Theorems · Theorem · geometry

EuclideanGeometry.dist_inversion_center

∀ {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] (c x : P) (R : ℝ), dist (EuclideanGeometry.inversion c R x) c = R ^ 2 / dist x c

Distance from the image of a point under inversion to the center. This formula accidentally works for x = c.

Defined in

Mathlib.Geometry.Euclidean.Inversion.Basic

Cited by

5 results in Mathlib

Foundations

Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor