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.

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

Author

Amiram Eldar, Nov 22 2021

Keywords

• nonn
• cons

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.

Examples

			0.56840607294451799910914006057025714776009440514583...
		

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.

Crossrefs

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

Programs

Mathematica

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

Formula

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