Triangulation -- Proof by Induction

• now prove that any triangulation of P consists of n-2 triangles:
• m₁ + m₂ = n + 2    (P₁ and P₂ share two vertices)
• by induction, any triangulation of P_i consists of m_i-2 triangles
• therefore, any triangulation of P consists of    (m₁ - 2) + (m₂ - 2) = n - 2 triangles

back