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The value of the two products in the chord theorem depends only on the distance of the intersection point S from the circle's center and is called the absolute value of the power of S; more precisely, it can be stated that: | | | | = | | | | = where r is the radius of the circle, and d is the distance between the center of the circle and the ...
In geometry, a disk (also spelled disc) [1] is the region in a plane bounded by a circle.A disk is said to be closed if it contains the circle that constitutes its boundary, and open if it does not.
Common lines and line segments on a circle, including a chord in blue. A chord (from the Latin chorda, meaning "bowstring") of a circle is a straight line segment whose endpoints both lie on a circular arc.
Each annulus ann(a; r, R) can be holomorphically mapped to a standard one centered at the origin and with outer radius 1 by the map . The inner radius is then r / R < 1. The Hadamard three-circle theorem is a statement about the maximum value a holomorphic function may take inside an annulus.
where a is the radius of the circle, (,) are the polar coordinates of a generic point on the circle, and (,) are the polar coordinates of the centre of the circle (i.e., r 0 is the distance from the origin to the centre of the circle, and φ is the anticlockwise angle from the positive x axis to the line connecting the origin to the centre of ...
The simplest example of a coordinate system is the identification of points on a line with real numbers using the number line.In this system, an arbitrary point O (the origin) is chosen on a given line.
The radius of the first arc must be chosen large enough to cause all successive arcs to end on the correct side of the next crossing point; however, all sufficiently-large radii work. For two lines, this forms a circle; for three lines on the sides of an equilateral triangle, with the minimum possible radius, it forms a Reuleaux triangle, and ...
A Jordan curve or a simple closed curve in the plane is the image of an injective continuous map of a circle into the plane, :.A Jordan arc in the plane is the image of an injective continuous map of a closed and bounded interval [,] into the plane.
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