## Discovering and Proving that Pi is Irrational, 2nd Edition

**Authors:** Timothy W. Jones

Ivan Niven's proof of the irrationality of pi 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 pi. This simplifying concept yields a more motivated proof of the irrationality of pi and pi squared.

**Comments:** 13 Pages. Additional clarifications and appendix added.

**Download:** **PDF**

### Submission history

[v1] 2017-12-10 12:27:40

[v2] 2017-12-22 10:37:51

**Unique-IP document downloads:** 30 times

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