^ Ghys, Étienne (2017), A singular mathematical promenade, Lyon: ENS Éditions, arXiv: 1612.^ Khan, Abdullah Lisitsa, Alexei Vernitski, Alexei (2021), "Gauss-Lintel, an algorithm suite for exploring chord diagrams", in Kamareddine, Fairouz Coen, Claudio Sacerdoti (eds.), Intelligent Computer Mathematics: 14th International Conference, CICM 2021, Timisoara, Romania, July 26-31, 2021, Proceedings, Lecture Notes in Computer Science, vol. 12833, Berlin: Springer, pp. 197–202, doi: 10.1007/978-7-9_16, S2CID 236150713.d is the perpendicular distance from the chord to the circle center. c is the angle subtended at the center by the chord. Chord Length 2 × r × sin (c/2) r is the radius of the circle. ^ Flajolet, Philippe Noy, Marc (2000), "Analytic combinatorics of chord diagrams" (PDF), in Krob, Daniel Mikhalev, Alexander A. Chord Length Using Perpendicular Distance from the Center.(1993), "The permuted analogues of three Catalan sets", Journal of Statistical Planning and Inference, 34 (1): 75–87, doi: 10.1016/0378-3758(93)90035-5, MR 1209991 A chord diagram is a finite trivalent undirected graph with an embedded oriented circle and all vertices on that circle, regarded modulo cyclic identifications. In algebraic geometry, chord diagrams can be used to represent the singularities of algebraic plane curves. 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. With this extra information, the chord diagram of a knot is called a Gauss diagram. To fully describe the knot, the diagram should be annotated with an extra bit of information for each pair, indicating which point crosses over and which crosses under at that crossing. In knot theory, a chord diagram can be used to describe the sequence of crossings along the planar projection of a knot, with each point at which a crossing occurs paired with the point that crosses it. The crossing pattern of chords in a chord diagram may be described by a circle graph, the intersection graph of the chords: it has a vertex for each chord and an edge for each two chords that cross. There is a Catalan number of chord diagrams on a given ordered set in which no two chords cross each other. The number of different chord diagrams that may be given for a set of 2 n. The intersection of the two perpendicular bisectors, O, is the center of the circle. Then draw the perpendicular bisectors of the chords. Chord diagrams are conventionally visualized by arranging the objects in their order around a circle, and drawing the pairs of the matching as chords of the circle. In the diagram below, first draw 2 non-parallel chords AB and CD. In mathematics, a chord diagram consists of a cyclic order on a set of objects, together with a one-to-one pairing ( perfect matching) of those objects. Cyclic order and one-to-one pairing of a set of objects The 15 possible chord diagrams on six cyclically-ordered points
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |