Time dependent gravity and cosmology! In our universe we have a gravitational constant – i.e gravity is not dependent on time. If gravity changed with respect to time then the gravitational force exerted by the Sun on Earth would lessen (or increase) over time with all other factors remaining the same. Interestingly time-dependent gravity was […]

The Tusi couple – A circle rolling inside a circle Numberphile have done a nice video where they discuss some beautiful examples of trigonometry and circular motion and where they present the result shown above: a circle rolling within a circle, with the individual points on the small circle showing linear motion along the diameters […]

The IB Maths Exploration Guide and the IB Maths Modelling and Statistics Guide are both suitable for all IB students: (Applications and Interpretations, Analysis and Approaches). They are both written by an IB teacher with an MSc. in Mathematics, 10 years experience teaching IB Standard and Higher Level and who has worked as an IB examiner […]

The Martingale system The Martingale system was first used in France in 1700s gambling halls and remains used today in some trading strategies. I’ll look at some of the mathematical ideas behind this and why it has remained popular over several centuries despite having a long term expected return of zero. The scenario You […]

This carries on our exploration of projectile motion – this time we will explore what happens if gravity is not fixed, but is instead a function of time. (This idea was suggested by and worked through by fellow IB teachers Daniel Hwang and Ferenc Beleznay). In our universe we have a gravitational constant – […]

Projectile Motion III: Varying gravity We can also do some interesting things with projectile motion if we vary the gravitational pull when we look at projectile motion. The following graphs are all plotted in parametric form. Here t is the parameter, v is the initial velocity which we will keep constant, theta is the angle […]