OFFSET
1,1
COMMENTS
A metasilver rectangle is introduced here as a rectangle such that if a silver rectangle is removed from one end, the remaining rectangle is metasilver. Recall that a rectangle is silver if the removal of 2 squares from one end leaves a rectangle having the same shape s=(length/width) as the original. This metasilver ratio is given by
s=2.774622899504489263198249637919477554666...;
s=[r,r,r,r...], a periodic continued fraction, r=1+sqrt(2);
s=[2,1,3,2,3,2,7,1,1,114,11,1,2,1,...], as at A188637.
LINKS
Clark Kimberling, A Visual Euclidean Algorithm, The Mathematics Teacher 76 (1983) 108-109.
FORMULA
Equals (1+sqrt(2)+sqrt(H))/2, where H=7+2*sqrt(2).
MATHEMATICA
t=1+2^(1/2); r=(t+(t^2+4)^(1/2))/2
FullSimplify[r]
N[r, 130]
RealDigits[N[r, 130]][[1]]
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Apr 06 2011
STATUS
approved