Offers an excerpt from a paper written by Nicolay Lobachevsky (1792-1856) on the topic of the then new non-Euclidean geometry in tribute to this scientist as his 200th birthday approaches. Lobachevsky discusses his ideas about parallel lines in the context of his new geometry. (MDH)

Designs and arrangements of pentominoes are examined. (SD)

A series of problems concerning a geoboard with "holes" is suggested. (SD)

In a series of activities involving map coloring, students can discover various combinatorial theorems including Euler's formula. (SD)

Provided is an analysis, using concepts from geometry, algebra, and trigonometry, to explain the apparent loss of area in the rug-cutting puzzle. (MNS)

The Peelle triangle is an organized presentation of information about points, segments, squares, and cubes. Developing the tables is discussed, with a proof. (MNS)

Explores the subject of fractal geometry focusing on the occurrence of fractal-like shapes in the natural world. Topics include iterated functions, chaos theory, the Lorenz attractor, logistic maps, the Mandelbrot set, and mini-Mandelbrot sets. Provides appropriate computer algorithms, as well as further sources of information. (JJK)

Focuses on the fascinating topic of soap films to allow students to use practical methods during their investigations into the underlying mathematics of soap film geometry. Provides directions and illustrations for the investigative mechanisms, as well as describing the mathematical equations involved. (JJK)

Fractal geometry is introduced through examples of computational exploration of coastlines, self-similar curves, random walks, and population growth. These explorations, which include the construction of algorithms and the subsequent development and application of simple computer programs, lend themselves to self-directed study and advanced…

Lines in the coordinatized plane which do not go through the origin can be designated by the ordered pair of intercepts. The enrichment unit described illustrates duality in mathematics. (SD)

This material shows how to use basic techniques, principles of counting, and geometry to count squares on geoboards. The methods are elementary in that the proofs are easily conceptualized. A discussion of other approaches illustrates that easily stated problems may lead to very difficult and sophisticated methods. (MP)

A possible logical flaw based on similar triangles is discussed with the Sherlock Holmes mystery, "The Muskgrave Ritual." The possible flaw has to do with the need for two trees to have equal growth rates over a 250-year period in order for the solution presented to work. (MP)

A complete characterization of minimum conditions for congruence of quadrilaterals is presented. Convex quadrilaterals are treated first, then concave quadrilaterals are considered. A study of such minimum conditions is seen to provide some interesting and important activities for students. Only background in triangle congruence is necessary. (MP)

This module, designed for use at the high school level as a four- to eight-hour topic, includes: the geometry of a sphere, the coordinate system used to describe points on the earth's surface, parallel and meridian sailing, and the solution of right spherical triangles. (Author/MK)

Some mathematical patterns are explored by visualizing and counting line segments, squares, cubes, and relationships between them. (JT)