Continuing our critique of the classical derivation of the formula for the area of a disk, we focus on the limiting processes in geometry. Evidence suggests that intuitive approaches in arguing about infinity, when geometric configurations are involved, are inadequate, and could easily lead to erroneous conclusions. We expose weaknesses and…

Humans possess a remarkable ability to recognise both simple patterns such as shapes and handwriting and very complex patterns such as faces and landscapes. To investigate one small aspect of human pattern recognition, in this study participants position lines of "best fit" to two-dimensional scatter plots of data. The study investigates…

The present study investigated (a) whether the perceived cognitive load was different when geometry problems with various levels of configuration comprehension were solved and (b) whether eye movements in comprehending geometry problems showed sources of cognitive loads. In the first investigation, three characteristics of geometry configurations…

Initial exposure to algebraic thinking involves the critical leap from working with numbers to thinking with variables. The transition to thinking mathematically using variables has many layers, and for all students an abstraction that is clear in one setting may be opaque in another. Geometric counting and the resulting algebraic patterns provide…

This reprinted "Mathematics Teacher" article gives a brief history of the mathematics of Escher's art. (Contains 9 plates.)

Designs and arrangements of pentominoes are examined. (SD)

After stating that almost any topic could be generalized, the author was challenged to generalize the topic of polyominoes. His response is presented in this article. (SD)

Using the overhead projector, or overlays on an original pattern, a variety of tessellations can be generated. Several illustrations are included. (SD)

A unit on the peoperties of a kite can include many geometric concepts: symmetry, distance, relationships between diagonals, area, altitude, angles, and others. (SD)

Examples of CLOPAK Networks, an approach to covering the plane with symmetrically arranged, close-packed geometric shapes, are given. Implications for the place of networks in geometry instruction are discussed. (MN)

Artistic configurations can be built using a rectangular array of points and number concepts or principles. (SD)

This pamphlet introduces the student to the basic ideas and procedures of transformational geometry through a series of worksheets. After developing intuitively the idea of rigid motion, vector diagrams are introduced, and translations are discussed in some detail. (SD)

When primary children were interviewed to determine their perceptions of embedded triangles, they failed to observe overlapping triangles. Possible explanations for this and other response patterns are discussed, and implications for schooling are explored. (SD)

Students, using the materials provided, can determine the number of diagonals, number of triangles formed by the diagonals, and degree measures of interior and exterior angles of regular polygons. The activity is designed to lead them to general formulae for polygons with n sides. (SD)