(a) If we start from latitude and proceed in a westerly direction, we can let denote the temperature at the point x at any given time. Assuming that T is a continuous function of x, show that at any fixed time there are at least two diametrically opposite points on the equator that have exactly the same temperature.
(b) Does the result in part (a) hold for points lying on any circle on the earth’s surface?
(c) Does the result in part (a) hold for barometric pressure and for altitude above sea level?

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(a) If we start from latitude and proceed in a westerly direction, we can let denote the temperature at the point x at any given time. Assuming that T is a continuous function of x, show that at any fixed time there are at least two diametrically opposite points on the equator that have exactly the same temperature.

(b) Does the result in part (a) hold for points lying on any circle on the earth’s surface?

(c) Does the result in part (a) hold for barometric pressure and for altitude above sea level?

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