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Since C = 2πr, the circumference of a unit circle is 2π. In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. [1] Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.
describes a right circular conoid with the unit circle of the x-y-plane as directrix and a directrix plane, which is parallel to the y--z-plane. Its axis is the line (,,) . Special features: The intersection with a horizontal plane is an ellipse.
For the two dimensions this model uses the interior of the unit circle for the complete hyperbolic plane, and the chords of this circle are the hyperbolic lines. For higher dimensions this model uses the interior of the unit ball, and the chords of this n-ball are the hyperbolic lines.
The Euclidean plane corresponds to the case ε 2 = −1, an imaginary unit. Since the modulus of z is given by = (+) = +, this quantity is the square of the Euclidean distance between z and the origin. For instance, {z | z z* = 1} is the unit circle.
In a Cartesian plane, one can define canonical representatives of certain geometric figures, such as the unit circle (with radius equal to the length unit, and center at the origin), the unit square (whose diagonal has endpoints at (0, 0) and (1, 1)), the unit hyperbola, and so on. The two axes divide the plane into four right angles, called ...
In the complex plane, the most obvious circle inversion map (i.e., using the unit circle centered at the origin) is the complex conjugate of the complex inverse map taking z to 1/z. The complex analytic inverse map is conformal and its conjugate, circle inversion, is anticonformal.
The unit hyperbola is a special case of the rectangular hyperbola, with a particular orientation, location, and scale. As such, its eccentricity equals . [1] The unit hyperbola finds applications where the circle must be replaced with the hyperbola for purposes of analytic geometry.
Parallel planes are planes in the same three-dimensional space that never meet. Parallel curves are curves that do not touch each other or intersect and keep a fixed minimum distance. In three-dimensional Euclidean space, a line and a plane that do not share a point are also said to be parallel. However, two noncoplanar lines are called skew lines.