login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A137615 Decimal expansion of volume of the Meissner Body. 4
4, 1, 9, 8, 6, 0, 0, 4, 5, 9, 6, 5, 0, 8, 0, 2, 2, 3, 3, 4, 2, 1, 3, 0, 0, 0, 0, 9, 6, 8, 3, 3, 8, 2, 7, 9, 1, 6, 5, 0, 7, 0, 3, 3, 5, 0, 8, 8, 6, 5, 1, 2, 1, 8, 5, 3, 1, 9, 4, 5, 1, 2, 3, 5, 8, 5, 9, 5, 0, 8, 3, 2, 4, 2, 3, 7, 9, 8, 3, 2, 2, 2, 4, 6, 5, 4, 2, 4, 9, 4, 4, 8, 4, 0, 2, 1, 2, 5, 2, 5, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The Meissner body is a three-dimensional generalization of the Reuleaux triangle having constant width 1. Although it is based on the Reuleaux tetrahedron, it is different from that. The Meissner body exists in two different versions.

REFERENCES

Johannes Boehm and E. Quaisser, Schoenheit und Harmonie geometrischer Formen - Sphaeroformen und symmetrische Koerper, Berlin: Akademie Verlag (1991), p. 71.

G. D. Chakerian and H. Groemer, Convex Bodies of Constant Width, in: P. Gruber and J. Wills (Editors), Convexity and its Applications, Basel / Boston / Stuttgart: Birkhäuser (1983), p. 68.

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.10 Reuleaux Triangle Constants, p. 513.

LINKS

Table of n, a(n) for n=0..100.

Bernd Kawohl and Christof Weber, Meissner's Mysterious Bodies, Mathematical Intelligencer, Volume 33, Number 3, 2011, pp. 94-101.

SwissEduc: Teaching and Learning Mathematics, Bodies of Constant Width (with informations, animations and interactive pictures of both Meissner bodies)

Eric Weisstein's MathWorld, Reuleaux Triangle

FORMULA

(2/3 - sqrt(3)/4 * arccos(1/3))* Pi.

EXAMPLE

0.4198600...

CROSSREFS

Cf. A102888, A137616, A137617, A137618.

Sequence in context: A105495 A256831 A010644 * A021990 A182545 A084887

Adjacent sequences:  A137612 A137613 A137614 * A137616 A137617 A137618

KEYWORD

cons,easy,nonn

AUTHOR

Christof Weber, Feb 04 2008

EXTENSIONS

Link corrected by Christof Weber, Jan 06 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 17 03:06 EST 2019. Contains 329216 sequences. (Running on oeis4.)