Affine.Simplex.isDiameter_ninePointCircle
∀ {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 : Fin (n + 1)),
s.ninePointCircle.IsDiameter (s.faceOppositeCentroid i) (s.eulerPoint i)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- InnerProductSpacestatement and proof · cited by 3,523
- MetricSpacestatement and proof · cited by 1,684
- NormedAddTorsorstatement and proof · cited by 1,325
- Affine.Simplexstatement and proof · cited by 471
- Affine.Simplex.faceOppositeCentroidstatement · cited by 39
- EuclideanGeometry.Sphere.IsDiameterstatement · cited by 31
- Affine.Simplex.ninePointCirclestatement · cited by 13
- Affine.Simplex.eulerPointstatement · cited by 10
- Affine.Simplex.faceOppositeCentroid_mem_ninePointCircleproof · cited by 2
- Affine.Simplex.midpoint_faceOppositeCentroid_eulerPointproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Affine.Simplex.orthogonalProjectionSpan_eulerPoint_mem_ninePointCircleproof · cited by 1
- Affine.Simplex.eulerPoint_mem_ninePointCircleproof · cited by 0