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...

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...

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...

holomorphic functions on the open unit disk, the Hardy space H2 consists of the functions f whose mean square value on the circle of radius r remains bounded...

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...

} for the unit circle and thus x = c cos ⁡ θ {\displaystyle x=c\cos \theta } and y = c sin ⁡ θ {\displaystyle y=c\sin \theta } for a circle of radius...

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...

unit circle and spatial directions in 3D are equivalent to a point on the unit sphere. The normalized vector û of a non-zero vector u is the unit vector...

turn (symbol tr or pla) is a unit of plane angle measurement that is the angular measure subtended by a complete circle at its center. It is equal to...

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...

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...

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...

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...

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, the...

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

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...

} 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...

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...

trend. If the other roots of the characteristic equation lie inside the unit circle—that is, have a modulus (absolute value) less than one—then the first...

"carrying around") is the perimeter of a circle or ellipse. The circumference is the arc length of the circle, as if it were opened up and straightened...

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...

plane is a rational distance from all four vertices of the unit square. Unit circle Unit cube Unit sphere Horn, Alastair N. (1991), "IFSs and the Interactive...

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...

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...

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...

interpreted as saying that the function eiφ is a unit complex number, i.e., it traces out the unit circle in the complex plane as φ ranges through the real...

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...

on a common circle. A polygon whose vertices are concyclic is called a cyclic polygon, and the circle is called its circumscribing circle or circumcircle...