Affine.Simplex.altitude_def
∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : MetricSpace P]
[inst_3 : NormedAddTorsor V P] {n : ℕ} (s : Affine.Simplex ℝ P n) (i : Fin (n + 1)),
s.altitude i =
AffineSubspace.mk' (s.points i) (affineSpan ℝ (s.points '' {i}ᶜ)).directionᗮ ⊓ affineSpan ℝ (Set.range s.points)The definition of an altitude.
- Defined in
- Mathlib.Geometry.Euclidean.Altitude
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Set.imagestatement · cited by 5,609
- Set.rangestatement · cited by 4,705
- InnerProductSpacestatement and proof · cited by 3,523
- Compl.complstatement · cited by 2,925
- MetricSpacestatement and proof · cited by 1,684
- NormedAddTorsorstatement and proof · cited by 1,325
- AffineSubspacestatement · cited by 871
- Affine.Simplexstatement and proof · cited by 471
- affineSpanstatement · cited by 417
Cited by2
Results whose statement or proof uses this declaration.
- Affine.Simplex.direction_altitudeproof · cited by 4
- Affine.Triangle.altitude_eq_mongePlaneproof · cited by 2