Undeniably omnipresent in our everyday lives, electronic signal compression is a classical example that illustrates the ubiquity of mathematics in high-end technology and sciences. When dealing with piles of files, it is essential that each file takes up as little storage space as possible while maintaining quality. The cloud-based--available…

We consider here a number of ideas for the classroom or lecture theatre associated with the mensuration of solids. In particular, the volumes of various tetrahedra are obtained in an indirect manner (by way of prisms and square-based pyramids). This activity develops problem-solving skills, spatial visualization and a from-first-principles…

Fermi problems are problems which, due to their difficulty, can be satisfactorily solved by being broken down into smaller pieces that are solved separately. In this article, we present different sequences of activities involving Fermi problems that can be carried out in Secondary School classes. The aim of these activities is to discuss…

Revisits and discusses the polar bear problem that was published in the March 1997 issue. The problem concerns a riddle: If you walk one mile south, one mile east, and one mile north, and end up in the same spot as you started, what kind of bear would you see? (ASK)

Describes simple experiments to explore the variables and links to a theoretical approach. Using genuine data, develops an application to the drive mechanism for a lift in a deep mine shaft; poses follow-up questions. (ASK)

Describes the Six Circle problem which consists of the numbers 1-6, six circles, and asks whether it is possible to put the numbers in the circles--which are configured in a triangle--so that the sums of the three numbers on either side are the same. (NB)

Provides an example of the modeling power of Mathematics, demonstrated in a piece of A-Level student coursework which was undertaken as part of the MEI Structured Mathematics scheme. A system of two masses and two springs oscillating in one dimension is found to be accurately modeled by a system of linear differential equations. (Author/ASK)

Explores the derivation of empirical models for the stopping distance of a car being driven at a range of speeds. Indicates that the calculation of stopping distances makes an excellent example of empirical modeling because it is a situation that is readily understood and particularly relevant to many first-year undergraduates who are learning or…

Reviews a number of interesting sites on the Internet for mathematics education and considers the different ways in which the information available can be used as a teaching resource. Provides practical guidance on how teachers might take information in text, graphic, and file formats and use it either for themselves or with pupils. (Author/ASK)

Computer algebra systems have great potential uses, but learning the basic concepts of algebra is itself a mathematical activity. Explores theoretical concepts that may be seen as essential enabling skills for computer algebra systems users. (Author/ASK)

Presents activities in which students are invited to re-create on their calculator screen images using graphical features of the graphing calculator. (ASK)

Discusses using black body function for radiative heat transfer, which can be used in a real-life application in a number of different topics in A-level and first-year undergraduate mathematical methods courses such as differentiation, solving nonlinear equations, and integration by substitution. (ASK)

Errant mathematical views are widely found among teachers, their students, and authors of applied mathematics texts. Suggests classroom experimentation, both to confirm the occurrence of these errors, and to apply the appropriate corrective teaching. (Author/ASK)

Observes the application of probability theory to a game between two players. Shows how basic techniques such as tree diagrams can be used to demonstrate optimum strategies, how the art of bluffing can be quantified, and how this might be applied to a game of poker. (Author/ASK)

Investigates the basic mechanics of cycling with a simple reckoning of how much effort is needed from the cyclist. The work done by the cyclist is quantified when the ride is on the flat and also when pedaling uphill. Proves that by making use of the available gears on a mountain bike, cycling uphill can be accomplished without pain. (Author/ASK)