A366185 Decimal expansion of the real root of the quintic equation x^5 + 3*x^4 + 4*x^3 + x -1 = 0.

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

Offset: 0

Author

Mikhail Gaichenkov, Oct 03 2023

Keywords

• nonn
• cons

Comments

The root appears in the problem of minimizing the area of self-intersection of a folded rectangle. A rectangle with sides a, b (a

The unique ratio of sides a/b=T=0.81502370129163... is derived based on the real root of the quintic. If a/b

Examples

			0.45913372331020753...
		

Links

• Mikhail Gaichenkov, Quintic equation with integer coefficients, Math Stackexchange, 2023.
• Mikhail Gaichenkov, Folded rectangle
• Index entries for algebraic numbers, degree 5

Programs

Mathematica

First[RealDigits[Root[#^5 + 3*#^4 + 4*#^3 + # - 1 &, 1], 10, 100]] (* Paolo Xausa, Jun 25 2024 *)

PARI

polrootsreal(x^5 + 3*x^4 + 4*x^3 + x-1)[1]

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