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For the sake of this challenge, you can assume that the world behaves nicely (everything is continuous, differentiable etc, the world is a sphere blah blah blah) but figurative bonus points if you assume fewer things. If you're looking for an easier challenge check out Challenge 10a.
The Challenge: Show that there exists a curve dividing the Earth into two pieces such that for every point p on the curve, the temperature at p and at -p (the point on the opposite side of the earth) are equal, or construct a temperature function in which no such dividing curve exists.
The Challenge: Show that there exists a curve dividing the Earth into two pieces such that for every point p on the curve, the temperature at p and at -p (the point on the opposite side of the earth) are equal, or construct a temperature function in which no such dividing curve exists.
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