw lines in centimeter units on a computer monitor with the Logo program. Presents four activities involving drawing geometric shapes. Provides a program to move a turtle slowly. (YP)

Explores the production of shadows for drawings using the LOGO computer language and Affine Geometry. Explains the methodology of the shadowing and lists the Affine Turtle procedures. Provides for different versions of LOGO. (MVL)

The production and application of images based on fractal geometry are described. Discussed are fractal language groups, fractal image coding, and fractal dialects. Implications for these applications of geometry to mathematics education are suggested. (CW)

Gives definitions of taxicab geometry and the MacDraw format for graphing. In the world of taxicab geometry, movement through the plane is along horizontal and vertical paths. Describes specific application to conic sections, including circle, ellipse, parabola, and hyperbola. Lists five references. (YP)

Describes some developmental changes in children's free creations with pattern blocks and demonstrates how to build on this natural interest to teach Logo programing. (PK)

Discusses the snowflake curve as a way to introduce the topic of sequences and series. Computer programs which produce graphic results are included. (PK)

Discusses the golden ratio and how to make golden triangles using recursive Logo programs. Presents some outputs of the Penrose tile patterns. (YP)

Describes experiences for engineering students to develop spatial awareness and reasoning capability. Describes geometric modeling, basic geometric concepts, operations, surface modeling, and conclusions. (YP)

Describes a sequence of activities for experimenting with scaling and includes a method for revising any turtle graphic procedure so that it can be drawn to a variety of scales. (PK)

Describes an activity intended to incorporate investigation into learning of mathematics. The example cited involved having fourth graders study perimeter and area of rectangles using Logo. The author suggests that what began as a simple exercise in investigating geometric concepts became an exciting exploration that touched on many topics. (PK)

Argues that Turtle Geometry has a great deal to offer mathematics teaching and learning. Suggests that it helps develop general problem-solving strategies and encourages new approaches to teaching and learning. (PK)