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  2. Crossing number (graph theory) - Wikipedia

    en.wikipedia.org/wiki/Crossing_number_(graph_theory)

    A variation of this concept, the rectilinear crossing number, requires all edges to be straight line segments, and may differ from the crossing number. In particular, the rectilinear crossing number of a complete graph is essentially the same as the minimum number of convex quadrilaterals determined by a set of n points in general position.

  3. Intersecting chords theorem - Wikipedia

    en.wikipedia.org/wiki/Intersecting_chords_theorem

    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.

  4. Planar graph - Wikipedia

    en.wikipedia.org/wiki/Planar_graph

    Scheinerman's conjecture (now a theorem) states that every planar graph can be represented as an intersection graph of line segments in the plane. The planar separator theorem states that every n-vertex planar graph can be partitioned into two subgraphs of size at most 2n/3 by the removal of O(√ n) vertices.

  5. File:Complete graph K5.svg - Wikipedia

    en.wikipedia.org/wiki/File:Complete_graph_K5.svg

    The following other wikis use this file: Usage on af.wikipedia.org Bespreking:Wetenskapstaal; Usage on ar.wikipedia.org نسبة ذهبية; نجمة خماسية

  6. Line segment - Wikipedia

    en.wikipedia.org/wiki/Line_segment

    Analogous to straight line segments above, one can also define arcs as segments of a curve. In one-dimensional space, a ball is a line segment. An oriented plane segment or bivector generalizes the directed line segment. Beyond Euclidean geometry, geodesic segments play the role of line segments.

  7. Chord (geometry) - Wikipedia

    en.wikipedia.org/wiki/Chord_(geometry)

    Common lines and line segments on a circle, including a chord in blue. 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.

  8. Complete bipartite graph - Wikipedia

    en.wikipedia.org/wiki/Complete_bipartite_graph

    The star graphs K 1,3, K 1,4, K 1,5, and K 1,6. A complete bipartite graph of K 4,7 showing that Turán's brick factory problem with 4 storage sites (yellow spots) and 7 kilns (blue spots) requires 18 crossings (red dots)

  9. Triangular number - Wikipedia

    en.wikipedia.org/wiki/Triangular_number

    The number of line segments between closest pairs of dots in the triangle can be represented in terms of the number of dots or with a recurrence relation: = = (); = + (), = In the limit , the ratio between the two numbers, dots and line segments is lim n → ∞ T n L n = 1 3 . {\displaystyle \lim _{n\to \infty }{\frac {T_{n}}{L_{n}}}={\frac {1 ...