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A circle of radius r for the Chebyshev distance (L ∞ metric) on a plane is also a square with side length 2r parallel to the coordinate axes, so planar Chebyshev distance can be viewed as equivalent by rotation and scaling to planar taxicab distance. However, this equivalence between L 1 and L ∞ metrics does not generalise to higher dimensions.
A page from Archimedes' Measurement of a Circle. Measurement of a Circle or Dimension of the Circle (Greek: Κύκλου μέτρησις, Kuklou metrēsis) [1] is a treatise that consists of three propositions, probably made by Archimedes, ca. 250 BCE. [2] [3] The treatise is only a fraction of what was a longer work. [4] [5]
With straightedge and compass, a diameter of a given circle can be constructed as the perpendicular bisector of an arbitrary chord. Drawing two diameters in this way can be used to locate the center of a circle, as their crossing point. [2] To construct a diameter parallel to a given line, choose the chord to be perpendicular to the line.
The term hypersphere is commonly used to distinguish spheres of dimension which are thus embedded in a space of dimension + , which means that they cannot be easily visualized. The n {\displaystyle n} -sphere is the setting for n {\displaystyle n} -dimensional spherical geometry .
The angular diameter, angular size, apparent diameter, or apparent size is an angular separation (in units of angle) describing how large a sphere or circle appears from a given point of view. In the vision sciences , it is called the visual angle , and in optics , it is the angular aperture (of a lens ).
Ptolemy used a circle of diameter 120, and gave chord lengths accurate to two sexagesimal (base sixty) digits after the integer part. [2] The chord function is defined geometrically as shown in the picture. The chord of an angle is the length of the chord between two points on a unit circle separated by that central angle.
One radian is defined as the angle at the center of a circle in a plane that subtends an arc whose length equals the radius of the circle. [6] More generally, the magnitude in radians of a subtended angle is equal to the ratio of the arc length to the radius of the circle; that is, =, where θ is the magnitude in radians of the subtended angle, s is arc length, and r is radius.
The dimension is an intrinsic property of an object, in the sense that it is independent of the dimension of the space in which the object is or can be embedded. For example, a curve, such as a circle, is