Theorems · Theorem · geometry

EuclideanGeometry.mul_dist_add_mul_dist_eq_mul_dist_of_cospherical

• #95 of the 100 theorems: Ptolemy’s Theorem
• 1000+ list: Ptolemy's theorem

∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] {P : Type u_2} [inst_2 : MetricSpace P]
  [inst_3 : NormedAddTorsor V P] {a b c d p : P},
  EuclideanGeometry.Cospherical {a, b, c, d} →
    EuclideanGeometry.angle a p c = Real.pi →
      EuclideanGeometry.angle b p d = Real.pi → dist a b * dist c d + dist b c * dist d a = dist a c * dist b d

Ptolemy’s Theorem.

Defined in

Mathlib.Geometry.Euclidean.Sphere.Ptolemy

Cited by

0 results in Mathlib

Foundations

Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor