TOPICS
Search

Hexagon Triangle Picking

DOWNLOAD Mathematica NotebookDownload Wolfram Notebook

Hexagon triangle picking considers a triangle formed by three points chosen independently and uniformly inside a regular hexagon of unit area. The mean triangle 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

An explicit probability density function for this random area is given by Philip (2010, pp. 19-20).

See also

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

Explore with Wolfram|Alpha

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.Philip, J. "The Area of a Random Triangle in a Regular Hexagon." Stockholm, Sweden: KTH Royal Institute of Technology, 2010. https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-127518.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, England: F. Hodgson and Son, pp. 100-105, 1867.

Referenced on Wolfram|Alpha

Hexagon Triangle Picking

Cite this as:

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

Subject classifications