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In geometry, a diameter of a circle is any straight line segment that passes through the centre of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid for the diameter of a sphere.
In two dimensions, the diameter can be obtained by computing the convex hull and then applying the method of rotating calipers.This involves finding two parallel support lines for the convex hull (for instance vertical lines through the two vertices with minimum and maximum -coordinate) and then rotating the two lines through a sequence of discrete steps that keep them as parallel lines of ...
In differential geometry, the diameter is an important global Riemannian invariant. Every compact set in a Riemannian manifold, and every compact Riemannian manifold itself, has finite diameter. For instance, the unit sphere of any dimension, viewed as a Riemannian manifold, has diameter .
Semicircle: one of the two possible arcs determined by the endpoints of a diameter, taking its midpoint as centre. In non-technical common usage it may mean the interior of the two-dimensional region bounded by a diameter and one of its arcs, that is technically called a half-disc. A half-disc is a special case of a segment, namely the largest one.
Diameter (computational geometry), the problem of computing the longest distance between two of given points or of the points in a polygon; Diameter (graph theory), the longest distance between two vertices of a graph; Diameter (group theory), the maximum diameter of a Cayley graph of the group
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.
The diameter symbol (Unicode character U+2300) is similar to the lowercase letter ø, and in some typefaces it even uses the same glyph, although in many others the glyphs are subtly distinguishable (normally, the diameter symbol uses an exact circle and the letter o is somewhat stylized).
In computational geometry, the method of rotating calipers is an algorithm design technique that can be used to solve optimization problems including finding the width or diameter of a set of points. The method is so named because the idea is analogous to rotating a spring-loaded vernier caliper around the outside of a convex polygon . [ 1 ]