1
$\begingroup$

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!

|cite|improve this question
$\endgroup$
  • 4
    $\begingroup$ 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
  • 1
    $\begingroup$ +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
1
$\begingroup$

I think the term you're looking for is "concentration of measure".

|cite|improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.