On which shaped planet am I the heaviest?

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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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Stereographic Lampshades

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I saw an article on the Guardian website here on the 3D-printing of shapes which project interesting patterns of light. Ignoring the strangely forced Halloween reference, I thought this would be an interesting project to attempt for an arbitrary pattern, perhaps as a personalised lampshade. Buoyed by the continuing high of leftover sweets from Friday night, let’s have a look.

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