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International Date Line
Is it possible to assign a time to every longitude on Earth, so that each longitude has a different time but the times at nearby longitudes are always close? The answer is no, which is mathematically equivalent to saying that there's no way to continuously map points on a real number line onto a circle. This explains why an International Date Line is needed. It allows most regions on Earth to have times similar to their neighbors, though, by convention, times are (usually) made in chunks of one hour between adjacent time zones. Then it takes care of the inevitable discontinuity by having it happen all at once, as a jump by one whole day on a longitude that passes mostly through open water in the Pacific. The fact that there doesn't exist any continuous one-to-one function from the circle onto the line follows from the Borsuk-Ulam theorem.
Related category
• TIME MEASUREMENT AND PUZZLES
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