The minimal enclosing circle of a set of points is the circle of smallest radius that contains every point in its interior or on its boundary.
Finding this circle is the minimal
enclosing circle problem, sometimes also known as the bomb problem or smallest
circle problem.
Jung's theorem states that every finite set of points with geometric span has an enclosing circle
with radius no greater than .
The minimal enclosing circle of a set of points can be found in the Wolfram Language using BoundingRegion[pts,
"MinDisk"].
Chrystal, Prof. "On the Problem to Construct the Minimum Circle Enclosing Given Points in a Plane." Proc. Edinburgh Math. Soc.3,
30-33, Feb. 1884.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.htmlGoodman,
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 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.
has an enclosing circle
with radius no greater than 
.
Given Points in a Plane." Proc. Edinburgh Math. Soc. 3,
30-33, Feb. 1884.Dyer, M. and Megiddo, N. "Linear Programming
in Low Dimensions." Ch. 38 in 
and Related Problems." SIAM J. Comput. 12,
759-776, 1983.Preparata, F. R. and Shamos, M. I.