There are always two points on opposite sides of the Earth with the exact same temperature. And we can prove that. Temperature changes continuously. If a and b are on opposite sides of the equator and D(a) = T(a) - T(b) is positive, then D(b) = T(b) - T(a) is negative. That means there must be some point x on the equator where D(x) = 0. At that point the two opposite sides are the same temperature. Mathematicians call this the Intermediate Value Theorem which means if there is a continuous function that changes from of a positive value to a negative value (or the other way around) then it must, at some point, pass through zero. Information: The Intermediate Value Theorem: http://en.wikipedia.org/wiki/Intermediate_value_theorem The general result, The Borsuk-Ulam Theorem: http://en.wikipedia.org/wiki/Borsuk%E2%80%93Ulam_theorem A lovely full explanation of why there is a point on Earth where temperature *and* pressure are the same http://mathforum.org/library/drmath/view/54746.html In laymans terms, continuous means you can draw the graph without taking pen from paper. It can be a smooth or jagged line, as long as the line isn't a strict vertical jump from one value to another. Temperature is regarded to be continuous due to the second law of thermodynamics which causes the transfer of heat between areas of different temperature http://en.wikipedia.org/wiki/Heat_transfer The temperature gradient might be steep, but not discontinuous. This is not an extraordinary claim. No one reads the description anyway. If you have you are part of an exclusive club. If you have read the description let me know by typing the secret word, "pineapple", in the comments. In return I will give you my respect, and maybe a thumbs up or something.

• published: 26 Jan 2014
• views: 18152