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

An algorithm for multiplying natural numbers is described. The algorithm provides a chance for some unusual drill and might serve as an enrichment topic. (MK)

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)

Possible ways of mechanization for counting using a binary system are discussed. Shows a binary representation of the numbers and geometric models having eight triples of lamps. Provides three problem sets. (YP)

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)

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)

A college course designed to teach students about the mathematics of symmetry using pieces of wallpaper and cloth designs is presented. Mathematical structures and the symmetry of graphic designs provide the starting point for instruction. (MP)

An approach to how to expand explorations of determinants is detailed that allows evaluation of the fourth order. The method is built from a close examination of the product terms found in the expansions of second- and third-order determinants. Students are provided with an experience in basic mathematical investigation. (MP)

Variations on a card trick are noted, with a formula for generalizing them. Another trick which can be proved with algebraic principles is then presented. (MNS)

Work with recurring decimals provides pupils with an opportunity for exploration and examination of a wide variety of mathematical ideas and strategies. Examples of work done by one group of pupils who were presented with an opportunity to explore such decimals is featured. (MP)

A procedure for constructing a magic cube is presented, with related teaching activities appropriate for students familiar or unfamiliar with the algorithm covered. (MP)

A modern adaptation of the historic lattice algorithm which can be used for multiplication and division is discussed. How it works is clearly illustrated. (MNS)

The trick focuses on a theorem that the sum of the digits of the difference between any natural number and the sum of its digits is divisible by nine. Two conditions of using the trick are noted. The reason that the theorem works is established through a proof. (MP)

An unusual way of using the long multiplication algorithm to solve problems is presented. It is conceptually harder, since it involves negative numbers but is easier to perform once mastered, since the size of the multiplication table required is smaller than the standard one. (MP)