

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
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OFFSET

0,1


COMMENTS

The Meissner body is a threedimensional 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: BirkhĂ¤user (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. 94101.
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



