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Hexagon Triangle Picking

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The mean triangle area of a triangle picked inside a regular hexagon with unit area is A^_=289/3888 (Woolhouse 1867, Pfiefer 1989). This is a special case of a general polygon triangle picking result due to Alikoski (1939).

HexagonTrianglePickingDistribution

The distribution of areas, illustrated above, is apparently not known exactly.

See also

Disk Triangle Picking, Pentagon Triangle Picking, Polygon Triangle Picking, Square Triangle Picking, Sylvester's Four-Point Problem, Triangle Triangle Picking

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References

Alikoski, H. A. "Über das Sylvestersche Vierpunktproblem." Ann. Acad. Sci. Fenn. 51, No. 7, 1-10, 1939.Pfiefer, R. E. "The Historical Development of J. J. Sylvester's Four Point Problem." Math. Mag. 62, 309-317, 1989.Solomon, H. Geometric Probability. Philadelphia, PA: SIAM, p. 114, 1978.Woolhouse, W. S. B. "Question 2471" Mathematical Questions, with Their Solutions, from the Educational Times, Vol. 8. London: F. Hodgson and Son, pp. 100-105, 1867.

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Hexagon Triangle Picking

Cite this as:

Weisstein, Eric W. "Hexagon Triangle Picking." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HexagonTrianglePicking.html

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