Derivation and Correlation between Pythagorus (560-479BC) and Mathieu's (1868) equation: Spectral nature between Mathieu's and Modified Mathieu's equation

We derive Pythagoras theorem. From the Pythagoras theorem, we also derive Mathieu’s equation via modified Mathieu’s equation. A spectral com- parison has been carried out between modified Mathieu’s equation and Mathieu’s equation. Apart from this, we also present discrete bound states corresponding to modified Mathieu’s equation of a quantum rectangular type of model potential.