Theorems · Definition · geometry

EuclideanGeometry.inversion

{V : Type u_1} →
  {P : Type u_2} →
    [inst : NormedAddCommGroup V] →
      [InnerProductSpace ℝ V] → [inst_2 : MetricSpace P] → [NormedAddTorsor V P] → P → ℝ → P → P

Inversion in a sphere in an affine space. This map sends each point x to the point y such that y -ᵥ c = (R / dist x c) ^ 2 • (x -ᵥ c), where c and R are the center and the radius the sphere.

Defined in

Mathlib.Geometry.Euclidean.Inversion.Basic

Cited by

47 results in Mathlib

Foundations

Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor