trisection point
التعريفات والمعاني
== English ==
=== Noun ===
trisection point (plural trisection points)
(geometry) Either of two points which trisect a given line segment.
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
{\displaystyle P_{4}P_{5}}
in the same diagram.
1998, Paul J. Nahin, An Imaginary Tale: The Story of
−
1
{\displaystyle {\sqrt {-1}}}
, Princeton University Press, 2010, paperback, page 88,
And if
λ
=
2
{\displaystyle \lambda =2}
, then
P
{\displaystyle P}
is a trisection point of
P
1
P
2
{\displaystyle P_{1}P_{2}}
and
z
=
z
1
+
2
z
2
3
{\displaystyle z={\frac {z_{1}+2z_{2}}{3}}}
.
Notice that this trisection point is closer to
P
2
{\displaystyle P_{2}}
than it is to
P
1
{\displaystyle P_{1}}
. The other trisection point, the one that is closer to
P
1
{\displaystyle P_{1}}
than it is to
P
2
{\displaystyle P_{2}}
, occurs for
λ
=
1
2
{\displaystyle \lambda ={\tfrac {1}{2}}}
, which gives
z
=
2
z
1
+
z
2
3
{\displaystyle z={\frac {2z_{1}+z_{2}}{3}}}
.
==== Translations ====
=== See also ===
trisector