Relationship between periodicity and symmetry

[HarishS]

In an online videolecture as well as in some texts regarding Fourier Series, i have come across a statement "Periodicity results from symmetry" and they quote the example of heat distribution in a ring.

 

My doubt is that won't be the heat distribution still be periodic even after the symmetry of the ring is broken- say there is a kink in only one half of the ring.

[Bignose]

The periodicity in that example is of the form [math]T(0) = T(2\pi)[/math] where the input to that function is the theta of the cylindrical coordinate system. If there is a kink or break in the ring, that statement may not hold anymore.

Edited July 15, 2012 by Bignose