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Search: id:A137618
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| A137618 |
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Decimal expansion of surface area of the solid of revolution generated by a Reuleaux triangle rotated around one of its symmetry axes. |
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+0
4
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| 2, 9, 9, 3, 3, 1, 7, 1, 7, 3, 4, 8, 3, 1, 3, 3, 6, 0, 3, 9, 8, 0, 4, 5, 6, 4, 3, 3, 2, 6, 6, 9, 5, 5, 3, 8, 9, 9, 5, 6, 4, 3, 8, 9, 9, 6, 3, 3, 6, 6, 1, 4, 7, 6, 6, 4, 7, 8, 7, 7, 2, 7, 2, 5, 8, 7, 5, 6, 1, 7, 8, 7, 1, 7, 6, 6, 0, 1, 6, 2, 4, 9, 5, 8, 8, 8, 1, 1, 8, 4, 9, 4, 4, 4, 7, 1, 6, 7, 2, 5, 3
(list; cons; graph; listen)
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OFFSET
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1,1
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COMMENT
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The rotated Reuleaux triangle is not only a surface of constant width, it is the minimum area surface of revolution width constant width (Campi et al. 1996).
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REFERENCES
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St. Campi, A. Colesanti and P. Gronchi, Minimum problems for volumes of convex bodies, Partial Differential Equations and Applications - Collected Papers in Honor of Carlo Pucci, Marcel Dekker (1996), pp. 43-55.
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LINKS
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SwissEduc: Teaching and Learning Mathematics, Gleichdick - Koerper konstanter Breite (in German)
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FORMULA
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2 * Pi - Pi^2 /3
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EXAMPLE
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2.99331717...
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MATHEMATICA
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k1[x_] := Sqrt[1 - (x - Sqrt[3]/2)^2]; k2[x_] := Sqrt[1 - x^2] - 1/2; 2*Pi*Integrate[k1[x]*Sqrt[1+D[k1[x], x]^2], {x, Sqrt[3]/2-1, 0}] + 2*Pi*Integrate[k2[x]*Sqrt[1+D[k2[x], x]^2], {x, 0, Sqrt[3]/2}]
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CROSSREFS
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Cf. A102888, A137615, A137616, A137617.
Sequence in context: A011072 A019702 A023400 this_sequence A021338 A021889 A016643
Adjacent sequences: A137615 A137616 A137617 this_sequence A137619 A137620 A137621
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KEYWORD
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cons,easy,nonn
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AUTHOR
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Christof Weber (christof.weber(AT)igb.uzh.ch), Feb 04 2008
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