unit circle


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unit circle

[′yü·nət ′sər·kəl]
(mathematics)
The locus of points in the plane which are precisely one unit from the origin.
References in periodicals archive ?
For a knot K in [S.sup.3], if its Alexander polynomial [[DELTA].sub.K](t) has a simple root on the unit circle, then the fundamental group of the manifold obtained by p/q-surgery along K is left-orderable if p/q is sufficiently close to 0.
It is submitted that in-charge Homicide Unit Circle Jahanian conducted investigation of case adding on receipt of information, SHO PS Jahanian and DPO Khanewal reached the spot.
Hence the eigenvalue [lambda] of the matrix A lies outside of the image of unit circle in the mapping [bar.[alpha]] : C [right arrow] C given by [bar.[alpha]](z) = z[alpha](z).
Students often have difficulties in making connections between right triangle and unit circle approaches (Martinez-Planell and Delgado, 2016), and conceptualizing a circle's radius as a unit of measure (Moore, LaForest, and Kim, 2012).
Moreover, [theta] = [pi]/4 rad, [theta] = 3[pi]/4 rad, [theta] = -3[pi]/4 rad, and [theta] = -[pi]/4 rad have been chosen as they are good representatives of those [theta]'s which their coordinates on the Euclidian plane, i.e., (cos([theta]), sin([theta])), are located on the portion of unit circle's arc in quadrants 1,2, 3, and 4 of such plane, respectively.
The x- and y-axes are defined for a unit circle. For the sake of simplicity and ease of use, the abscissa and ordinate are first considered as real lines.
has all eigenvalues within the unit circle, where [mathematical expression not reproducible] is denoted as the inverse of [mathematical expression not reproducible].
A simply connected domain D in the complex plane C whose boundary is homeomorphic to the unit circle is called a Jordan domain.
In Figure 7(a), when [k.sub.at_critical]=0.1 and 0.5, the pole is inside the unit circle, and the system is in a stable state.
and we show that it is derived from the empirical version of Caratheodory function, used in the literature on orthogonal polynomials on the unit circle. We also show that this approach leads to Fourier series density estimation; however no truncation of the series is required.
[??] is a locally stable hyperbolic fixed point as long as all eigenvalues [lambda] of (6) are located inside the unit circle in the complex plane.
The cosines and sines of these angles are assigned to the x and y coordinates of the unit circle. This creates a semi-circle which is then filled in blue colour.