A093577 Decimal expansion of (3/4)*sqrt(2).

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

Offset: 1

Author

Eric W. Weisstein, Apr 01 2004

Keywords

• nonn
• cons

Comments

Side length of Prince Rupert's cube: the largest cube that can be passed through a given unit cube (slightly larger than the given cube!).

Examples

			1.060660171779821286601266543157273558927253906532711...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.14, p. 524.
• Clifford A. Pickover, The Math Book, Sterling Publishing Co. (New York), 2009, p. 214.
• D. J. E. Schrek, Prince Rupert's problem and its extension by Pieter Nieuwland, Scripta Math. 16 (1950), pp. 73-80 and 261-267.
• David Wells, Penguin Dictionary of Curious and Interesting Geometry, 1991, p. 195.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Prince Rupert's Cube.
• Index entries for algebraic numbers, degree 2.

Programs

Magma

SetDefaultRealField(RealField(100)); Sqrt(9/8); // G. C. Greubel, Aug 17 2018

Mathematica

RealDigits[3 Sqrt[2]/4, 10, 110][[1]] (* Bruno Berselli, Sep 20 2012 *)

PARI

sqrt(9/8) \\ Charles R Greathouse IV, Nov 26 2014

Formula

Equals Sum_{k>=0} binomial(2*k,k)/36^k. - Amiram Eldar, Aug 04 2022