InnerProductGeometry.sin_angle_mul_norm_eq_sin_angle_mul_norm
∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] (x y : V),
Real.sin (InnerProductGeometry.angle x y) * ‖x‖ = Real.sin (InnerProductGeometry.angle y (x - y)) * ‖x - y‖Law of sines (sine rule), vector angle form.
- Defined in
- Mathlib.Geometry.Euclidean.Triangle
- 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.
Cites39
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
- Norm.normstatement and proof · cited by 5,413
- mul_oneproof · cited by 3,885
- InnerProductSpacestatement and proof · cited by 3,523
- one_mulproof · cited by 2,841
- add_zeroproof · cited by 2,707
- MulZeroClass.mul_zeroproof · cited by 2,091
- Real.piproof · cited by 1,774
- mul_assocproof · cited by 1,667
- MulZeroClass.zero_mulproof · cited by 1,625
- eq_or_neproof · cited by 1,117
Cited by2
Results whose statement or proof uses this declaration.
- EuclideanGeometry.sin_angle_mul_dist_eq_sin_angle_mul_distproof · cited by 1
- InnerProductGeometry.sin_angle_div_norm_eq_sin_angle_div_normproof · cited by 0