Affine.Triangle.orthocenter_eq_mongePoint
∀ {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] (t : Affine.Triangle ℝ P), t.orthocenter = Affine.Simplex.mongePoint tThe orthocenter equals the Monge point.
- Defined in
- Mathlib.Geometry.Euclidean.MongePoint
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.Trianglestatement and proof · cited by 75
- Affine.Triangle.orthocenterstatement · cited by 23
- Affine.Simplex.mongePointstatement · cited by 20
Cited by7
Results whose statement or proof uses this declaration.
- Affine.Triangle.dist_orthocenter_reflection_circumcenterproof · cited by 3
- Affine.Triangle.orthocenter_mem_altitudeproof · cited by 2
- Affine.Triangle.eq_orthocenter_of_forall_mem_altitudeproof · cited by 1
- Affine.Triangle.altitudeFoot_mem_ninePointCircleproof · cited by 0
- Affine.Triangle.orthocenter_eq_smul_vsub_vadd_circumcenterproof · cited by 0
- Affine.Triangle.eulerPoint_eq_midpointproof · cited by 0
- Affine.Triangle.orthocenter_vsub_circumcenter_eq_sum_vsubproof · cited by 0