Best Laid Plans of Lions and Men |

Written by Mike James | |||

Sunday, 09 April 2017 | |||

Can a man survive a lion attack by two lions? The answer is yes if the question is about mathematics and not real lions. This is almost a classic mathematical conundrum. The problem was originally posed by J.E. Littlewood, a famous mathematician. He was a friend of and collaborator with the even more famous mathematician, G.H. Hardy. The problem is a strange one, almost a game scenario. Take a playing area of a given shape, perhaps with internal holes where neither man nor lion can go, and see if the man can find an algorithm that avoids the lions for all time. The lions and the man are assumed to move at unit speed so it is more a game of geometric strategy than pouncing. There are a number of variations on the question. For example, a single lion and a single man in a circular arena. In this case an algorithm that evades the lion is known:
You can prove that no matter what strategy the lion uses, i.e. what path it takes, the distance between the man and the lion is positive and therefore the lion never catches the man. However, if there are two lions in the circular arena the man cannot escape. In the case of the two lions and an arena of any shape with holes the solution wasn't known until the publication of a recent paper from a group of researchers from the Department of Computer Science at the University of Copenhagen, Denmark:
So what does the 2D area look like? After all it might be important if you ever have to choose the arena in which you are to meet two hungry lions. Well that isn't a simple shape! But it is even more complex than you might imagine. The description in the paper says:
This is difficult to interpret until you enlarge the image:
Yes the accessible part of the region is more like a long wiggly corridor! The second result is also worth a thought. If you are pursued by a pack of any size, as long as it is finite, you can mange to avoid capture as long as you can run faster than any of the pack. So if you are pursued by a posse pick the fastest horse. The paper is to be presented at SoCG'17, the 33rd International Symposium on Computational Geometry, taking place in Brisbane Australia in July. ## More InformationBest Laid Plans of Lions and Men ## Related Articles//No Comment - Turmits are Turing-universal, The Whale Swarm Algorithm & Rules That Govern Fish //No Comment - Approximate Edit Distance, Irrational Guards & DCT In 14 Additions Six Degrees Of Separation Is New
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Last Updated ( Sunday, 09 April 2017 ) |