Affine.Simplex.sum_inv_height_sq_smul_vsub_eq_zero
∀ {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),
∑ i, (s.height i)⁻¹ ^ 2 • (s.points i -ᵥ s.altitudeFoot i) = 0- Defined in
- Mathlib.Geometry.Euclidean.Incenter
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites64
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- SetLike.coeproof · cited by 8,199
- Submoduleproof · cited by 7,192
- Finset.sumstatement and proof · cited by 5,195
- Set.rangeproof · cited by 4,705
- InnerProductSpacestatement and proof · cited by 3,523
- Finset.univstatement and proof · cited by 3,473
- Compl.complproof · cited by 2,925
- add_zeroproof · cited by 2,707
- Finset.sum_congrproof · cited by 2,323
Cited by1
Results whose statement or proof uses this declaration.
- Affine.Simplex.inv_height_eq_sum_mul_inv_distproof · cited by 1