THE SIMPLEST PROOF THAT PHI IS IRRATIONAL

By Zehava YACHAS


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(Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger)

Written: Nov. 21, 2011.


Dedicated to Jeffrey Outlaw SHALLIT

In 1975, high-school student Jeffrey Shallit published a simple proof that the Golden Ratio, φ, is irrational. The present proof is yet simpler, since it does not use divisibility, only additivity.


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