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Somewhat simple question, but it's the following. Consider D-volumes (that is, the equivalent volume measurement in D dimensions) of spheres of ever-higher dimensions. The percent of D-volume concentrated in a $\epsilon$ crust around the sphere is

$1-(1-\epsilon)^D$ (This derivation is pretty easy so leaving it out.)

For a given $\epsilon$, this percentage gets much higher as D gets higher.

My question is, I want to say that the 'topology' of spheres changes as you go into higher dimensions. But I know that's not right at all. What is the correct word for the phenomenon I'm describing?

Thanks!

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    $\begingroup$ Perhaps you're looking for 'density'? I'm not quite sure, myself, but it needs a name if it doesn't already have one. If you need to coin a phrase for this, how about "crustiness"? $\endgroup$ – Jesse Smith Jul 11 '13 at 20:57
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    $\begingroup$ +1 for crustiness. That's great. I might still use that even if there is an existing word. :) $\endgroup$ – Kurt Spindler Jul 11 '13 at 20:59
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I think the term you're looking for is "concentration of measure".

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