Equivalent Equator Empirical Experience! (Posted on 2005-03-27)

	Submitted by Old Original Oskar!
Rating: 2.8000 (5 votes)
Solution:	(Hide)
Let f(x) be the temperature along the Equator; f(x+2π)=f(x). Let g(x)= f(x+π)-f(x); then, g(x+π)= f(x+2π)-f(x+π)= f(x)-f(x+π)= -g(x). Unless g(x) is always 0 (which would provide infinite opposite points with the same temperature) it changes sign between x and x+π, so by continuity it must be zero somewhere. QED As to the "logical" argument, the points on the meridian could be very near the Equator, where winter and summer are very similar, or they could be near the poles, both at very low temperatures.

	Subject	Author	Date
	No Subject	Jud	2005-08-16 12:56:34
	No Subject	kat	2005-04-06 01:15:24
	Simple solution	ajosin	2005-03-28 16:14:58
	re: Solution	Charlie	2005-03-28 13:35:38
	Solution	David	2005-03-28 05:18:35
	Solution	Ken Haley	2005-03-28 01:06:32
	Bolzano solution	e.g.	2005-03-28 00:27:13
	Proof	Larry	2005-03-27 22:23:40
	counter-counterargument	Tristan	2005-03-27 20:27:49
	A related theorem (partial spoiler)	Larry	2005-03-27 19:30:02
	re: possibly	lenny	2005-03-27 14:35:20
	possibly	lenny	2005-03-27 14:26:19