OFFSET
1,2
COMMENTS
Decimal expansion of the length/width ratio of a (2/e)-extension rectangle. See A188640 for definitions of shape and r-extension rectangle.
A (2/e)-extension rectangle matches the continued fraction [1,2,3,3,1,15,1,3,7,1,2,4,...] for the shape L/W=(1+sqrt(1+e^2))/e. This is analogous to the matching of a golden rectangle to the continued fraction [1,1,1,1,1,1,1,1,...]. Specifically, for the (2/e)-extension rectangle, 1 square is removed first, then 2 squares, then 3 square2, then 3 squares,..., so that the original rectangle of shape (1+sqrt(1+e^2))/e is partitioned into an infinite collection of squares.
EXAMPLE
1.433400573405154846331906919976752328843391...
MATHEMATICA
r = 2/E; t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
ContinuedFraction[t, 120]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Apr 12 2011
STATUS
approved