A history of perfect numbers is presented, which briefly covers the 27 values known at this time. (MP)

There are many uses for the shortest path algorithm presented which are limited only by our ability to recognize when a problem may be converted into the shortest path in a graph representation. (Author/TG)

The evolution of Archimedes' method is traced from its geometrical beginning as a means to approximate pi to its modern version as an analytical technique for evaluating inverse circular and hyperbolic functions. It is felt the web of old and new algorithms provides considerable instructional material, and ideas are offered. (MP)

Problems with apportioning seats within the House of Representatives every 10 years are discussed. The history of the problem and the nature of the politics involved are reviewed, and the current method in use is detailed along with its flaws. A call for a more sensible system is made. (MP)

An approach to using the method of least squares, a scheme for computing the best-fitting line directly from a set of points, is detailed. The material first looks at fitting a numerical value to a set of numbers. This provides tools for solving the line-fitting problem. (MP)

The problem of finding cube roots when limited to a calculator with only square root capability is discussed. An algorithm is demonstrated and explained which should always produce a good approximation within a few iterations. (MP)

Several subtraction algorithms are analyzed to see if they involve borrowing. The main focus is on an analysis of a procedure called the residue method. The operational arithmetic which underlies the symbolic manipulations is examined and conditions where the method does and does not use borrowing are highlighted. (MP)

Describes a pattern which emerged from an examination of the digits of the squares of numbers. Provides eight examples having the pattern at the units or tens digit of the number. (YP)

Two worksheets are given, outlining algorithms to help students determine the day of the week an event will occur and to find the date for Easter. The activity provides computational practice. A computer program for determining Easter is also included. (MNS)

The game of Yahtzee is discussed in terms of the various outcomes of turns in the game and their point values and the probabilities associated with achieving specific combinations of dice values. Several tables and methods of table construction are noted, and several challenge exercises are included. (MP)

Details are given of a simple computer program written in BASIC which calculates the sine of an angle through an application of DeMoivre's Theorem. The program is included in the material, and the program's success is discussed in terms of why the approximation works. (MP)

Five problems on the generation and study of prime and related numbers are discussed. Solutions to the problems posed will be in next month's presentation. (MP)

This is the second unit of a 15-unit School Mathematics Study Group (SMSG) mathematics text for high school students. Topics presented in the first chapter (Informal Algorithms and Flow Charts) include: changing a flat tire; algorithms, flow charts, and computers; assignment and variables; input and output; using a variable as a counter; decisions…

Three alternative methods of finding averages of two numbers are presented. (MP)

Examples of student-developed methods for dividing fractions and dividing and multiplying whole numbers are presented. Both are selected to show mathematical creativity in general mathematics students which would often be overlooked. (MP)