
PHI=(1+ Sqrt[5])/2;
A= Sqrt[5]-2;

g1[x_]:= x/A;
g2[x_]:= -x/A+2;
g3[x_]:= -x + 2/PHI/PHI
g4[x_]:= x/A + 1-1/A


g[y_]:=(
x=y-Floor[y];
z=If[x>1-A,g4[x],If[x>(1-A)/2,g3[x],If[x>A,g2[x],g1[x]]]];
z)



ss[w_]:=(
x=Simplify[w];
x1=Expand[Numerator[x]];
x2=Expand[Denominator[x]];
test=x2-Floor[x2];
If[test==0,Simplify[w],s0[w]])

s0[w_]:=(
x=Simplify[w];
x1=Expand[Numerator[x]];
x2=Expand[Denominator[x]];
a1=Coefficient[x2,Sqrt[5],0];
a2=Coefficient[x2,Sqrt[5],1];
x3=a1 - a2 Sqrt[5];
y1=Simplify[x1 x3];
y2=Simplify[x2 x3];
y=Simplify[y1/y2])




start=24/7 + 73 PHI/59;
start=start-Floor[start];
start=N[start,1000];
t1=Table[Nest[g,start,k],{k,1,1000}];
t2=t1/start;
t3=Rationalize[t2,.00000001];
Position[t3,t3[[201]]]