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…

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)

Examines the gear system of a mountain bike to discover any redundancy in the many gear settings available to the cyclist. Suggests a best strategy for changing up through the gears on a typical 21-gear system and an adjustment to the available gears that would result in a smoother change. (Author/ASK)