A349577 - OEIS

%I #6 Nov 22 2021 08:09:02

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

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

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

%N Decimal expansion of the volume of the solid formed by the intersection of 4 right circular unit-diameter cylinders whose axes pass through the diagonals of a cube.

%C Equivalently, the axes of the cylinders can be placed along the lines joining the vertices of a regular tetrahedron with the centers of the faces on the opposite sides.

%C This constant was first calculated by Moore (1974).

%C The corresponding volumes in the analogous cases of 2 and 3 mutually orthogonal cylinders are 2/3 (A010722) and 2 - sqrt(2) (A101465), respectively.

%H Paul Bourke, <a href="http://paulbourke.net/geometry/cylinders/">Intersecting cylinders</a>, 2003-2016.

%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.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SteinmetzSolid.html">Steinmetz Solid</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Steinmetz_solid">Steinmetz solid</a>.

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

%e 0.56840607294451799910914006057025714776009440514583...

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

%Y Cf. A010722, A101465, A349578, A349579, A349580.

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, Nov 22 2021