Can you solve Oxford University’s Interview Question? The excellent Youtube channel Mind Your Decisions is a gold mine for potential IB maths exploration topics. I’m going to follow through my own approach to problem posed in the video. The problem is to be able to trace the movement of the midpoint of a ladder as […]
Using Maths to model the spread of The Chinese Coronavirus (Wuhan flu) The Wuhan coronavirus is the latest virus to warrant global fears over a disease pandemic. Throughout history we have seen pandemic diseases such as the Black Death in Middle Ages Europe and the Spanish Flu at the beginning of the 20th century. More recently we […]
Square Triangular Numbers Square triangular numbers are numbers which are both square numbers and also triangular numbers – i.e they can be arranged in a square or a triangle. The picture above (source: wikipedia) shows that 36 is both a square number and also a triangular number. The question is how many other square triangular […]
Rational Approximations to Irrational Numbers This year two mathematicians (James Maynard and Dimitris Koukoulopoulos) managed to prove a long-standing Number Theory problem called the Duffin Schaeffer Conjecture. The problem is concerned with the ability to obtain rational approximations to irrational numbers. For example, a rational approximation to pi is 22/7. This gives 3.142857 and therefore […]
When do 2 squares equal 2 cubes? Following on from the hollow square investigation this time I will investigate what numbers can be written as both the sum of 2 squares, 2 cubes and 2 powers of 4. i.e a2+b2 = c3+d3 = e4+f4. Geometrically we can think of this as trying to find an […]
Hollow Cubes investigation Hollow cubes like the picture above [reference] are an extension of the hollow squares investigation done previously. This time we can imagine a 3 dimensional stack of soldiers, and so try to work out which numbers of soldiers can be arranged into hollow cubes. Therefore what we need to find is what […]
