The author has written an unpublished summary of his reactions to an earlier article on number patterns used to provoke mathematical investigations. His work is an additional demonstration of the potential mathematics that can be stimulated from such investigations. (JP)

Describes several activities to provide opportunity for the discovery of number patterns and shows the need for care in the descriptions of such patterns. (Author)

The problem of determining the number of squares on a checkerboard is extended to finding the number of rectangles on an n x n board and finding the total numbers of cubes and rectangular solids in an n x n x n cube. (DT)

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

A discussion of some number patterns which arose from a consideration of the number of diagonals of a general polygon. (MM)

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)

Topics discussed in this column include patterns of inverse multipliers in modular arithmetic; diagrams for product sets, set intersection, and set union; function notation; patterns in the number of partitions of positive integers; and tessellations. (DT)

Patterns generated by the set of natural or counting numbers are discussed. Included are quartic, odd, square, and triangular numbers. (MK)

What often catches student interest and provides needed motivation for learning is the remarkable patterns and unexpected, interesting ideas that fill mathematics. It is felt mathematics should be taught as an enchanting and multifaceted art as well as a tool and a science. (MP)