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A258403
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Decimal expansion of the area of the regular 10-gon (decagon) of circumradius = 1.
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2
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2, 9, 3, 8, 9, 2, 6, 2, 6, 1, 4, 6, 2, 3, 6, 5, 6, 4, 5, 8, 4, 3, 5, 2, 9, 7, 7, 3, 1, 9, 5, 3, 6, 3, 8, 4, 2, 9, 8, 8, 2, 6, 2, 1, 8, 8, 2, 1, 5, 7, 2, 9, 9, 5, 5, 3, 6, 1, 3, 6, 2, 4, 0, 3, 7, 8, 6, 3, 9, 2, 3, 7, 0, 8, 1, 1, 7, 5, 9, 7, 8, 7, 5, 4, 2, 5, 2, 0, 2, 4, 9, 3, 1, 3, 7, 0, 6, 6, 7, 9, 8
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OFFSET
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1,1
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COMMENTS
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Quartic number of degree 4 and denominator 2; minimal polynomial 16x^4 - 500x^2 + 3125. - Charles R Greathouse IV, Apr 20 2016
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LINKS
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Eric Weisstein's MathWorld, Decagon
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FORMULA
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Equals (5/2)*sqrt((5-sqrt(5))/2).
Area formulas from triangle to dodecagon, with circumradius 1:
n-gon area(n) = (1/2)*n*sin(2*Pi/n)
3-gon (3*sqrt(3))/4
4-gon 2
5-gon (5/4)*sqrt((5+sqrt(5))/2)
6-gon (3*sqrt(3))/2
7-gon (7/2)*cos((3*Pi)/14)
8-gon 2*sqrt(2)
9-gon (9/2)*sin((2*Pi)/9)
10-gon (5/2)*sqrt((5-sqrt(5))/2)
11-gon (11/2)*sin((2*Pi)/11)
12-gon 3
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EXAMPLE
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2.9389262614623656458435297731953638429882621882157299553613624...
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MATHEMATICA
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RealDigits[(5/2)*Sqrt[(5 - Sqrt[5])/2], 10, 101] // First
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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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