A method of using vector analysis is presented that is an application of calculus that helps to find the best angle for tacking a boat into the wind. While the discussion is theoretical, it is seen as a good illustration of mathematical investigation of a given situation. (MP)

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

A problem in applied mathematics is presented that is thought fit for a study project by secondary students. The analysis includes topics in beginning algebra, theory of interest, and theory of sums of series of infinite length and looks at trade-offs between price and mileage. (MP)

Several sample problems from the "Ladies Diary," published in the early 1700s, are reviewed. They provide a fascinating glimpse of the mathematics considered useful in the eighteenth and early nineteenth centuries. (MP)

The application of the Hamilton method for apportioning seats in the United States House of Representatives is presented based on the 1980 census. It is felt that this method is preferable to the equal proportion method currently used if for no other reason than the greater appearance of fairness. (MP)

A possible logical flaw based on similar triangles is discussed with the Sherlock Holmes mystery, "The Muskgrave Ritual." The possible flaw has to do with the need for two trees to have equal growth rates over a 250-year period in order for the solution presented to work. (MP)

Two kinds of secret writing, codes and ciphers, are discussed. The weakness of a ciphering system mentioned in the March 1981 issue is pointed out, and an alternate method is presented. Programs written in BASIC are presented which can be used to encipher messages and help break ciphers. (MP)

A discussion of the mathematics of rugby is related to an earlier article about mathematics and the physical world. (MP)

A Norman window consists of a semi-circular section mounted surmounting a rectangular section. Modifications to a simple problem are presented that assume parts of the window are made with stained glass. The goal is to maximize the level of light transmission with a fixed perimeter. (MP)

The game of Yahtzee is analyzed to some extent through methods of elementary probability. Several different problems are posed, and these serve to illustrate both mathematical concerns and game play strategy. Solutions are provided to all questions at the conclusion and suggestions for further questions are presented. (MP)

A brief introduction to the broad field of curve-fitting is provided to help explain the reasoning behind least-squares data fitting, and also to provide useful equations for two functional forms of interest in chemistry. Appendices give program examples written in Fortran and detail the method of Guggenheim. (MP)

A problem-posing approach is used to change a door problem that involves a linear hallway into one in which doors are in a circle. The new problem is noted to relate mathematically to concepts behind the spirograph. It is hoped the material will encourage teachers to use problem-posing. (MP)

The question is asked, "How many gifts in total were given in 'The Twelve Days of Christmas' song," and is shown to relate to several other problems. Most of the number patterns and partitions dealt with are viewed to be usable with students in junior and senior high school. (MP)

The beauty of discovering some simple yet elegant proof either to something new or to an already established fact is discussed. A combinatorial problem that deals with covering a checkerboard with dominoes is presented as a starting point for individual investigation of similar problems. (MP)