Discovering and Proving that π Is Irrational

Ivan Niven's proof of the irrationality of π is often cited because it is brief and uses only calculus. However it is not well motivated. Using the concept that a quadratic function with the same symmetric properties as sine should when multiplied by sine and integrated obey upper and lower bounds for the integral, a contradiction is generated for rational candidate values of π This simplifying concept yields a more motivated proof of the irrationality of π and π2.