Prove that at any time there are two opposite points along the Equator, which have exactly the same temperature. Assume the temperature function varies continuously as you move along the Equator.

Counterargument: This is patently impossible. If there are such points on the Equator, there must also be similar points on any circle around the Earth, such as a meridian. But in that case, we'd have one point in the north hemisphere, in winter, and the other in the south, in summer; that doesn't make sense!

What's wrong with this reasoning?

What is wrong with having two identical temperatures with one in summer and one in winter?  There are many other factors, such as night and day, bodies of water, and the latitude.  Near the equator, winter and summer hardly make a difference.

If we were to say that in December every point in the southern hemisphere is strictly warmer than every point in the northern hemisphere, then the equator must be a single constant temperature.  In this case, there doesn't need to be any match in temperature between the northern and southern hemispheres.  If the equator only varies slightly, then the matching temperatures will probably be very near the equator.

Posted by Tristan on 2005-03-27 20:27:49