HAIRY BALL THEOREM AND IT’S APPLICATION

HAIRY BALL THEOREM.

Abstract

On an even dimensional $n$-sphere there will be no non-vanishing continuous tangent vector field . Here we will provide a proof of this theorem using a geometric approach . Since we live in a three dimensional space so this theorem on $2$-sphere is much more interesting . We can visualize the real life application of Hairy Ball theorem on $2$-sphere . Along with the proof of Hairy Ball theorem we will provide some real life applications of the theorem with mathematical justifications.