Theorems · Theorem · number theory
niven_angle_eq
∀ {θ : ℝ},
(∃ r, θ = ↑r * Real.pi) →
(∃ q, Real.cos θ = ↑q) → θ ∈ Set.Icc 0 Real.pi → θ ∈ {0, Real.pi / 3, Real.pi / 2, Real.pi * (2 / 3), Real.pi}Niven's theorem, giving the possible angles for θ in the range 0 .. π.
- Defined in
- Mathlib.NumberTheory.Niven
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- Real.pistatement and proof · cited by 1,774
- Set.Iccstatement and proof · cited by 1,702
- le_of_ltproof · cited by 1,175
- le_of_not_gtproof · cited by 430
- Real.cosstatement and proof · cited by 424
- mul_posproof · cited by 374
- div_posproof · cited by 337
- Real.pi_posproof · cited by 173
Cited by1
Results whose statement or proof uses this declaration.
- niven_angle_div_pi_eqproof · cited by 1