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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 number of different chord diagrams that may be given for a set of cyclically ordered objects is the double factorial ()!!. [1] There is a Catalan number of chord diagrams on a given ordered set in which no two chords cross each other. [2] The crossing pattern of chords in a chord diagram may be described by a circle graph, the intersection ...
English: This is a graphical construction of the various trigonometric functions from a chord AD (angle θ) of the unit circle centered at O. In addition to the modern trigonometric functions sin (sine), cos (cosine), tan (tangent), cot (cotangent), sec (secant), and csc (cosecant), the diagram also includes a few trigonometric functions that have fallen into disuse: chord, versin (versine or ...
It illustrates the dependence of the length of a chord of a circle upon the angle that it subtends. As in [[Ptolemy]]'s [[Almagest]], the diameter of the circle is 120. 2011-03-11 17:28: 603×585× (3961 bytes) Michael Hardy: I drew this using xfig. It illustrates the dependence of the length of a chord of a circle upon the angle that it subtends.
The diameter is the longest chord of the circle. Among all the circles with a chord AB in common, the circle with minimal radius is the one with diameter AB. If the intersection of any two chords divides one chord into lengths a and b and divides the other chord into lengths c and d, then ab = cd.
A chord of a circle is a geometric line segment whose endpoints both lie on the circle. Chord diagrams are also known as radial network diagrams and may sometimes be referred to as a type of circular layout. Chord diagram showing cumulative electricity trade (2015–2065) among African countries (TWh)
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Chord diagram (music), a diagram showing the fingering of a chord on a guitar or other fretted musical instrument; Chord diagram (information visualization), a diagram showing a many-to-many relationship between objects as curved arcs within a circle; Chord diagram (mathematics), a circularly ordered set with a one-to-one pairing, often drawn ...