Theorems · Theorem · geometry

EuclideanGeometry.Sphere.secondInter_eq_lineMap

∀ {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] (s : EuclideanGeometry.Sphere P) (p p' : P),
  s.secondInter p (p' -ᵥ p) =
    (AffineMap.lineMap p p') (-2 * inner ℝ (p' -ᵥ p) (p -ᵥ s.center) / inner ℝ (p' -ᵥ p) (p' -ᵥ p))

If the vector passed to secondInter is given by a subtraction involving the point in secondInter, the result of secondInter may be expressed using lineMap.

Defined in

Mathlib.Geometry.Euclidean.Sphere.SecondInter

Cited by

0 results in Mathlib

Foundations

Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor