Theorems · Theorem · geometry

EuclideanGeometry.angle_add_angle_add_angle_eq_pi

• #27 of the 100 theorems: Sum of the Angles of a Triangle

∀ {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 : P} (p₃ : P),
  p₂ ≠ p₁ →
    EuclideanGeometry.angle p₁ p₂ p₃ + EuclideanGeometry.angle p₂ p₃ p₁ + EuclideanGeometry.angle p₃ p₁ p₂ = Real.pi

The sum of the angles of a triangle (possibly degenerate, where two given vertices are distinct), angle-at-point.

Defined in

Mathlib.Geometry.Euclidean.Triangle

Cited by

10 results in Mathlib

Foundations

Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor