This column solicits mistakes, fallacies, anomalies, et cetera, that raise interesting mathematical issues and may prove useful to teachers. Included in this issue are yet another proof that zero equals one and a differentiation that yields three equals two. (Author/JJK)

Decimal expansions of fractions are considered. Theorems and corollaries for some properties and for prime and composite denominators are presented. It is suggested that students write computer programs to deliver decimal expansions. (MNS)

Reviewed are short articles that contain new insights on topics taught in the early years of undergraduate mathematics. Included are the elementary theory of curves defined by the combination of polynomials, the differentiability of the sine function, and another proof of the irrationality of the square root of two. (Author/JJK)

Examples of diversions with cards that may be used to illustrate the concept of a cyclic group and structural properties of the integers modulo a prime are presented. (MNS)

Considered is the open-ended question of the various means of marking an n-inch ruler so that the distance of any integral number of inches from 1 to n can be ascertained with a single measurement. The relationship between a sparsely marked ruler, which is one gracefully marked with the fewest number of marks, and specific discrete graphs is…

Presents an example from the combinatorial theory of partially ordered sets. Discusses algorithms of on-line antichain partitioning problems, a topic in discrete optimization. (YP)

Clapping music for two performers provides the basis for a series of mathematical problems in combinatorics and group theory. A discussion provides insight about how to avoid overlooking global extrema in constrained max-min problems when solving systems of algebraic equations. (JJK)

To illustrate that the writing and utilizing of declarative language programs can be a straightforward task in a logic class, a logic system is defined and a truth-table generator and validator are implemented using PROLOG programing language. Also, using BASIC programing language, an example of a contour map is presented. (JJK)

The complexity of the proof of the Fundamental Theorem of Algebra makes it inaccessible to lower level students. Described are more understandable attempts of proving the theorem and a historical account of Euler's efforts that relates the progression of the mathematical process used and indicates some of the pitfalls encountered. (MDH)

Determines which chessboards contain a chromatic rectangle having all four corners the same color for any black-white coloring. Expands the problem to a three color problem. (YP)

Summing powers of integers is presented as an example of finite differences and antidifferences in discrete mathematics. The interrelation between these concepts and their analogues in differential calculus, the derivative and integral, is illustrated and can form the groundwork for students' understanding of differential and integral calculus.…

Solves the problem of defining a smooth piecewise linear approximation to a given function. Discusses some alternative approaches to the problem. (YP)

Describes an experiment to determine which of four objects, hollow cylinders, solid cylinders, hollow balls, and solid balls, will reach the bottom of an inclined plane first when released simultaneously. Provides solutions to the problem and supplementary exercises. (MDH)

Implements a table algorithm on a spreadsheet program and obtains functions for several number sequences such as the Fibonacci and Catalan numbers. Considers other applications of the table algorithm to integers represented in various number bases. (YP)

Shows step-by-step use of spreadsheets with an example from linear programing using the Simplex method. Describes pivot choosing and partial Gauss-Jordan elimination procedures. (YP)