Ramanujan’s Taxi Cabs and the Sum of 2 Cubes The Indian mathematician Ramanujan (picture cite: Wikipedia) is renowned as one of great self-taught mathematical prodigies. His correspondence with the renowned mathematician G. H Hardy led him to being invited to study in England, though whilst there he fell sick. Visiting him in hospital, Hardy remarked that […]

Waging war with maths: Hollow squares The picture above [US National Archives, Wikipedia] shows an example of the hollow square infantry formation which was used in wars over several hundred years. The idea was to have an outer square of men, with an inner empty square. This then allowed the men in the formation to […]

Finding the volume of a rugby ball (prolate spheroid) With the rugby union World Cup currently underway I thought I’d try and work out the volume of a rugby ball using some calculus. This method works similarly for American football and Australian rules football. The approach is to consider the rugby ball as an […]

The Shoelace Algorithm to find areas of polygons This is a nice algorithm, formally known as Gauss’s Area formula, which allows you to work out the area of any polygon as long as you know the Cartesian coordinates of the vertices. The case can be shown to work for all triangles, and then can be […]

Soap Bubbles and Catenoids Soap bubbles form such that they create a shape with the minimum surface area for the given constraints. For a fixed volume the minimum surface area is a sphere, which is why soap bubbles will form spheres where possible. We can also investigate what happens when a soap film is formed […]

For students taking their exams in 2021 there is a big change to the IB syllabus – there will now be 4 possible strands: IB HL Analysis and Approaches, IB SL Analysis and Approaches, IB HL Applications and Interpretations, IB SL Applications and Interpretations. IB Applications and Interpretations There is a reasonable cross-over between the […]