generalized circle

generalized circle

English

Alternative forms

• generalised circle

Noun

generalized circle (plural generalized circles)

1. (geometry, inversive geometry) A circle or a line, the two being regarded as types of a single form.
   • 1965, H. F. Weinberger, A First Course in Partial Differential Equations with Complex Variables and Transform Methods‎, page 247:

     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 ${\\displaystyle \\zeta =1/z}$ the generalized circle (53.3) goes into

     (53-4)    ${\\displaystyle \\beta \\left|\\zeta \\right|^{2}-p\\zeta -{\\overline {p}}{\\overline {\\zeta }}+\\alpha =0}$,

     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.

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

     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).

Synonyms

• (circle or line): circline, cline

See also

• Inversive geometry on Wikipedia.Wikipedia