EuclideanGeometry.Sphere.thales_theorem
- 1000+ list: Thales's theorem
∀ {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} {s : EuclideanGeometry.Sphere P},
s.IsDiameter p₁ p₃ → (EuclideanGeometry.angle p₁ p₂ p₃ = Real.pi / 2 ↔ p₂ ∈ s)Alias of EuclideanGeometry.Sphere.angle_eq_pi_div_two_iff_mem_sphere_of_isDiameter.
Thales' theorem: The angle inscribed in a semicircle is a right angle.
- Defined in
- Mathlib.Geometry.Euclidean.Angle.Sphere
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- NormedAddCommGroupstatement · cited by 15,752
- InnerProductSpacestatement · cited by 3,523
- Real.pistatement · cited by 1,774
- MetricSpacestatement · cited by 1,684
- NormedAddTorsorstatement · cited by 1,325
- EuclideanGeometry.Spherestatement · cited by 233
- EuclideanGeometry.anglestatement · cited by 187
- EuclideanGeometry.Sphere.IsDiameterstatement · cited by 31
Cited by1
Results whose statement or proof uses this declaration.
- Affine.Simplex.orthogonalProjectionSpan_eulerPoint_mem_ninePointCircleproof · cited by 1