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In the Gauss diagram of a knot, every chord crosses an even number of other chords, or equivalently each pair in the diagram connects a point in an even position of the cyclic order with a point in an odd position, and sometimes this is used as a defining condition of Gauss diagrams. [5] In algebraic geometry, chord diagrams can be used to ...
A chord (from the Latin chorda, meaning "bowstring") of a circle is a straight line segment whose endpoints both lie on a circular arc. If a chord were to be extended infinitely on both directions into a line, the object is a secant line. The perpendicular line passing through the chord's midpoint is called sagitta (Latin for "arrow").
Chord diagrams get their name from terminology used in geometry. 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 ...
In geometry, a line segment is a part of a straight line that is bounded by two distinct endpoints (its extreme points), and contains every point on the line that is between its endpoints. It is a special case of an arc , with zero curvature .
In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal.
In the mathematical area of graph theory, a chordal graph is one in which all cycles of four or more vertices have a chord, which is an edge that is not part of the cycle but connects two vertices of the cycle.
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 ...
Secant-, chord-theorem. For the intersecting secants theorem and chord theorem the power of a point plays the role of an invariant: . Intersecting secants theorem: For a point outside a circle and the intersection points , of a secant line with the following statement is true: | | | | = (), hence the product is independent of line .
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