On which shaped planet am I the heaviest?

Continuing on from my last post concerning optimisation and Lagrange multipliers, I came across a neat little paper on the arXiv here, which asks and answers the question: what shape should a planet be to maximise the gravitational force at a given position? This is a fun problem, solved using an extension of the techniques from the last post, namely the use of Lagrange multipliers to optimise a function given some constraint.

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It’s that time of year again where I am forced to come face to face with my one and only flaw: wrapping presents. Yes, the great staff of Debenhams may as well be superheroes to me, expertly taping seams and tying ribbons while I look on with envious bewilderment. My efforts in comparison look like they’ve washed ashore after six months at sea due to a tragically festive shipping accident. In an attempt to reclaim some Christmas pride then, let’s see if there is anything interesting in the present wrapping process, without, you know, actually doing any wrapping.

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