I spent some time this week-end trying to find a mathematical puzzle whose solution is 2718, for the “Mathematics on a shelf” competition, and the first trail was to look into properties of Euler’s number . The following result is not useful in any way, but it is amazing: an approximation of using all the digits from to exactly once, and which is correct to decimal digits (that’s more than digits!):

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This entry was posted on 11/05/2010 at 08:55 and is filed under Mathematical games. You can follow any responses to this entry through the RSS 2.0 feed.
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29/06/2010 at 15:19 |

Do you have any clue how one can come to this kind of very precise approximation? A series expansion…?

29/06/2010 at 21:46 |

I haven’t tracked down the original publication, but I would guess that a large dose of luck was required!

21/03/2012 at 09:55 |

There isn’t any luck involved. e is the limit of (1 +t) to the power of 1/t, as t tends to zero. If you look at the given expression, you will see that this is what your approximation is using. t is certainly very small in this case, hence the degree of accuracy of the approximation.

Nigel Burin ( The Manchester Grammar School)