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A188657
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Decimal expansion of (3+sqrt(73))/8.
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0
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1, 4, 4, 3, 0, 0, 0, 4, 6, 8, 1, 6, 4, 6, 9, 1, 3, 9, 5, 9, 8, 3, 9, 5, 6, 0, 4, 0, 7, 7, 9, 9, 6, 3, 3, 0, 4, 3, 2, 4, 3, 0, 6, 9, 1, 6, 1, 9, 1, 6, 6, 0, 2, 8, 0, 2, 3, 8, 5, 8, 1, 4, 0, 6, 7, 2, 1, 4, 5, 6, 1, 0, 2, 4, 1, 5, 9, 1, 2, 2, 9, 7, 6, 3, 5, 1, 2, 1, 5, 0, 3, 7, 6, 3, 3, 7, 6, 1, 7, 8, 7, 0, 0, 0, 7, 9, 0, 8, 1, 5, 8
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OFFSET
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1,2
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COMMENTS
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Decimal expansion of the length/width ratio of a (3/4)-extension rectangle.
See A188640 for definitions of shape and r-extension rectangle for ratio r.
A (3/4)-extension rectangle matches the continued fraction [1,2,3,1,7,1,3,2,1,1,2,3,1,7,1,3,2,...] for the shape L/W= (3+sqrt(73))/8. This is analogous to the matching of a golden rectangle to the continued fraction [1,1,1,1,1,1,1,...]. Specifically, for the (3/4)-extension rectangle, 1 square is removed first, then 2 squares, then 3 squares, then 1 square, then 7 squares,..., so that the original rectangle is partitioned into an infinite collection of squares.
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LINKS
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EXAMPLE
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1.4430004681646...
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MAPLE
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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