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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

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

Does this answer your question?… – 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

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
... 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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