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: http://youtu.be/bW9FZIO2FZY

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

3. 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

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A Youtube video presentation can be accessed here: http://youtu.be/bW9FZIO2FZY

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

3. 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

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