EuclideanGeometry.dist_eq_dist_mul_sin_angle_div_sin_angle
∀ {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] {p₁ p₂ p₃ : P},
¬Collinear ℝ {p₁, p₂, p₃} →
dist p₁ p₂ = dist p₃ p₁ * Real.sin (EuclideanGeometry.angle p₂ p₃ p₁) / Real.sin (EuclideanGeometry.angle p₁ p₂ p₃)A variant of the law of sines, requiring that the points not be collinear.
- Defined in
- Mathlib.Geometry.Euclidean.Triangle
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- 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
- one_mulproof · cited by 2,841
- mul_commproof · cited by 2,262
- MetricSpacestatement and proof · cited by 1,684
- Dist.diststatement and proof · cited by 1,539
- NormedAddTorsorstatement and proof · cited by 1,325
- one_ne_zeroproof · cited by 885
- ne_of_gtproof · cited by 637
Cited by1
Results whose statement or proof uses this declaration.
- EuclideanGeometry.angle_side_angleproof · cited by 1