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 α_1 :β_1 :γ_1 and α_2 :β_2 :γ_2 is α:β:γ, where α | = | n a α_1 α_2 + b[α_2 β_1 + (n - 1) α_1 β_2] + c[α_2 γ_1 + (n - 1) α_1 γ_2] β | = | a[α_1 β_2 + (n - 1) α_2 β_1] + n b β_1 β_2 + c[β_2 γ_1 + (n - 1) β_1 γ_2] γ | = | a[α_1 γ_2 + (n - 1) α_2 γ_1] + b[β_1 γ_2 + (n - 1) β_2 γ_1] + n c γ_1 γ_2.

bisection | midpoint | series multisection | trisection