A336198 Decimal expansion of the radius of a sphere centered on the surface of a unit-radius sphere and dividing it into two parts of equal volume.

1, 2, 2, 8, 5, 4, 4, 8, 6, 3, 7, 3, 5, 2, 2, 0, 9, 0, 3, 4, 4, 8, 9, 9, 4, 4, 9, 7, 6, 8, 5, 2, 9, 3, 4, 6, 5, 6, 4, 4, 1, 9, 1, 6, 4, 5, 5, 1, 8, 6, 0, 2, 6, 4, 1, 5, 9, 0, 8, 1, 9, 5, 2, 4, 5, 1, 0, 9, 7, 2, 7, 2, 3, 4, 4, 6, 8, 8, 4, 6, 7, 2, 9, 6, 0, 0, 7

Offset: 1

Author

Amiram Eldar, Jul 11 2020

Keywords

• nonn
• cons

Comments

The solution to the grazing goat problem in three dimensions.

Examples

			1.228544863735220903448994497685293465644191645518602...
		

Links

• Marshall Fraser, The Grazing Goat in n Dimensions, The Two-Year College Mathematics Journal, Vol. 15, No. 2 (1984), pp. 126-134.
• Mark D. Meyerson, Return of the Grazing Goat in n Dimensions, The College Mathematics Journal, Vol. 15, No. 5 (1984), pp. 430-432.
• Eric Weisstein's World of Mathematics, Goat Problem.
• Wikipedia, Goat problem.

Crossrefs

Cf. A019699, A133731.

Programs

Mathematica

RealDigits[x /. Solve[3*x^4 - 8*x^3 + 8 == 0 && x > 0, {x}, Reals][[1]], 10, 100][[1]]

Formula

The smaller of the 2 real roots of the equation 3*x^4 - 8*x^3 + 8 = 0.