Isovolume Problem
المؤلف:
Bogomolny, A
المصدر:
"Isoperimetric Theorem and Inequality." http://www.cut-the-knot.org/do_you_know/isoperimetric.shtml.
الجزء والصفحة:
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12-10-2018
2302
Isovolume Problem
Find the surface enclosing the maximum volume per unit surface area, 
. The solution is a sphere, which has
The fact that a sphere solves the isovolume problem was only proved as recently as 1882 by Schwarz (Haas 2000).
REFERENCES:
Bogomolny, A. "Isoperimetric Theorem and Inequality." http://www.cut-the-knot.org/do_you_know/isoperimetric.shtml.
Haas, J. "General Double Bubble Conjecture in 
Solved." Focus: The Newsletter of the Math. Assoc. Amer., No. 5, pp. 4-5, May/June 2000.
Isenberg, C. "The Maximum Volume Contained by a Closed Surface of Fixed Area." Appendix VI in The Science of Soap Films and Soap Bubbles. New York: Dover, pp. 174-177, 1992.
Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, p. 214, 1999.
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