trisection point

English

Noun

trisection point (plural trisection points)

1. (geometry) Either of two points which trisect a given line segment.

   The centroid of a triangle is, by definition, the point of intersection of the three medians: moreover, it is a trisection point of each of the medians.

   • 1959 [Doubleday], William R. Gondin, Bernard Sohmer, Intermediate Algebra & Analytic Geometry Made Simple, 1967, W. H. Allen, page 147,

     Find the trisection points of the line $P_4{P}_5$ in the same diagram.

   • 1965, Paul A. White, Vector Analytic Geometry, Dickenson Publishing Company, page 73:

     In triangle $ABC$, let $E$ be the midpoint of $BC$ and $D$ the trisection point of $AC$ nearest $C$.

   • 1998, Paul J. Nahin, An Imaginary Tale: The Story of $\sqrt{-1}$, Princeton University Press, 2010, paperback, page 88,

     And if $\lambda =2$, then $P$ is a trisection point of $P_1{P}_2$ and

     $z=\frac{z_1+2z_2}{3}$.

     Notice that this trisection point is closer to $P_2$ than it is to $P_1$. The other trisection point, the one that is closer to $P_1$ than it is to $P_2$, occurs for $\lambda =\frac{1}{2}$, which gives

     $z=\frac{2z_1+z_2}{3}$.

Translations

either of two points that trisect a line segment

See also

• trisector