InnerProductGeometry.angle_add_eq_arctan_of_inner_eq_zero
∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] {x y : V},
inner ℝ x y = 0 → x ≠ 0 → InnerProductGeometry.angle x (x + y) = Real.arctan (‖y‖ / ‖x‖)An angle in a right-angled triangle expressed using arctan.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
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
- Nat.cast_oneproof · cited by 2,501
- mul_commproof · cited by 2,262
- LT.lt.ne'proof · cited by 1,417
- Inner.innerstatement and proof · cited by 1,089
- norm_nonnegproof · cited by 725
- Real.sqrtproof · cited by 545
- mul_addproof · cited by 413
Cited by4
Results whose statement or proof uses this declaration.
- InnerProductGeometry.tan_angle_add_of_inner_eq_zeroproof · cited by 5
- EuclideanGeometry.angle_eq_arctan_of_angle_eq_pi_div_twoproof · cited by 2
- Orientation.oangle_add_right_eq_arctan_of_oangle_eq_pi_div_twoproof · cited by 2
- InnerProductGeometry.angle_sub_eq_arctan_of_inner_eq_zeroproof · cited by 1