Take the tour ×  (Sorry for bad english, please.)  M. Postnikov
in his lections on geometry write that the theorem  Sphere
$S^{n-1}$ isn't retract of ball $B^n$.  calls "Drum theorem"
because for $n=2$ it mean that we can stretch a film over a
circle and make drum.  But I don't understand. Why?
share|improve this question Well, if the Disk would retract to
the circle, the drum would not drum if you drum it. The material
would flow smoothly to it's border –  Blah Mar 16 '12 at 10:58
@Blah: Cool! Thanks! It's so simple... –  Corvus Mar 16 '12 at
11:10 add comment  1 Answer  up vote 2 down vote accepted  The
explanation by Blah is spot on: if a disk could retract to its
boundary, the drum head would collapse onto the rim of the drum
instead of remaining stretched.  M.M. Postnikov liked this
illustration enough that he included it in the Topology article
of БСЭ. Loose translation:  This fact, essentially the material
of elementary geometry, which for $n=2$ is immediately obvious
as the possibility to stretch dru