generalized circle

generalized circle (plural generalized circles)

  1. (geometry, inversive geometry) A circle or a line, the two being regarded as types of a single form.
    • (53-4)    \beta \left | \zeta \right |^2 - p\zeta - \overline{p}\overline{\zeta} + \alpha = 0,
      which is a generalized circle in the ζ-plane.
    • 1999, David A. Brannan, Matthew F. Esplen, Jeremy J. Gray, Geometry, page 252 ↗,
      For any Apollonian family of circles defined by the point circles A and B, the Coaxal Circles Theorem states that every generalized circle through A and B meets each of the Apollonian circles at right angles.

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