Random Polygon

A random polygon is a polygon generated in some random way. Kendall conjectured that the shape of a random polygon is close to a disk as the area of the polygon becomes large (Stoyan et al. 1987, Kovalenko 1999).

See also

Crofton Cell

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Kovalenko, I. N. "Proof of David Kendall's Conjecture Concerning the Shape of Large Random Polygons." Cybern. Sys. Anal. 33, 461-467, 1997.Kovalenko, I. N. "A Simplified Proof of a Conjecture of D. G. Kendall Concerning Shapes of Random Polygons." J. Appl. Math. Stoch. Anal. 12, 301-310, 1999.Miles, R. E. "A Heuristic Proof of a Long-Standing Conjecture of D. G. Kendall Concerning the Shapes of Certain Large Random Polygons." Adv. Appl. Prob. (SGSA) 27, 397-471, 1997.Stoyan, D.; Kendall, W. S.; and Mecke, J. Stochastic Geometry and Its Applications, 2nd ed. New York: Wiley, 1987.

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Random Polygon

Cite this as:

Weisstein, Eric W. "Random Polygon." From MathWorld--A Wolfram Web Resource.

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