Affine.Simplex.median_eq_line_point_centroid
∀ {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.median i = line[k, s.points i, s.centroid]The median of a simplex is the line through the vertex and the centroid.
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- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
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- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- le_antisymmproof · cited by 2,068
- HVAdd.hVAddproof · cited by 1,820
- AddTorsorstatement and proof · cited by 1,657
- one_smulproof · cited by 1,374
- DivisionRingstatement and proof · cited by 1,062
- CharZerostatement and proof · cited by 932
- AffineSubspacestatement and proof · cited by 871
- VSub.vsubproof · cited by 817
- Affine.Simplexstatement and proof · cited by 471
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