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Kako izmeriti pi v primeru zombijevske apokalipse

Objavljeno: 17. april, 2014 | Avtor: | Ni Komentarjev »

Nekoč smo poizkusili s tekmovanjem za najbolj izvirno metodo za merjenje stevila pi. Za primer opis, kako so se tega lotili v Montrealu.

The ratio between a circle’s circumference and its di- ameter, named π, is a mathematical constant of crucial importance to science, yet most scientists rely on pre- computed approximations of π for their research. This is problematic, because scientific progress relies on infor- mation that will very likely disappear in case of a cata- clysmic event, such as a zombie apocalypse. In such case, scientific progress might even stop entirely. This moti- vates the need for a robust, yet easily applicable method to estimate π.

We first lay down the theoretical framework for Monte Carlo methods, including importance sampling and pro- pose a probabilistic interpretation of π within this frame- work. We then introduce the idea of computing π using importance sampling with a ballistic-based proposal dis- tribution and suggest a robust way of dealing with the unknown generating distribution. Finally, we compare the obtained estimation of π with the true value.

We feel confident that ballistic Monte Carlo methods such as the one presented in this paper constitute reli- able ways of computing mathematical constants should a tremendous civilization collapse occur.

 

Vir: A Ballistic Monte Carlo Approximation of π



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