Theorems · Theorem · convex and discrete geometry

Finset.centerMass_pair

∀ {R : Type u_1} {E : Type u_3} {ι : Type u_5} [inst : Field R] [inst_1 : AddCommGroup E] [inst_2 : Module R E]
  (i j : ι) (w : ι → R) (z : ι → E) [inst_3 : DecidableEq ι],
  i ≠ j → {i, j}.centerMass w z = (w i / (w i + w j)) • z i + (w j / (w i + w j)) • z j

Defined in

Mathlib.Analysis.Convex.Combination

Cited by

0 results in Mathlib

Foundations

Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldAddCommGroupModuleDecidableEq