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Things of interest in Maths & Science

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If a mathematician wants to cross a road, they will think carefully about their optimal path. The total distance of the path should be minimised, but they prefer walking on the sidewalk to the road. If there is no extra discomfort from being on the road, the best path is a straight line, but as it increases it is better to cross the road more directly.  The resulting path is exactly the same as a ray of light refracting through a block of glass [with relative refractive index equal to the ratio of these ‘discomfort levels’]. Fermat’s principle says that light will want to spend less time in the glass (on the road), as it actually travels more slowly in the glass. [video] [code] [more]

If a mathematician wants to cross a road, they will think carefully about their optimal path. The total distance of the path should be minimised, but they prefer walking on the sidewalk to the road. If there is no extra discomfort from being on the road, the best path is a straight line, but as it increases it is better to cross the road more directly.  The resulting path is exactly the same as a ray of light refracting through a block of glass [with relative refractive index equal to the ratio of these ‘discomfort levels’]. Fermat’s principle says that light will want to spend less time in the glass (on the road), as it actually travels more slowly in the glass. [video] [code] [more]

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Matt Henderson

I post original stuff about maths, space, computational linguistics and other things that I like. This blog is meant to be accessible and interesting to people of all backgrounds. My undergrad was maths in Cambridge, and I'm now starting research in Speech and Language technology. Email me at If you're new, check out this overview of my posts. All code posted is in Mathematica.

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