Number Theory


Intimations of the Irrationality of Pi From Reflections of the Rational Root Test

Authors: Timothy W. Jones

The rational root test gives a means for determining if a root of a polynomial is rational. If none of the possible rational roots are roots, then if the roots are real, they must be irrational. Combining this observation with Taylor polynomials and the Taylor series for $\sin (x)$ gives intimations that $\pi$, and $e$, are likely irrational.

Comments: 4 Pages. Additional comments and examples added.

Download: PDF

Submission history

[v1] 2019-06-11 07:12:25
[v2] 2019-06-13 07:12:16

Unique-IP document downloads: 22 times is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus