
Take any circle: There are two points opposite each other at equal temperatures - ColinWright
http://hippomath.blogspot.com/2011/06/equal-temperatures-at-two-opposite.html#more
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hammock
This is just a (very intriguing) application of the intermediate value theorem
- i think that's what it's called - which basically says that if you have a
continuous function that starts and ends at the same place, then there are two
points along that function that have the same value.

You could draw whatever shape you want - circle, square, squiggle, as long as
it starts and ends in the same place, and the dependent variable is continuous
as well (e.g. temperature, pressure, etc)

IVT says if I climb up a mountain from sea level to 10', then I was at exactly
5' elevation at least once on the journey. So if I climb up AND down a
mountain from sea level to 10', I was at exactly 5' at least twice.

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ColinWright
It's more than that, because this is talking about getting two points exactly
opposite each other.

Yes, you still use the IVT, but there's slightly more you need to do.
Specifically, something like taking the angle from 0 to 180, and then
computing the difference between f(x) and f(x+180). That lets you use the IVT
to show that there has to be a zero, and there's your result.

Or something.

