Definition of Circular points at infinity. Meaning of Circular points at infinity. Synonyms of Circular points at infinity

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Definition of Circular points at infinity

Circular points at infinity
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.
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 letter. (a) (Com.) See under Credit. (b) (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 36. --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 or Globular sailing (Naut.), the method of sailing by the arc of a great circle. Circular saw. See under Saw.

Meaning of Circular points at infinity from wikipedia

- projective geometry, the circular points at infinity (also called cyclic points or isotropic points) are two special points at infinity in the complex projective...
- denote the circular points at infinity. Draw the m tangents to C through each of I and J. There are two sets of m lines which will have m2 points of intersection...
- all circles 'p**** through' the circular points at infinity I = [1:i:0] and J = [1:−i:0]. These of course are complex points, for any representing set of...
- geometry. They have the advantage that the coordinates of points, including points at infinity, can be represented using finite coordinates. Formulas involving...
- in complex algebraic geometry is a conic p****ing through the circular points at infinity and has underlying topological space a 2-sphere rather than a...
- developed the concept of parallel lines meeting at a point at infinity and defined the circular points at infinity that are on every circle of the plane. These...
- curve is circular if and only if G(1, i, 0) = G(1, −i, 0) = 0. In other words, the curve is circular if it contains the circular points at infinity, (1, i...
- the line at infinity of the Euclidean plane and the absolute points are two special points on that line called the circular points at infinity. Lines containing...
- complex projective plane) the points I(1: i: 0) and J(1: −i: 0). These points are called the circular points at infinity. In polar coordinates, the equation...
- the n=2 subsection of the article on the Fubini-Study metric. Circular points at infinity del Pezzo surface Toric geometry Fake projective plane C. E....