English

Noun

generalised circle ‎(plural generalised circles)

1. Alternative form of generalized circle
   • 2005, R. Warcham, J. Cameron, J. Lasenby, Applications of Conformal Geometric Algebra, Hongbo Li, Peter J. Olver, Gerald Sommer (editors), Computer Algebra and Geometric Algebra with Applications, 6th International Workshop IWMM 2004 and International Workshop GIAE 2004, Revised Selected Papers, page 333,

     It becomes convenient, therefore, to group planes and spheres by the collective term generalised spheres and, similarly, to define a generalised circle as either a circle or a line.

   • 2008, Christopher Stone, Ther Use of Linear Fractional Transformations to Produce Building Plans, Stephen R. Wassell, Kim Williams (editors), Nexus Network Journal: Architecture and Mathematics, Volume 10, Number 2, page 342,

     Strictly straight lines through the point at infinity appear as straight lines but are regarded as generalised circles.

   • 2012, Circle of Apollonius, entry in Concise Dictionary of Mathematics, V&S Publishers, India, page 75,

     Thus, if A, B, and C are given distinct points in the plane, then the locus of points P satisfying (1) is called a “generalised circle.” It may either be a true circle or a line. In this sense a line is a generalised circle of infinite radius.