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Happy National Pi Day: Spotlighting one of math's most seductive numbers

(NBC NEWS) - If robots do take over one day, humans may be obliged to celebrate all sorts of holidays dedicated to mathematical constants that interest our AI overlords. For now we mark only a few such days, including e Day (in honor of the natural logarithm e), Mole Day(recognizing the Avogadro constant used in chemistry), and, of course, Pi Day, which occurs every March 14.

Why celebrate the number pi (π) on March 14? Because it's the fourteenth day of the third month of the year, and 3 and 14 are the first three digits of pi’s decimal expansion. If you really want to show you’re a pi aficionado, you can start your celebration at 1:59 p.m. and 26 seconds, because with those five additional digits you have pi’s first eight digits: 3.1415926.

Those eight numbers are just the beginning of pi’s true value. Unlike most numbers we encounter in everyday life, pi has digits to the right of the decimal point that go on not just for a long time but forever — and in an unpredictable way. The Swiss mathematician Johann Heinrich Lambert proved that in 1761.

The short way to say this is that pi is an irrational number, one that cannot be represented as a fraction and thus has an infinite and never-repeating decimal expansion. And since the 19th Century, pi has been known to be transcendental, meaning that no combination of its powers can add up to a whole number. This distinguishes it again from more familiar irrational numbers like the square root of two (whose second power is equal to two).


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