<p>I just finished reading the proof that the average height of a random binary of given size $n$ is asymptotically $2\sqrt{\pi n}$.</p>

<p>I'm now searching for an intuitive, or geometric, or visual proof of this asymptotic equivalence. In other words, I'm trying to find an intuitive arguments that shows that this number grows like $\sqrt{n}$.</p>

<p>Any ideas?<br>
Thanks!</p>

<p>Note: This is a duplicate of <a href="https://math.stackexchange.com/questions/16457">https://math.stackexchange.com/questions/16457</a> , but I couldn't find how to move it to this website. Sorry!</p>

CC BY-SA 2.5
2011-01-05T19:35:07.080Z
you can ask a moderator on math.SE to migrate it over here. I can't do it, because a mod on the originating site needs to do it. If you want to, best to flag it for mod attention and ask them to do it.
Suresh Venkat
CC BY-SA 2.5
2011-01-06T18:22:24.703Z
I should note that this question already has some good answers on math.SE, raising the question of whether it needs to continue here.
Suresh Venkat
CC BY-SA 2.5
2011-01-08T20:08:55.793Z
Is this a random labeled or unlabeled binary tree (I expect for the $\sqrt{n}$ bound it doesn't matter).
Peter Shor 
<randomness><proofs><tree><pr.probability>
Geometric / Visual explanation that the average height of a random binary tree of given size $n$ is asymptotically $2\sqrt{\pi n}$
Clément
# Geometric / Visual explanation that the average height of a random binary tree of given size $n$ is asymptotically $2\sqrt{\pi n}$

(Asked by: username_0 on 2011-01-05)

I just finished reading the proof that the average height of a random binary of given size $n$ is asymptotically $2\sqrt{\pi n}$.

I'm now searching for an intuitive, or geometric, or visual proof of this asymptotic equivalence. In other words, I'm trying to find an intuitive arguments that shows that this number grows like $\sqrt{n}$.

Any ideas?  
Thanks!

Note: This is a duplicate of <https://math.stackexchange.com/questions/16457> , but I couldn't find how to move it to this website. Sorry!

**Tags:** randomness, proofs, tree, pr.probability

> **Comments:**
> **username_1**: you can ask a moderator on math.SE to migrate it over here. I can't do it, because a mod on the originating site needs to do it. If you want to, best to flag it for mod attention and ask them to do it.  
> **username_1**: I should note that this question already has some good answers on math.SE, raising the question of whether it needs to continue here.  
> **username_2**: Is this a random labeled or unlabeled binary tree (I expect for the $\sqrt{n}$ bound it doesn't matter).  

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## 0 answers

