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Marcus du Sautoy hosts a puzzle panel game, and presents contestants with a problem about a despatch rider. He can travel a certain speed on sand, and twice as fast over grass. What path should he take in order to cover the diagonal distance between two points most quickly? This turns out to be a very complex problem involving Pythagoras and calculus, but the application to the refraction of light brings it back to practical applications - like why things look less far away under water.
This clip is from:
First broadcast:
14 February 2005

Classroom Ideas

A complex speed and distance problem is examined - looking for the quickest path through sand and grass. The true solution requires calculus and pythagoras, but the problem can be investigated using trial and error too as part of a unit on speed-time graphs, or more advanced geometry.

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