The Tropical Temperatures Problem: Think of the temperature at each point on the equator of the earth at a particular time (time does not change). (a) Suppose a random point somewhere on the equator is chosen and its temperature recorded. Is there any reason to believe there must be another point on the equator where the temperature is exactly the same? (b) Is there any reason to believe there are two points somewhere on the equator where the temperatures are exactly the same? (c) Is there any reason to believe there are two diametrically opposite points on the equator of the earth where the temperatures are exactly the same? Find at least two ways to think about the problem and arrive at a solution.