The 2018 Monte Carlo World Cup

The world cup is almost once more amongst us, which means interminable weeks of breathless coverage, punditry, and heartfelt professions that each match will be played at 110%. In an effort to inject some more quantitative rigour to a field which, apparently, could do with some, let’s try and predict how the whole thing will play out.

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Axes of rotation

I recently tried my hand at throwing axes at a wall, courtesy of Whistle Punks in London. While this was a fun and satisfyingly macho activity, I noticed that the attendants were careful to position people at various distances from the target to increase their chances of success. This piqued my curiosity, so here I’ll have a look at why that might be.

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Two Come Along at Once

As the old saying goes, you wait ages for a bus and then two come along at once (or more!). Is this true though? My own anecdotal evidence would suggest yes, every single bloody time. However, we love data and maths in this blog almost as much as we hate waiting for the bus, so let’s have a more thorough look at the issue.

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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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