Meaning of generalized circle | Babel Free

Definitions

A circle or a line, the two being regarded as types of a single form.

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,”

“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.”

“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).”

CEFR level