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%I #6 Dec 13 2019 16:29:57
%S 1,8,9,5,6,4,3,9,2,3,7,3,8,9,6,0,0,0,1,6,4,7,0,1,1,7,9,8,4,3,2,0,0,2,
%T 1,2,2,2,4,6,1,1,4,1,4,4,1,9,1,9,9,2,9,7,5,6,5,1,8,1,0,5,3,0,9,7,6,7,
%U 1,7,1,0,6,3,8,6,9,4,2,7,2,1,6,5,1,0,9,0,3,8,9,8,7,3,3,6,1,2,5,8,1,6,9,4,0,0,2,2,6,3,4,9,3,9,6,4,3,5,2,1
%N Decimal expansion of (3+sqrt(21))/4.
%C The rectangle R whose shape (i.e., length/width) is (3+sqrt(21))/4, can be partitioned into rectangles of shapes 3/2 and 2 in a manner that matches the periodic continued fraction [3/2, 2, 3/2, 2, ...]. R can also be partitioned into squares so as to match the periodic continued fraction [1,1,8,1,1,2,1,1,8,1,1,2,,...]. For details, see A188635.
%e 1.895643923738960001647011798432002122246...
%t FromContinuedFraction[{3/2, 2, {3/2, 2}}]
%t ContinuedFraction[%, 100] (* [1,1,8,1,1,2,... *)
%t RealDigits[N[%%, 120]] (* A190289 *)
%t N[%%%, 40]
%t RealDigits[(3+Sqrt[21])/4,10,120][[1]] (* _Harvey P. Dale_, Dec 13 2019 *)
%Y A188635.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, May 07 2011
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