Theorems · Theorem · geometry

Affine.Simplex.centroid_mem_median

∀ {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] {n : ℕ} [inst_4 : NeZero n] [CharZero k] (s : Affine.Simplex k P n) (i : Fin (n + 1)),
  s.centroid ∈ s.median i

The centroid lies on the median from any vertex.

Defined in: Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid
Cited by: 1 results in Mathlib
Foundations: Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: DivisionRing AddCommGroup Module AddTorsor NeZero CharZero

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Cites25

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Modulestatement and proof · cited by 20,661
AddCommGroupstatement and proof · cited by 12,871
mul_oneproof · cited by 3,885
Nat.cast_oneproof · cited by 2,501
Nat.cast_zeroproof · cited by 1,870
HVAdd.hVAddproof · cited by 1,820
mul_assocproof · cited by 1,667
AddTorsorstatement and proof · cited by 1,657
DivisionRingstatement and proof · cited by 1,062
CharZerostatement and proof · cited by 932
AffineSubspacestatement and proof · cited by 871
VSub.vsubproof · cited by 817

Cited by1

Results whose statement or proof uses this declaration.

Affine.Simplex.median_eq_line_point_centroidproof · cited by 0