Multisection
Multisection of a mathematical quantity or figure is division of it into a number of (usually) equal parts. Division of a quantity into two equal parts is known as bisection, and into three equal parts is known as trisection.
The coordinates of the first n-multisection of a line segment with endpoints given in trilinear coordinates by alpha_1:beta_1:gamma_1 and alpha_2:beta_2:gamma_2 is alpha:beta:gamma, where
alpha = naalpha_1alpha_2+b[alpha_2beta_1+(n-1)alpha_1beta_2]+c[alpha_2gamma_1+(n-1)alpha_1gamma_2]
(1)
beta = a[alpha_1beta_2+(n-1)alpha_2beta_1]+nbbeta_1beta_2+c[beta_2gamma_1+(n-1)beta_1gamma_2]
(2)
gamma = a[alpha_1gamma_2+(n-1)alpha_2gamma_1]+b[beta_1gamma_2+(n-1)beta_2gamma_1]+ncgamma_1gamma_2.
(3)
See also
Bisection, Midpoint, Series Multisection, TrisectionExplore with Wolfram|Alpha
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Cite this as:
Weisstein, Eric W. "Multisection." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Multisection.html