The mathematical tidbit for today is the Borsuk–Ulam theorem, which states that every continuous function *f* from the *n*-dimensional sphere to *n*-dimensional space must satisfy *f*(*p*) = *f*(−*p*) for some point *p*.

In particular, every continuous function *f* from a 2-dimensional sphere (say, the Earth’s surface) to the plane must satisfy *f*(*p*) = *f*(*q*) for some antipodal pair of points *p* and *q*.

Thus, if we can describe weather by a pair of numbers (say, temperature and rainfall), there must be an antipodal pair of points *p* and *q* with the same weather (because two numbers specify a point in the plane).

The maps above (for average maximum temperature) and below (for rainfall) show July weather at various places on Earth, and a pair of points with the same weather is highlighted.

It’s a miracle that it works in **this** case, of course, because the maps only define temperature and rainfall on the land; I would not have been able to recognise a suitable antipodal pair of points if one or both were at sea.

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