Maths at Bondi Beach

Number theory

1.  How to derive Cardano's formula for the cubic.  A detailed paper can be downloaded here:  All you wanted to know about solving cubics but were afraid to ask

A Youtube video presentation can be accessed here:
Or download here

2. Ever wondered how the residents of Easter Island managed to get those huge stone heads in place? Well, that’s a bit like wondering how they solved quartic equations in the 16th century without computers.  To understand how it was done have a look at the  following paper which builds upon my paper on how to solve cubic equations (which you should read first or watch the video): Solving a quartic by the method of radicals.pdf

 In 2015 two physicists, Friedmann and Hagen, produced a novel quantum mechanical proof of Wallis’ formula for Pi.  This naturally attracted a lot attention and since that time Cortese and Garcia have generalised the approach.  The purpose of this article is a detailed verification of the calculations.  In the course of verifying the work of Friedmann and Hagen I noticed that they appeared to be unaware of an analytical expression for the ratio of two Gamma functions which formed a critical part of a limiting argument (it appeared they ran some numerical estimates).  Every step in the calculations is set out and there is  also a proof of the orthonormality of associated Legendre functions which figure essentially in the integration of the spherical  harmonic functions.  Download the paper here:  Quantum mechanical derivation of the Wallis formula for Pi.pdf