Theorems · Theorem · geometry

EuclideanGeometry.angle_self_orthogonalProjection

∀ {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] (p : P) {p' : P} {s : AffineSubspace ℝ P}
  [inst_4 : s.direction.HasOrthogonalProjection] (h : p' ∈ s),
  EuclideanGeometry.angle p (↑((EuclideanGeometry.orthogonalProjection s) p)) p' = Real.pi / 2

Defined in

Mathlib.Geometry.Euclidean.Angle.Unoriented.Projection

Cited by

4 results in Mathlib

Foundations

Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorSubmodule.HasOrthogonalProjection