A349580 Decimal expansion of the 5-dimensional Steinmetz solid formed by the intersection of 5 unit-diameter 5-dimensional cylinders whose axes are mutually orthogonal and intersect at a single point.

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

Offset

0,2

Comments

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 2^5. The constant here, for a unit-diameter cylinders, is analogous to the 3-dimensional case given by Moore (1974).

Links

Table of n, a(n) for n=0..99.

A. J. Hildebrand, Lingyi Kong, Abby Turner and Ananya Uppal, Applications of n-dimensional Integrals: Random Points, Broken Sticks and Intersecting Cylinders, Illinois Geometry Lab Project Report, University of Illinois at Urbana-Champaign, December 11, 2012.

Lingyi Kong, Luvsandondov Lkhamsuren, Abigail Turner, Aananya Uppal and A. J. Hildebrand, Intersecting Cylinders: From Archimedes and Zu Chongzhi to Steinmetz and Beyond, Illinois Geometry Lab Project Report, University of Illinois at Urbana-Champaign, April 25, 2013.

Moreton Moore, Symmetrical Intersections of Right Circular Cylinders, The Mathematical Gazette, Vol. 58, No. 405 (1974), pp. 181-185.

Formula

Equals 8 * (Pi/12 - arccot(2*sqrt(2))/sqrt(2)).

Example

0.17198723701328857806510936213684483040318641193634...

Mathematica

RealDigits[8 * (Pi/12 - ArcCot[2*Sqrt[2]]/Sqrt[2]), 10, 100][[1]]

Crossrefs

Cf. A101465, A188615, A349577, A349578, A349579.

Sequence in context: A282823 A200500 A199669 * A197019 A048835 A124970

Adjacent sequences: A349577 A349578 A349579 * A349581 A349582 A349583

Keyword

nonn,cons

Author

Amiram Eldar, Nov 22 2021

Status

approved