Magnetic recording head theory is based on the Karlqvist approximation to solve the Laplace equation
over a polygonal domain that originates from a magnetostatic approach to describe the magnetic field
produced by the read/write head in the recording medium. The approximation is reviewed and compared
to various approaches dealing with solving the Laplace equation using different boundary conditions.
The solution is obtained by the Green function, Fourier transform, Fourier series and finally by
conformal mapping methods that allow us, on one hand, to comply with the Sommerfeld edge condition
required at angular points and on the other, to obtain exact results.