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How can we represent geometrically $$n^n,\quad n \in \mathbb{N}$$
For example if $n = 1 \longrightarrow$ a line segment of unit length, $n = 2\longrightarrow$ a square of side $2$ unit's......
Regards, vishal

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up vote 3 down vote accepted

$n^n$ can be thought of as the volume of a hypercube, with each dimension being length $n$, with $n$ dimensions.

http://en.wikipedia.org/wiki/Hypercube

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how many unit hypercube's are there in $$n^n hypercube?$$ –  vishal Jan 16 '13 at 19:30
    
@vishal $n^n$ unit hypercubes. $(\frac{n^n}{1})$, one unit of each $n$ will results in $n$ units per dimension, with $n$ dimensions gives $n^n$ –  Rustyn Jan 16 '13 at 19:32
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Wouldn't it be more accurate to say, "with each side being length $n$"? –  000 Jan 17 '13 at 6:26
    
Sure. I was talking about how many units there were per side length @limitless –  Rustyn Jan 17 '13 at 6:42

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