mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. Frequently, especially in trigonometry, the unit circle is the circle of radius...

Circle packing in a circle is a two-dimensional packing problem with the objective of packing unit circles into the smallest possible larger circle. If...

so it has singularities on the unit circle – thus one cannot take the contour integral over the unit circle. The circle method is specifically how to compute...

complex numbers with absolute value 1, that is, the unit circle in the complex plane or simply the unit complex numbers T = { z ∈ C : | z | = 1 } . {\displaystyle...

from the area of a unit circle. Consider the unit circle circumscribed by a square of side length 2. The transformation sends the circle to an ellipse by...

respectively. The circle that is centred at the origin with radius 1 is called the unit circle. Thought of as a great circle of the unit sphere, it becomes...

points on the unit circle (Trautman 1998). In fact, a point in the Cartesian plane with coordinates (x, y) belongs to the unit circle if x2 + y2 = 1...

Circle packing in a square is a packing problem in recreational mathematics where the aim is to pack n unit circles into the smallest possible square...

be viewed as closed vector subspaces of the complex Lp spaces on the unit circle T = { z ∈ C : | z | = 1 } {\displaystyle \mathbb {T} =\{z\in \mathbb...

length in GeoGebra a = 0.478631328575115 [ unit of length ] {\displaystyle a=0.478631328575115\;[{\text{unit of length}}]} Side length of the tridecagon...

any real value in terms of the lengths of certain line segments in a unit circle. More modern definitions express the sine and cosine as infinite series...

definition of defining x = cos θ and y sin θ for the unit circle and thus x = c cos θ and y = c sin θ for a circle of radius c and reflecting our triangle in the...

Acid". Trigonometric ratios can also be represented using the unit circle, which is the circle of radius 1 centered at the origin in the plane. In this setting...

since the set formed by all such roots is dense on the boundary of the unit circle, there is no analytic continuation of L c ( z ) {\displaystyle {\mathcal...

space; the unit circle is a special case, the unit ⁠ 1 {\displaystyle 1} ⁠-sphere in the plane. An (open) unit ball is the region inside of a unit sphere...

} Unit disks are special cases of disks and unit balls; as such, they contain the interior of the unit circle and, in the case of the closed unit disk...

real line, geometrical definitions using the standard unit circle (i.e., a circle with radius 1 unit) are often used; then the domain of the other functions...

In mathematics, the rational points on the unit circle are those points (x, y) such that both x and y are rational numbers ("fractions") and satisfy x2 + y2 = 1...

evaluated along the z-domain's unit circle. The s-domain's left half-plane maps to the area inside the z-domain's unit circle, while the s-domain's right...

performed Unit angle, a full turn equal to an angle of 1 Unit circle, a circle with a radius of length 1 Unit cube, a cube with sides of length 1 Unit fraction...

four points on the unit circle, yet the class of all convex sets in the plane does shatter every finite set of points on the unit circle. Let A be a set...

function. The concept of unit circle (the set of all vectors of norm 1) is different in different norms: for the 1-norm, the unit circle is a square oriented...

idea is to use a hash function that maps both the BLOB and servers to a unit circle, usually 2 π {\displaystyle 2\pi } radians. For example, ζ = Φ   %  ...

subtended at the centre of a circle by an arc that is equal in length to the radius. The unit was formerly an SI supplementary unit and is currently a dimensionless...

orthogonal polynomials on the unit circle are families of polynomials that are orthogonal with respect to integration over the unit circle in the complex plane...

the unit hyperbola forms the basis for an alternative radial length r = x 2 − y 2 . {\displaystyle r={\sqrt {x^{2}-y^{2}}}.} Whereas the unit circle surrounds...

sphere of unit radius, place its center at the origin of the complex plane, oriented so that the equator on the sphere coincides with the unit circle in the...

{x}{2}}} . This is the one-dimensional stereographic projection of the unit circle parametrized by angle measure onto the real line. The general transformation...

stable if and only if all of its eigenvalues are strictly inside the unit circle of the complex plane. A solution to the algebraic Riccati equation can...

the s-plane representation (in discrete time, respectively, inside the unit circle of the z plane). Since inverting a system function leads to poles turning...