Orthogonality of inversive plane

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This term is related to: incidence geometry
View other terms related to incidence geometry | View facts related to incidence geometry
This term is related to: inversive geometry
View other terms related to inversive geometry | View facts related to inversive geometry

Definition

Given an inversive plane an orthogonality of the inversive plane is a binary relation satisfying the following:

  • It is symmetric
  • Given two points and a circle through only one of them, there is a unique circle through both that is orthogonal to the earlier circle
  • A circle orthogonal to two circles in a bundle is orthogonal to every circle in that bundle