The Hairy Ball Theorem (HBT) was first postulated (and then proved) by Luitzen Egbertus Jan Brouwer in 1912. An informal statement of the theorem is that :
“One cannot comb the hair on a coconut”.
Temptations to classify the theorem as trivial should be strongly resisted – as it’s still finding relevance in many current research areas. Take, for example, the domain of Quantum Field Theory – the quote above coming from a recent research article in which it features, a paper by Dr. Cihan Saçlioğlu (pictured) of the Faculty of Engineering and Natural Sciences, at Sabanci University, Istanbul, Turkey. ‘Conservation laws, equivalence principle and forbidden radiation modes.’ (Published in the journal Resonance, Volume 17, Number 3, 2012),
Dr. Saçlioğlu’s paper not only draws attention to the relevance of the HBT to the study of electromagnetic and gravitational radiation (monopolic and dipolic), but also points out that :
"On the other hand, one can comb the hair on a doughnut which is the
wavefront of an electric dipole source at a fixed distance from the
source; the field lines correspondent to the 'hair'. At a given instant, one can find lines of E tangential to circles parallel to the circular hole in the middle, intersected by circles of B running perpendicular to them. "
The paper can be read in full here :
