Affine.Simplex.reflection_circumcenter_eq_affineCombination_of_pointsWithCircumcenter
∀ {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) {i₁ i₂ : Fin (n + 1)},
i₁ ≠ i₂ →
(EuclideanGeometry.reflection (affineSpan ℝ (s.points '' {i₁, i₂}))) s.circumcenter =
(Finset.affineCombination ℝ Finset.univ s.pointsWithCircumcenter)
(Affine.Simplex.reflectionCircumcenterWeightsWithCircumcenter i₁ i₂)The reflection of the circumcenter of a simplex in an edge, in
terms of pointsWithCircumcenter.
- Defined in
- Mathlib.Geometry.Euclidean.Circumcenter
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites63
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Submodulestatement · cited by 7,192
- Set.imagestatement and proof · cited by 5,609
- Finset.sumproof · cited by 5,195
- InnerProductSpacestatement and proof · cited by 3,523
- Finset.univstatement and proof · cited by 3,473
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- Finset.cardproof · cited by 2,327
Cited by1
Results whose statement or proof uses this declaration.
- Affine.Triangle.dist_orthocenter_reflection_circumcenterproof · cited by 3