Channel: singingbanana

Category: Education

Tags: james grimeproblemmathematicsmathspuzzleearthequatortemperaturemathsingingbananaintermediate value theorem

Description: 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. Here's a great simulation by mrFryd4y for how this might look youtu.be/JzV3ombeXxY Information: The Intermediate Value Theorem: en.wikipedia.org/wiki/Intermediate_value_theorem The general result, The Borsuk-Ulam Theorem: 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 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. Bless you, but some people are really over-thinking the definition of temperature. How is temperature measured by meteorologists? They stick a thermometer in the air en.wikipedia.org/wiki/Temperature_measurement#Surface_air_temperature Temperature is regarded to be continuous due to the second law of thermodynamics which causes the transfer of heat between areas of different temperature 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. Pineapple Count (07-09-16): 186 pineapples.