# The drum theorem in topology

M. M. Postnikov in the book "Smooth Manifolds" called a statement

The sphere $S^{n-1}$ isn't a retract of the ball $B^n$.

the "Drum theorem" because for $n=2$ it mean that we can stretch a film over a circle and make a drum.

How the statements are related?

• 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

This fact, essentially the material of elementary geometry, which for $n=2$ is immediately obvious as the possibility to stretch drumhead on a hoop, still has no proof without the methods of algebraic topology.
этот, по существу, элементарно-геометрический и (при $n = 2$) наглядно очевидный факт (физически означающий возможность натянуть на круглый обруч барабан) до сих пор не удалось доказать без привлечения алгебраико-топологических методов.