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May 5th, 2007, 07:09 AM  #1 
Site Founder Joined: Nov 2006 From: France Posts: 824 Thanks: 7  Intermediate values theorem
Here's a spectacular, though very easy, application of the intermediate values theorem: prove that there exist two diametrically opposed points of the earth with equal temperature (assuming the temperature is continuously distributed, and assimilating the earth to a perfect 3 dimensional ball).

May 18th, 2007, 11:22 AM  #2 
Newbie Joined: Apr 2007 From: France Posts: 1 Thanks: 0 
Let D(p) be the diametrically opposed point of p and let T(p) be the temperature of p. Manifestly f(p)=T(p)T(D(p)) is a continuous function defined on a compact set, and f(D(p))=f(p) , so there is Po such that f(Po)=0 and finally T(Po)=T(D(Po)) (q.e.d) 

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intermediate, theorem, values 
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