In this teaching oriented article, I am introducing the concept of an equilateral rhombus, which is completely characterized. Three main theorems are given with proofs in Section 2. Most of the time, the rhombuses that are discussed are not squares. For a given circle of a specified radius sigma greater than?0, there is exactly one equilateral…

The 2000 US presidential election between Al Gore and George W. Bush has been the most intriguing and controversial in American history. Using the Florida ballot data, Wu showed that the 2000 election result could have been reversed had the "butterfly ballot effect" been eliminated. Through a combinatorial approach, Harger concluded that Gore…

This article analyses mathematical modelling from several different perspectives and contrasts modelling with problem solving. Then it describes the ways in which modelling, applications, and problem solving are approached in several Latin American countries. It further describes workshops for secondary schools and for university teachers in which…

It is known that any totally skew quantity with (n + 1) indices, each of which ranges over n values, vanishes identically. The aim of this short note is to show that this is equivalent to the simple fact that any (n + 1) vectors in an n-dimensional vector space are linearly dependent.

Using the methods of finite difference equations the discrete analogue of the parabolic and catenary cable are analysed. The fibonacci numbers and the golden ratio arise in the treatment of the catenary.

Two techniques for determining a straight line fit to data are compared. This article reviews two simple techniques for fitting a straight line to a set of data, namely the method of averages and the method of least squares. These methods are compared by showing the results of a simple analysis, together with a number of tests based on randomized…

The paper reviews some recent advances in interior-point methods for linear programming and indicates directions in which future progress can be made. Most of the interior-point methods belong to any of three categories: affine-scaling methods, potential reduction methods and central path methods. These methods are discussed together with…

Presents answers to a survey (n=257) on the state of science education for 11- to 16-year olds in the United Kingdom. Survey topics include class size, per pupil expenditure, extent of laboratory technician support, textbook provision, condition of laboratory facilities, reprographics costs, and technology use. (WRM)

Successful programs of continuing professional education must involve both the improvement of the learner's competence and the restructuring of the work environment to stimulate, encourage, recognize, and reward improved performance. (Journal availability: Subscription Manager, MOBIUS, University of California Press, Berkeley CA 94720.) (SK)