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Decimal expansion of the 4-dimensional Steinmetz solid formed by the intersection of 4 unit-diameter 4-dimensional cylinders whose axes are mutually orthogonal and intersect at a single point.
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%I #5 Nov 22 2021 08:09:18

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

%T 7,1,3,4,3,3,4,5,1,9,3,3,3,1,6,2,1,3,6,0,5,7,0,3,3,9,9,0,0,0,0,2,9,4,

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

%N Decimal expansion of the 4-dimensional Steinmetz solid formed by the intersection of 4 unit-diameter 4-dimensional cylinders whose axes are mutually orthogonal and intersect at a single point.

%C The constant given by Hildebrand et al. (2012) and Kong et al. (2013) is for unit-radius cylinders, and is thus larger by a factor of 2^4. The constant here, for a unit-diameter cylinders, is analogous to the 3-dimensional case given by Moore (1974).

%H A. J. Hildebrand, Lingyi Kong, Abby Turner and Ananya Uppal, <a href="https://conf.math.illinois.edu/igl/Projects-Fall2012/Hildebrand2/report.pdf">Applications of n-dimensional Integrals: Random Points, Broken Sticks and Intersecting Cylinders</a>, Illinois Geometry Lab Project Report, University of Illinois at Urbana-Champaign, December 11, 2012.

%H Lingyi Kong, Luvsandondov Lkhamsuren, Abigail Turner, Aananya Uppal and A. J. Hildebrand, <a href="https://faculty.math.illinois.edu/~hildebr/ugresearch/cylinder-spring2013report.pdf">Intersecting Cylinders: From Archimedes and Zu Chongzhi to Steinmetz and Beyond</a>, Illinois Geometry Lab Project Report, University of Illinois at Urbana-Champaign, April 25, 2013.

%H Moreton Moore, <a href="http://www.jstor.org/stable/3615957">Symmetrical Intersections of Right Circular Cylinders</a>, The Mathematical Gazette, Vol. 58, No. 405 (1974), pp. 181-185.

%F Equals 3 * (Pi/4 - arctan(sqrt(2))/sqrt(2)).

%e 0.32966191362422503979540474867758757134334519333162...

%t RealDigits[3 * (Pi/4 - ArcTan[Sqrt[2]]/Sqrt[2]), 10, 100][[1]]

%Y Cf. A101465, A195696, A349577, A349578, A349580.

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, Nov 22 2021