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A272487
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Decimal expansion of the edge length of a regular heptagon with unit circumradius.
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9
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8, 6, 7, 7, 6, 7, 4, 7, 8, 2, 3, 5, 1, 1, 6, 2, 4, 0, 9, 5, 1, 5, 3, 6, 6, 6, 5, 6, 9, 6, 7, 1, 7, 5, 0, 9, 2, 1, 9, 9, 8, 1, 4, 5, 5, 5, 7, 4, 9, 1, 9, 7, 5, 2, 8, 8, 9, 0, 9, 4, 6, 0, 7, 0, 6, 4, 4, 0, 6, 5, 0, 3, 3, 0, 6, 3, 9, 6, 8, 4, 3, 0, 4, 1, 5, 6, 8, 0, 4, 3, 5, 4, 8, 9, 1, 2, 2, 0, 4, 1, 7, 7, 4, 8, 8
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OFFSET
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0,1
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COMMENTS
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The edge length e(m) of a regular m-gon is e(m) = 2*sin(Pi/m). In this case, m = 7, and the constant, a = e(7), is the smallest m for which e(m) is not constructible using a compass and a straightedge (see A004169). With an odd m, in fact, e(m) would be constructible only if m were a Fermat prime (A019434).
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LINKS
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FORMULA
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Equals 2*sin(Pi/7) = 2*cos(Pi*5/14).
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EXAMPLE
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0.8677674782351162409515366656967175092199814555749197528890946...
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MATHEMATICA
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RealDigits[2*Sin[Pi/7], 10, 120][[1]] (* Harvey P. Dale, Mar 07 2020 *)
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PROG
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(PARI) 2*sin(Pi/7)
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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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