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Tim Urban
@waitbutwhy
Writer, infant
Joined March 2013
910 Following    899.9K Followers
No one: Mathematicians:
This single expression matches the first 18,457,734,525,360,901,453,873,570 digits of e. Euler’s number e is an irrational constant that begins 2.71828… and continues infinitely without repeating. In 2004, Richard Sabey constructed a special expression that uses each of the digits 1 through 9 exactly once. That expression is identical to the classic limit form (1 + 1/n)^n for an extraordinarily large value of n. Because the difference between (1 + 1/n)^n and the true value of e shrinks roughly like 1/(2n), the result agrees with e for precisely as many decimal places as there are digits in that enormous n—exactly 18,457,734,525,360,901,453,873,570 places. The equality of the two power-tower representations of n is an algebraic identity, so the digit count is rigorous rather than approximate. This remains one of the most extreme known pandigital approximations to e.
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