On the problem to construct the minimum circle enclosing n given points in a plane

Chrystal

doi:10.1017/S0013091500037238

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If we consider the circle circumscribing any triangle ABC (see figures 11, 12), and diminish its radius still causing it to pass through A and B: then if ACB be an acute angle, C passes without the circle, but if ACB be an obtuse angle, C remains within the circle. If C be a right angle, the radius of the circle, being ½AB, cannot be farther diminished.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Drezner, Zvi 1983. Constrained Location Problems in the Plane and on a Sphere. IIE Transactions, Vol. 15, Issue. 4, p. 300.

Austin, Robert F. 1984. Spatial Statistics and Models. p. 293.

Melville, Robert C. 1985. Computational Geometry. Vol. 2, Issue. , p. 267.

Oommen, B. John 1986. A Learning Automaton Solution to the Stochastic Minimum-Spanning Circle Problem. IEEE Transactions on Systems, Man, and Cybernetics, Vol. 16, Issue. 4, p. 598.

Chen, R. and Handler, G. Y. 1987. Relaxation method for the solution of the minimax location-allocation problem in euclidean space. Naval Research Logistics, Vol. 34, Issue. 6, p. 775.

Jadhav, Shreesh Mukhopadhyay, Asish and Bhattacharya, Binay 1992. Foundations of Software Technology and Theoretical Computer Science. Vol. 652, Issue. , p. 92.

Mezei, Mihaly 1997. Optimal position of solute for simulations. Journal of Computational Chemistry, Vol. 18, Issue. 6, p. 812.

Boltyanski, V. Martini, H. and Soltan, V. 1999. Geometric Methods and Optimization Problems. Vol. 4, Issue. , p. 231.

Hearn, Donald W. 2001. Encyclopedia of Optimization. p. 2398.

Plastria, Frank 2002. Facility Location. p. 37.

Bernasconi, A. and Papadopoulos, I.V. 2005. Efficiency of algorithms for shear stress amplitude calculation in critical plane class fatigue criteria. Computational Materials Science, Vol. 34, Issue. 4, p. 355.

Liu, Shunjia Zeng, Yi and Hu, Bo 2008. Minimum Spanning Circle Method for Using Spare Subcarriers in PAPR Reduction of OFDM Systems. IEEE Signal Processing Letters, Vol. 15, Issue. , p. 513.

Cera, M. Mesa, J. A. Ortega, F. A. and Plastria, F. 2008. Locating a Central Hunter on the Plane. Journal of Optimization Theory and Applications, Vol. 136, Issue. 2, p. 155.

Yildirim, E. Alper 2008. Two Algorithms for the Minimum Enclosing Ball Problem. SIAM Journal on Optimization, Vol. 19, Issue. 3, p. 1368.

Hearn, Donald W. 2008. Encyclopedia of Optimization. p. 3607.

Chen, Doron and Chen, Reuven 2009. New relaxation-based algorithms for the optimal solution of the continuous and discrete p-center problems. Computers & Operations Research, Vol. 36, Issue. 5, p. 1646.

Dieudonné, Yoann and Petit, Franck 2009. Algorithmic Aspects of Wireless Sensor Networks. Vol. 5804, Issue. , p. 230.

Dearing, P.M. and Zeck, Christiane R. 2009. A dual algorithm for the minimum covering ball problem in. Operations Research Letters, Vol. 37, Issue. 3, p. 171.

Drezner, Zvi 2011. Foundations of Location Analysis. Vol. 155, Issue. , p. 63.

Dieudonné, Yoann and Petit, Franck 2012. Self-stabilizing gathering with strong multiplicity detection. Theoretical Computer Science, Vol. 428, Issue. , p. 47.

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On the problem to construct the minimum circle enclosing n given points in a plane

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