OFFSET
0,1
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 2^4. The constant here, for a unit-diameter cylinders, is analogous to the 3-dimensional case given by Moore (1974).
LINKS
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 3 * (Pi/4 - arctan(sqrt(2))/sqrt(2)).
EXAMPLE
0.32966191362422503979540474867758757134334519333162...
MATHEMATICA
RealDigits[3 * (Pi/4 - ArcTan[Sqrt[2]]/Sqrt[2]), 10, 100][[1]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Nov 22 2021
STATUS
approved