The Euler constant $e$

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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 )?

Does this answer your question? http://math.stackexchange.com/questions/159707/is-there-any-geometric-way-to-characterize-e/159711#159711 — Qiaochu Yuan, Oct 11 '12 at 06:55

score 2 · Answer 1 · answered Oct 11 '12 at 08:54

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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?

answered Oct 11 '12 at 08:54

draks ...

18,449

1

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 05:46
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... which was not requested. – draks ... Oct 15 '12 at 07:16
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

The Euler constant $e$

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