Affine.Simplex.affineSpan_faceOpposite_eq_orthRadius_insphere
∀ {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) [Fact (Module.finrank ℝ V = n)]
(i : Fin (n + 1)), affineSpan ℝ (Set.range (s.faceOpposite i).points) = s.insphere.orthRadius (s.touchpoint ∅ i)- Defined in
- Mathlib.Geometry.Euclidean.Incenter
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound
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- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Finsetstatement · cited by 13,712
- Set.rangestatement · cited by 4,705
- InnerProductSpacestatement and proof · cited by 3,523
- Factstatement and proof · cited by 2,726
- Module.finrankstatement and proof · cited by 1,770
- 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
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