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Minimal Enclosing Circle


The minimal enclosing circle problem, sometimes also known as the bomb problem, is the problem of finding the circle of smallest radius that contains a given set of points in its interior or on its boundary. This smallest circle is known as the minimal enclosing circle.

Jung's theorem states that every finite set of points with geometric span d has an enclosing circle with radius no greater than d/sqrt(3).


See also

Circumcircle, Enclosing Circle, Jung's Theorem, Obtuse Triangle

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References

Chrystal. "On the Problem to Construct the Minimum Circle Enclosing n Given Points in a Plane." Proc. Edinburgh Math. Soc., Third Meeting, p. 30, Jan 9, 1885.Dyer, M. and Megiddo, N. "Linear Programming in Low Dimensions." Ch. 38 in Handbook of Discrete and Computational Geometry (Ed. J. E. Goodman and J. O'Rourke). Boca Raton, FL: CRC Press, pp. 669-710, 1997.Elisoff, J. and Unger, R. "Minimal Enclosing Circle Problem." Oct. 1998. http://www.cs.mcgill.ca/~cs507/projects/1998/jacob/problem.html.Goodman, J. E. and O'Rourke, J. Handbook of Discrete and Computational Geometry. Boca Raton, FL: CRC Press, 1997.Megiddo, N. "Linear-Time Algorithms for Linear Programming in R^3 and Related Problems." SIAM J. Comput. 12, 759-776, 1983.Preparata, F. R. and Shamos, M. I. Computational Geometry: An Introduction. New York: Springer-Verlag, 1985.Rademacher, H. and Toeplitz, O. The Enjoyment of Mathematics: Selections from Mathematics for the Amateur. Princeton, NJ: Princeton University Press, 1957.Skyum, S. "A Simple Algorithm for Computing the Smallest Enclosing Circle." Inform. Proc. Lett. 3, 121-125, 1991.

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Minimal Enclosing Circle

Cite this as:

Weisstein, Eric W. "Minimal Enclosing Circle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MinimalEnclosingCircle.html

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