OFFSET
1,2
COMMENTS
The rectangle R whose shape (i.e., length/width) is (1+sqrt(1+2x))/2, where x=sqrt(2), can be partitioned into rectangles of shapes 1 and sqrt(2) in a manner that matches the periodic continued fraction [1, x, 1, x, ...]. R can also be partitioned into squares so as to match the nonperiodic continued fraction [1, 2,11,32,1,4,10,2,1,...] at A190261. For details, see A188635.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
EXAMPLE
1.478318343478515956422104436385022215253...
MATHEMATICA
PROG
(PARI) (1+sqrt(1+2*sqrt(2)))/2 \\ G. C. Greubel, Dec 26 2017
(Magma) [(1+Sqrt(1+2*Sqrt(2)))/2]; // G. C. Greubel, Dec 26 2017
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, May 06 2011
STATUS
approved