View source for Talk:Golden ratio

==Golden ratio==

Strangely, the figure in the original article is erroneous! ED=EB, not BD=EB.

<center><asy>

pair A=(-1,0);
pair B=(0,0);
pair E=(0,0.5);
pair C=A+(0.5*(sqrt(5)-1),0);
pair D=(-1/sqrt(5), 0.5*(1-1/sqrt(5)));

draw( A--B--E--cycle,currentpen+1.5 );
dot(A,currentpen+3.5); dot(B,currentpen+3.5); dot(E,currentpen+3.5); dot(C,currentpen+3.5); dot(D,currentpen+3.5);

draw( shift(E)*scale(0.5)*unitcircle,currentpen+1 );
draw( shift(A)*scale(0.5*(sqrt(5)-1))*unitcircle,currentpen+1 );

draw( shift(B)*scale(0.5)*unitcircle, dashed+red );

clip(A+(-0.15,-0.15)--B+(0.15,-0.15)--E+(0.15,0.15)--A+(-0.15,0.15)--cycle);

label("$A$",A,S); label("$B$",B,S); label("$C$",C,S);
label("$E$",E,N); label("$D$",D,N);

label( "\small Golden Ratio construction", (-0.5,0.8) );

shipout(scale(100)*currentpicture);
</asy></center>