You don’t need any technical ability at calculus to solve the problem, however, only a simple insight. As each dog moves, the one chasing it must change its direction. So what’s this got to do with the dogs? Well, they are running in such a way that their direction is changing continuously at every point. To shed light on any continuous shape, object, motion, process or phenomenon – no matter how wild or complicated it may appear – reimagine it as an infinite series of simpler parts, analyse those, and then add the results back together to make sense of the original whole. He calls the big idea behind calculus the Infinity Principle: One of the aims of Strogatz’s book is to demystify calculus, so the general reader can appreciate what it is and how it is important it is to the modern world. Strogatz, a professor at Cornell, is both a world class mathematician and one of the best popular mathematics authors writing today. The dogs-in-pursuit problem was suggested to me by Steven Strogatz, author of the magnificent Infinite Powers: How Calculus Reveals the Secrets of the Universe, which is out this week. How far does each dog travel before the group collision?įor bonus points, can you work out how far the dogs would travel if they started at the three corners of an equilateral triangle of side length 1, or the five corners of a regular pentagon of side length 1? Would the distance be further or shorter than in the case wih the square? The dogs start at the same time, they all run at the same speed, and at every moment each dog is running directly towards the neighbouring dog.ĭuring the pursuit, the dogs will run in a spiral before they all meet in the centre. Each dog starts running towards the dog immediately anti-clockwise to it. Today’s problem is a classic puzzle and an excuse to post this picture of Melbourne’s annual sausage dog race, the Running of the Wieners.įour dogs are in four corners of a square of side length 1.
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