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

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