Fantastic theorem in math

  Who tells math is hard and boring(unfortunately sometimes it is), look at these theorem below, you will find how interesting math can be.
  1.A drunk people can always finds his home but a drunk bird can never find its way. This has been proved easily, suppose there is enough time, the drunk man walk in the city by random, the chance he return his home is 100%. Well, it's a little pity for a drunk bird for the chance it fly back to its home is only about 34%, for the bird can fly south, north, west, east, up and down.

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  In higher dimension, the chance you can come back is become lower and lower as the dimension goes up, 19.3% in 4-dimision space, and 7.3% in 8-dimision space.

  2.Hairy all theorem: There is no nonvanishing continuous tangent vector field on even dimensional n-spheres. Simply to say, you can never smooth all the hair on a ball.

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  3.ham sandwich theorem: Give a sandwich,you can half the bread, the cheese and the ham with just one cut. More general,given n measurable "objects" in n-dimensional space, it is possible to divide all of them in half (with respect to their measure, i.e. volume) with a single (n − 1)-dimensional hyperplane.

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 These theorems are just what we can learn from school, the only difference is we have found these interesting applications. Maybe the reason why some theorem in math is boring just because we have not found the interest in it, these fantastic word is just waiting for you!!!

Reference: http://www.guokr.com/article/53059/
           http://en.wikipedia.org/wiki/Hairy_ball_theorem
           http://en.wikipedia.org/wiki/Ham_sandwich_theorem