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Is there any geometric way to characterize $e$?

We know that the length of perimeter of a circle of unit diameter is $\pi$ ; is there a similar geometric interpretation of $e$ , without invoking complex numbers, in terms of lenth ( and not area )?

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marked as duplicate by Raskolnikov, Marc van Leeuwen, Rudy the Reindeer, Rahul, lhf Oct 11 '12 at 11:21

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Does this answer your question? math.stackexchange.com/questions/159707/… –  Qiaochu Yuan Oct 11 '12 at 6:55
    
@ Qiaochu Yuan:- Ah! I get it , it's still an open problem. –  Souvik Dey Oct 11 '12 at 7:44

1 Answer 1

Do a step of length $1$, then a step of half the previous one, then one third the previous one, then one forth the previous one,...

How far do you get?

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That's quite a good way of converting the definition of e into a geometrical construction , but the process does not end after a finite terms. –  Souvik Dey Oct 15 '12 at 5:46
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... which was not requested. –  draks ... Oct 15 '12 at 7:16
    
Oh , sorry for not clarifying that , but however it does not matter cause the question is closed now. –  Souvik Dey Oct 17 '12 at 12:47

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