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Cleaver


Cleavers

A perimeter-bisecting segment of a polygon originating from the midpoint of one side. Each cleaver M_1C_1, M_2C_2, and M_3C_3 in a triangle DeltaA_1A_2A_3 is parallel to an angle bisector of the triangle (shown as dashed lines above). In addition, the three cleavers concur in a point S known as the cleavance center, which is the Spieker center, i.e., incenter of the medial triangle (Honsberger 1995, p. 2).


See also

B-Line, Cleavance Center, Medial Triangle, Midpoint, Splitter

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References

Avishalom, D. "Perimeter-Bisectors in a Triangle" [Hebrew]. Riveon Lematematika 13, 46-49, 1959.Avishalom, D. "The Perimetric Bisection of Triangles." Math. Mag. 36, 60-62, 1963.Honsberger, R. "Cleavers and Splitters." Episodes in Nineteenth and Twentieth Century Euclidean Geometry. Washington, DC: Math. Assoc. Amer., pp. 1-14, 1995.Jarden, D. "Synthetical Proof for the Theorem on the Center of Perimeter-Bisectors in a Triangle" [Hebrew]. Riveon Lematematika 13, 50, 1959.

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Cleaver

Cite this as:

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

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