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Steiner Curvature Centroid

A Steiner curvature centroid is the geometric centroid of the system obtained by placing a mass equal to the magnitude of the exterior angle at each vertex (Honsberger 1995, p. 120). This property was suggested to Honsberger by a reviewer who confused it with the true Steiner point X_(99). The Steiner curvature centroid is Kimberling center X_(1115), and has triangle center function

alpha=(pi-A)/a,

making it a transcendental center.

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References

Honsberger, R. "The Steiner Point and the Tarry Point." §10.5 in Episodes in Nineteenth and Twentieth Century Euclidean Geometry. Washington, DC: Math. Assoc. Amer., pp. 119-124, 1995.Kimberling, C. "Encyclopedia of Triangle Centers: X(1115)=Steiner Curvature Centroid." https://faculty.evansville.edu/ck6/encyclopedia/ETCPart2.html#X1115.

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Steiner Curvature Centroid

Cite this as:

Weisstein, Eric W. "Steiner Curvature Centroid." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SteinerCurvatureCentroid.html

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