%phi.tex:
%%a Plain TeX file by Doron Zeilberger (x pages)

%begin macros
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\baselineskip=14pt
\parskip=10pt
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\def\2{{\overline{2}}}
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\def\Tilde{\char126\relax}
\def\frac#1#2{{#1 \over #2}}
%\headline={\rm  \ifodd\pageno  \RightHead  \else  \LeftHead  \fi}
%\def\RightHead{\centerline{
%Title
%}}
%\def\LeftHead{ \centerline{Doron Zeilberger}}
%end macros
\bf
\centerline
{
THE SIMPLEST PROOF THAT PHI IS IRRATIONAL
}
\rm
\medskip
\centerline{ {\it ZEHAVA YACHAS}}
\smallskip
\centerline{Student, Golda's Ganon Nursery School, Ein Kesef}
\bigskip
For any pair of positive integers $(p,q)$ such that $\phi=p/q$, where $\phi$ is the positive root of $\phi=1+1/\phi$, 
there is yet another pair $(q,p-q)$ with the same property, and whose sum is smaller. 
Since $\phi \neq 2/1$, there can't be such a pair. \halmos

\end