Theorems · Theorem · geometry

EuclideanGeometry.image_inversion_perpBisector

∀ {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 y : P} {R : ℝ},
  R ≠ 0 →
    y ≠ c →
      EuclideanGeometry.inversion c R '' ↑(AffineSubspace.perpBisector c y) =
        Metric.sphere (EuclideanGeometry.inversion c R y) (R ^ 2 / dist y c) \ {c}

Defined in

Mathlib.Geometry.Euclidean.Inversion.ImageHyperplane

Cited by

0 results in Mathlib

Foundations

Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor