Affine.Simplex.midpoint_faceOppositeCentroid_eulerPoint
∀ {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} [hn : NeZero n] (s : Affine.Simplex ℝ P n) (i : Fin (n + 1)),
midpoint ℝ (s.faceOppositeCentroid i) (s.eulerPoint i) = s.ninePointCircle.center- 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.
Cites74
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- mul_oneproof · cited by 3,885
- InnerProductSpacestatement and proof · cited by 3,523
- Finset.univproof · cited by 3,473
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- HVAdd.hVAddproof · cited by 1,820
- MetricSpacestatement and proof · cited by 1,684
- IsUnitproof · cited by 1,602
- add_commproof · cited by 1,535
Cited by1
Results whose statement or proof uses this declaration.
- Affine.Simplex.isDiameter_ninePointCircleproof · cited by 2