Affine.Simplex.orthogonalProjection_eq_circumcenter_of_dist_eq
∀ {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) {p : P} {r : ℝ},
(∀ (i : Fin (n + 1)), dist (s.points i) p = r) → ↑(s.orthogonalProjectionSpan p) = s.circumcenterIf a point has the same distance from all vertices of a simplex, the orthogonal projection of that point onto the subspace spanned by that simplex is its circumcenter.
- Defined in
- Mathlib.Geometry.Euclidean.Circumcenter
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Submodulestatement · cited by 7,192
- Set.rangestatement · cited by 4,705
- InnerProductSpacestatement and proof · cited by 3,523
- MetricSpacestatement and proof · cited by 1,684
- Dist.diststatement and proof · cited by 1,539
- NormedAddTorsorstatement and proof · cited by 1,325
- AffineSubspacestatement · cited by 871
- Affine.Simplexstatement and proof · cited by 471
- affineSpanstatement · cited by 417
Cited by1
Results whose statement or proof uses this declaration.
- EuclideanGeometry.eq_or_eq_reflection_of_dist_eqproof · cited by 0