Theorems · Theorem · geometry

Finset.centroid_pair

∀ (k : Type u_1) {V : Type u_2} {P : Type u_3} [inst : DivisionRing k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
  [inst_3 : AddTorsor V P] {ι : Type u_4} [inst_4 : DecidableEq ι] [Invertible 2] (p : ι → P) (i₁ i₂ : ι),
  Finset.centroid k {i₁, i₂} p = 2⁻¹ • (p i₂ -ᵥ p i₁) +ᵥ p i₁

The centroid of two points, expressed directly as adding a vector to a point.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Centroid

Cited by

1 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleAddTorsorDecidableEqInvertible