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A186282
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Decimal expansion of non-right-angle, in degrees, of unique 14th class of convex pentagonal tiling.
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1
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1, 1, 0, 6, 7, 6, 6, 7, 2, 5, 2, 3, 0, 0, 7, 1, 1, 8, 6, 2, 9, 1, 9, 7, 5, 2, 4, 0, 3, 3, 8, 6, 5, 8, 7, 0, 8, 0, 5, 4, 8, 8, 6, 7, 1, 8, 6, 5, 1, 6, 2, 4, 0, 5, 4, 8, 9, 9, 0, 7, 3, 8, 9, 5, 3, 5, 0, 7, 7, 2, 9, 7, 6, 8, 1, 5, 5, 9, 6, 6, 8, 5, 3, 4, 8, 5, 2, 2, 5, 2, 5, 3, 4, 9, 5, 3, 1, 7, 6, 2
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OFFSET
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3,4
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COMMENTS
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These are the 5 angles, in radians and in degrees:
A = Pi/2 = 90 deg,
B = Pi/2 + arccos((sqrt(57)-3)/8) = 145.338336261... deg,
C = Pi - 2*arccos((sqrt(57)-3)/8) = 69.323327476... deg,
D = Pi - arccos((sqrt(57)-3)/8) = 124.661663738... deg,
E = 2*arccos((sqrt(57)-3)/8) = 110.676672523... deg.
Ratios of sides are AB:BC:CD:DE:EA = d:1:2:2:1 with d = sqrt(22*sqrt(57)-50)/4 = 2.693700493... (End)
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REFERENCES
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Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, 1999.
Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, pp. 177-179, 208, and 211, 1991.
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LINKS
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FORMULA
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EXAMPLE
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110.676672523... degrees.
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MATHEMATICA
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2*ArcCos[(Sqrt[57]-3)/8]*180/Pi // RealDigits[#, 10, 100]& // First (* Jean-François Alcover, Mar 09 2013 *)
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PROG
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(PARI) solve(x=Pi, Pi/2, 3*cos(x/2) + 2*cos(x) - 1)*180/Pi \\ Michel Marcus, Aug 19 2019
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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