trisection point

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

     Find the trisection points of the line ${\displaystyle P_{4}P_{5}}$ in the same diagram.

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

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

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

     And if ${\displaystyle \lambda =2}$, then ${\displaystyle P}$ is a trisection point of ${\displaystyle P_{1}P_{2}}$ and

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

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

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

• trisector