What is "circular points at infinity"

Circular \Cir"cu*lar\, a. [L. circularis, fr. circulus circle: cf. F. circulaire. See Circle.]

1. In the form of, or bounded by, a circle; round.

2. repeating itself; ending in itself; reverting to the point of beginning; hence, illogical; inconclusive; as, circular reasoning.

3. Adhering to a fixed circle of legends; cyclic; hence, mean; inferior. See Cyclic poets, under Cyclic.

   Had Virgil been a circular poet, and closely adhered to history, how could the Romans have had Dido?
   --Dennis.

4. Addressed to a circle, or to a number of persons having a common interest; circulated, or intended for circulation; as, a circular letter.

   A proclamation of Henry III., . . . doubtless circular throughout England.
   --Hallam.

5. Perfect; complete. [Obs.] A man so absolute and circular In all those wished-for rarities that may take A virgin captive. --Massinger. Circular are, any portion of the circumference of a circle. Circular cubics (Math.), curves of the third order which are imagined to pass through the two circular points at infinity. Circular functions. (Math.) See under Function. Circular instruments, mathematical instruments employed for measuring angles, in which the graduation extends round the whole circumference of a circle, or 360[deg]. Circular lines, straight lines pertaining to the circle, as sines, tangents, secants, etc. Circular note or Circular letter.

   1. (Com.) See under Credit.

   2. (Diplomacy) A letter addressed in identical terms to a number of persons.

      Circular numbers (Arith.), those whose powers terminate in the same digits as the roots themselves; as 5 and 6, whose squares are 25 and 3

6. 
   --Bailey.
   --Barlow.

   Circular points at infinity (Geom.), two imaginary points at infinite distance through which every circle in the plane is, in the theory of curves, imagined to pass.

   Circular polarization. (Min.) See under Polarization.

   Circular sailing or Globular sailing (Naut.), the method of sailing by the arc of a great circle.

   Circular saw. See under Saw.

Infinity \In*fin"i*ty\, n.; pl. Infinities. [L. infinitas; pref. in- not + finis boundary, limit, end: cf. F. infinit['e]. See Finite.]

1. Unlimited extent of time, space, or quantity; eternity; boundlessness; immensity.
   --Sir T. More.

   There can not be more infinities than one; for one of them would limit the other.
   --Sir W. Raleigh.

2. Unlimited capacity, energy, excellence, or knowledge; as, the infinity of God and his perfections.
   --Hooker.

3. Endless or indefinite number; great multitude; as an infinity of beauties.
   --Broome.

4. (Math.) A quantity greater than any assignable quantity of the same kind.

   Note: Mathematically considered, infinity is always a limit of a variable quantity, resulting from a particular supposition made upon the varying element which enters it.
   --Davies & Peck (Math. Dict.).

5. (Geom.) That part of a line, or of a plane, or of space, which is infinitely distant. In modern geometry, parallel lines or planes are sometimes treated as lines or planes meeting at infinity.

   Circle at infinity, an imaginary circle at infinity, through which, in geometry of three dimensions, every sphere is imagined to pass.

   Circular points at infinity. See under Circular.

In projective geometry, the circular points at infinity (also called cyclic points or isotropic points) are two special points at infinity in the complex projective plane that are contained in the complexification of every real circle.