generalized circle

plural generalized circles · alternative generalised circle

1. inversive geometrygeometryA circle or a line, the two being regarded as types of a single form.

   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.

   1999, David A. Brannan, Matthew F. Esplen, Jeremy J. Gray, Geometry, page 252

   2 more examples

   We shall speak of lines and circles as generalized circles. A line is a generalized circle that passes through the point at infinity. Under the inversion #92;zeta#61;1#47;z the generalized circle (53.3) goes into (53-4) β|ζ|²-pζ-◌̅p◌̅ζ+α=0,

   1965, H. F. Weinberger, A First Course in Partial Differential Equations with Complex Variables and Transform Methods, page 247

   This is why it makes sense to call every circle and every straight line a generalized circle. Thus the geodesics of ds consist of all arcs of generalized circles which lie wholly within Ω and are orthogonal to w (see Figure 2).

   2001, Elie Zahar, Poincaré's Philosophy: From Conventionalism to Phenomenology, page 84

   Synonyms: circline, cline