In this article we set up a mathematical model to represent the effects of the forces which operate during the rowing of racing shells. The analysis is conducted in terms of eights, but could apply equally well to fours, pairs and double or quad sculls, and even (with obvious verbal changes) to single sculls. McMahon as well as McMahon and Bonner have previously considered various numbers of rowers in racing shells, and reached conclusions suggesting that consideration of an eight is representative of all possible combinations of rowers.

The centenary of the birth of Oliver Heaviside last year has been the occasion of celebration by electrical engineers and physicists in this and other countries. In the discussions of his work much has been said about the Operational Calculus ; and as the versions of its history which have been given both in these commemorative celebrations and in most of the textbooks of the subject are seriously incorrect, this may serve as an occasion to recount that history more correctly. The story in widest circulation is that the Operational Calculus was discovered by Heaviside (Boole being sometimes—and incorrectly—named as the discoverer of its applications to ordinary differential equations) and rejected by British mathematicians because of Heaviside’s lack of rigour. The facts, as I shall show, are that the Calculus was well known in Britain and France before Heaviside’s birth, and that the rejection of his paper had nothing to do with his use of symbolic methods.

We are looking for all triangles with sides of integer lengths a, b, and c say, with an angle of 60° opposite the side of length a.

Everyone knows that the condition for the quadratic to have two equal roots, i.e. to have a repeated root, is that its discriminant should be zero. We should remark, at the outset, that we are concerned only with ordinary polynomials whose coefficients are complex numbers. Indeed, little is lost if a reader assumes that all our polynomials are real, i.e. have real numbers for all their coefficients, though their complex roots must be considered as well as their real ones.

It is common today for students in elementary calculus to possess a powerful graphics calculator, such as the TI-82. These machines have had a dramatic impact on how teachers present the subject. The teacher population is clearly divided when it comes to the emphasis on the use of the calculators. There are instances, though, where it is difficult to argue with the calculator's effectiveness as a teaching tool in calculus. One such case is in using Newton's method to find the roots of an equation, for once the algorithm is presented, it is merely a matter of performing the numerical calculations for the sequence of iterates, and this is an operation that the TI-82 does very well.

We are concerned with the problem of constructing on a sphere maps whose faces (regions) all have the same number of edges.

In Euclidean plane geometry there exists an interesting, although limited, duality between the concepts angle and side, similar to the general duality between points and lines in projective geometry. Perhaps surprisingly, this duality occurs quite frequently and is explored fairly extensively in.

The square is self-dual regarding these concepts as it has all angles are equal, as well as all its sides.