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Triangle Circumscribing


Every convex body B in the Euclidean plane with area A can be inscribed in a triangle of area at most equal to 2A (Gross 1918, Eggleston 1957). The worst possible fit corresponds (exclusively) to the case that B is a parallelogram.


See also

Tetrahedron Circumscribing

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References

Bonnesen, T. and Fenchel, W. Theory of Convex Bodies. BCS Associates, pp. 81-93, 1987.Eggleston, H. G. Problems in Euclidean Space: Applications of Convexity. New York: Pergamon, pp. 149-160, 1957.Fejes-Tóth, L. "Eine Bemerkung zur Approximation durch n-Eckringe." Compositio Math. 7, 474-476, 1940.Finch, S. R. "Geometric Probability Constants." §8.1 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 479-484, 2003.Gross, W. "Über affine Geometrie XIII: Eine Minimumeigenschaft der Ellipse und des Ellipsoids." Berichte über die Verhandlungen der Königlich Sächsischen Gesellschaft der Wissenschaften zu Leipzig, Math.-Phys. Kl. 70, 38-54, 1918.Hodges, J. L. "An Extremal Problem of Geometry." J. London Math. Soc. 26, 311-312, 1951.

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Triangle Circumscribing

Cite this as:

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

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