This column contains brief notes on graphing in three dimensions; patterns in Pascal's triangle; plotting graphs by computer; and an application of the hypocycloid. (MM)

Students use a series of isosceles right triangles constructed on a geoboard to discover patterns and form generalizations. (MP)

Pascal's triangle can be used as early as grades five and six to teach children to recognize mathematical patterns. Children can be guided to discover patterns or sequences of numbers if they begin with pictures or physical objects which they can manipulate and count. (Author/BB)

Worksheets and instructions are provided for a lesson on tessellations made with regular polygons. Patterns for equilateral triangles, squares, regular pentagons, and regular hexagons, each having sides one inch long, are included. (DT)

A discussion is given of the technique used to create repeating patterns with interlocking congruent figures using reflection, rotation, translation, and glide reflection. (MP)

Symmetry properties of wallpaper patterns are analyzed. (DT)

Some classroom discoveries are reported concerning artistic patterns related to Pascal's triangle that can be generated by the computer. (MP)

A learning activity relating modular arithmetic to patterns of figures determined by points equally spaced around a circle is described. (SD)

Beginning with a set of design cards and a rectangular grid, students can generate interesting and colorful designs using rotations, reflections, and translations. (SD)

While repairing a sleeping bag, the author observed that the quilt stitching was unicursal. This led to development of a classroom activity relating the stitching patterns of quilts to the highest common factor of the numbers of "bumps" in each direction. (SD)

Paper squares, each divided into eight congruent triangles, can be used in a variety of activities introducing ideas related to symmetry, pattern, and geometric transformations. (SD)