Holy cow, I wrote a book!
An Australian mathematician
applied intermediate value theory to the problem of keeping a
table from wobbling:
Just rotate the table and you'll eventually find a spot.
A few things struck me about that article.
First, that it explains that intermediate value theory
"is the same principle underlying the fact that there will always
be two points with exactly the same temperature somewhere on Earth."
While that's true, it's way overkill.
Intermediate value theory lets you find two points on any circle
with the same temperature;
you don't need a whole sphere.
(Perhaps they got the scenario mixed up with the
Borsuk-Ulam theorem, which shows the significantly stronger result that
you can find two antipodal points on the Earth
with the same temperature and pressure.)
The next thing that struck me is that the author
to illustrate the article.
But then again, it was an Australian article, so maybe that's just normal
Finally, the article concludes that the theorem may help you place
Well, sure, if you don't care which direction the door faces.