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A366185
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Decimal expansion of the real root of the quintic equation x^5 + 3*x^4 + 4*x^3 + x -1 = 0.
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1
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4, 5, 9, 1, 3, 3, 7, 2, 3, 3, 1, 0, 2, 0, 7, 5, 3, 9, 4, 6, 7, 5, 1, 1, 4, 6, 3, 0, 0, 1, 6, 5, 3, 9, 8, 6, 5, 1, 3, 3, 9, 0, 8, 8, 2, 1, 9, 9, 5, 3, 4, 4, 6, 5, 4, 5, 4, 6, 4, 2, 8, 8, 5, 6, 8, 7, 0, 9, 4, 4, 9, 4, 5, 5, 7, 4, 3, 2, 4, 5, 8, 0, 0, 7, 1, 7, 1, 7, 7, 3, 6, 4, 4, 4, 9, 1, 7, 9, 6, 5, 1, 7, 6, 3, 1, 3, 3, 0
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OFFSET
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0,1
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COMMENTS
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The root appears in the problem of minimizing the area of self-intersection of a folded rectangle. A rectangle with sides a, b (a<b) is folded along the line that passes through the center of the rectangle in order to get the minimum area of crossing intersections: a unique rectangle exists for two solutions with equal area but different shapes - triangle and pentagon.
The unique ratio of sides a/b=T=0.81502370129163... is derived based on the real root of the quintic. If a/b<T ('long' rectangle) the angle to fold is Pi/4. If a/b=1 (square) the angle is Pi/8.
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LINKS
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EXAMPLE
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0.45913372331020753...
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PROG
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(PARI) polrootsreal(x^5 + 3*x^4 + 4*x^3 + x-1)[1]
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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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