Dictionary

generalized circle en · NOUN

Meanings

1. (qualifier:inversive geometry) A circle or a line, the two being regarded as types of a single form.
   • 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
   • 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:
   • 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:

Forms

Synonyms

cline (circle or line) · circline (circle or line)