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A349577
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.
3
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, 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, 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
OFFSET
0,1
COMMENTS
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.
This constant was first calculated by Moore (1974).
The corresponding volumes in the analogous cases of 2 and 3 mutually orthogonal cylinders are 2/3 (A010722) and 2 - sqrt(2) (A101465), respectively.
LINKS
Paul Bourke, Intersecting cylinders, 2003-2016.
Moreton Moore, Symmetrical Intersections of Right Circular Cylinders, The Mathematical Gazette, Vol. 58, No. 405 (1974), pp. 181-185.
Eric Weisstein's World of Mathematics, Steinmetz Solid.
Wikipedia, Steinmetz solid.
FORMULA
Equals (3/2) * sqrt(2) * (2 - sqrt(3)).
EXAMPLE
0.56840607294451799910914006057025714776009440514583...
MATHEMATICA
RealDigits[(3/2) * Sqrt[2] * (2 - Sqrt[3]), 10, 100][[1]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Nov 22 2021
STATUS
approved