The problem of creating lamp shades to specific design parameters allows rich and interesting explorations in the mathematics of circles and triangles. This interactive project helps students build their spatial reasoning and is especially appropriate during a unit on either the Pythagorean theorem or similar triangles. (Contains 7 figures and 1…

Adam, an 11th grader, was identified as gifted and accepted into a two week summer enrichment program. He signed up for "Geometry with Flash Programming." He had no prior programming experience but had a strong and healthy self-image as mathematics student. Although Adam had a positive attitude toward mathematics and saw himself as a successful…

Whether they are third graders or teacher candidates, students can learn about perimeter and area while having fun manipulating two-dimensional figures into three-dimensional objects. In this article, the author describes a common mathematical activity for geometry students by creating nets for a cube. By making connections between nets in two…

The triangle congruence conditions are a central focus to nearly any course in Euclidean geometry. The author presents a hands-on activity that uses straws and pipe cleaners to explore and justify the triangle congruence conditions. (Contains 4 figures.)

Detailed instructions are given for the construction of the rhombic dodecahedron templates. A discussion of symmetries is included as background information. (MP)

This article provides an overview of vertex-edge graphs as an essential topic in the high school mathematics curriculum, including rationale, recommendations, and sample applications. A classroom-ready activity with full teacher notes is also included. (Contains 1 table and 9 figures.)

A mathematical derivation is given, developing the cardioid as an epicycloid locus. Curve-stitched designs are given for a family of epicycloids. (MP)

Geoff Giles died suddenly in 2005. He was a highly original thinker in the field of geometry teaching. As early as 1964, when teaching at Strathallen School in Perth, he was writing in "MT27" about constructing tessellations by modifying the sides of triangles and (irregular) quadrilaterals to produce what he called "trisides" and "quadrisides".…

Some practical, hands-on ways in which ideas about geodesic domes can be used in secondary school mathematics are described. Instructions for constructing a one-frequency geodesic sphere are given. (MP)

Worksheets and instructions are given for this activity whose objective is to develop the relationship between the lengths of the sides of a triangle and its classification by angle. (MP)

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

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)

Relationships among the sides are developed for right triangles whose sides are in the ratios 1:3, 1:4, and 1:5. The golden ratio appears in the results which can be used in secondary mathematics. (DC)

This article describes the use of digital images of real-life phenomena and interactive software to carry out mathematics investigations. (Contains 13 figures.)

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