A perimeter-bisecting segment of a polygon originating from the midpoint of one side. Each cleaver , , and in a triangle is parallel to an angle bisector of the triangle (shown as dashed lines above). In addition, the three cleavers concur in a point known as the cleavance center, which is the Spieker center, i.e., incenter of the medial triangle (Honsberger 1995, p. 2).
Cleaver
See also
B-Line, Cleavance Center, Medial Triangle, Midpoint, SplitterExplore with Wolfram|Alpha
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.Referenced on Wolfram|Alpha
CleaverCite this as:
Weisstein, Eric W. "Cleaver." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Cleaver.html