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 $\lambda ={\tfrac {1}{2}}$, which gives

     $z={\frac {2z_{1}+z_{2}}{3}}$.

Translations

either of two points that trisect a line segment

See also

• trisector