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A330934
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Decimal expansion of the area of a sofa that can be moved around a 90-degree turn both to the right and to the left in a hallway of unit width.
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0
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1, 6, 4, 4, 9, 5, 5, 2, 1, 8, 4, 2, 5, 4, 4, 0, 8, 5, 1, 6, 6, 8, 8, 0, 9, 3, 4, 7, 6, 0, 0, 6, 3, 3, 6, 8, 5, 1, 9, 4, 2, 5, 2, 8, 6, 4, 0, 9, 8, 9, 6, 2, 6, 3, 6, 8, 8, 9, 3, 4, 5, 7, 0, 8, 0, 1, 0, 3, 2, 9, 9, 1, 0, 8, 1, 5, 3, 7, 7, 9, 2, 9, 1, 9, 2, 7, 2, 5, 9, 1, 4, 9, 2, 0, 7, 5, 4, 4, 6, 7, 7, 2, 9, 0, 8
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OFFSET
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1,2
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COMMENTS
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According to Dan Romik, this may be the largest possible area of such a sofa. He gives the closed-form formula below for the area of this shape which consists of "18 distinct pieces, each of which is given by a separate formula obtained as the solution of some differential equation." See the D. Romik link for a picture of this shape and animations of this and related sofas.
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LINKS
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FORMULA
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Equals (3 + 2*sqrt(2))^(1/3) + (3 - 2*sqrt(2))^(1/3) - 1 + atan(((sqrt(2) + 1)^(1/3) - (sqrt(2) - 1)^(1/3))/2) [D. Romik].
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EXAMPLE
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1.644955218425440851668809347600633685194252864098962636889345708010329...
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MATHEMATICA
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RealDigits[(3 + 2*Sqrt[2])^(1/3) + (3 - 2*Sqrt[2])^(1/3) - 1 + ArcTan[((Sqrt[2] + 1)^(1/3) - (Sqrt[2] - 1)^(1/3))/2], 10, 120][[1]] (* Amiram Eldar, Jun 18 2023 *)
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PROG
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(PARI) {default(realprecision, 200);
my(sr2 = sqrt(2)); (3+2*sr2)^(1/3) + (3-2*sr2)^(1/3) - 1 + atan(((sr2+1)^(1/3) - (sr2-1)^(1/3))/2)}
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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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