Affine.Simplex.ExcenterExists.signedInfDist_excenter
∀ {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} [inst_4 : NeZero n] {s : Affine.Simplex ℝ P n} {signs : Finset (Fin (n + 1))},
s.ExcenterExists signs →
∀ (i : Fin (n + 1)),
(s.signedInfDist i) (s.excenter signs) =
(if i ∈ signs then -1 else 1) * ↑(SignType.sign (∑ j, s.excenterWeightsUnnorm signs j)) * s.exradius signsThe signed distance between the excenter and its projection in the plane of each face is the exradius.
- Defined in
- Mathlib.Geometry.Euclidean.Incenter
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
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
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Finsetstatement and proof · cited by 13,712
- Finset.sumstatement and proof · cited by 5,195
- InnerProductSpacestatement and proof · cited by 3,523
- Finset.univstatement and proof · cited by 3,473
- absproof · cited by 1,814
- MetricSpacestatement and proof · cited by 1,684
- mul_assocproof · cited by 1,667
- NormedAddTorsorstatement and proof · cited by 1,325
- OrderHomstatement · cited by 934
Cited by3
Results whose statement or proof uses this declaration.
- Affine.Simplex.ExcenterExists.dist_excenterproof · cited by 6
- Affine.Simplex.signedInfDist_incenterproof · cited by 0