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%I #18 Aug 04 2022 05:54:27
%S 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,
%T 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,
%U 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
%N Decimal expansion of (3/4)*sqrt(2).
%C 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!).
%D Clifford A. Pickover, The Math Book, Sterling Publishing Co. (New York), 2009, p. 214.
%D D. J. E. Schrek, Prince Rupert's problem and its extension by Pieter Nieuwland, Scripta Math. 16 (1950), pp. 73-80 and 261-267.
%D David Wells, Penguin Dictionary of Curious and Interesting Geometry, 1991, p. 195.
%H G. C. Greubel, <a href="/A093577/b093577.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrinceRupertsCube.html">Prince Rupert's Cube</a>.
%F Equals Sum_{k>=0} binomial(2*k,k)/36^k. - _Amiram Eldar_, Aug 04 2022
%e 1.060660171779821286601266543157273558927253906532711...
%t RealDigits[3 Sqrt[2]/4, 10, 110][[1]] (* _Bruno Berselli_, Sep 20 2012 *)
%o (PARI) sqrt(9/8) \\ _Charles R Greathouse IV_, Nov 26 2014
%o (Magma) SetDefaultRealField(RealField(100)); Sqrt(9/8); // _G. C. Greubel_, Aug 17 2018
%K nonn,cons
%O 1,3
%A _Eric W. Weisstein_, Apr 01 2004
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