plane). However, parallel (non-crossing) pairs of lines are less restricted in hyperbolic line arrangements than in the Euclidean plane: in particular, the relation of being parallel is an equivalence relation for Euclidean lines but not for hyperbolic lines. The intersection graph of the lines in a hyperbolic arrangement can be an arbitrary circle graph. The corresponding concept to hyperbolic line arrangements for pseudolines is a weak pseudoline arrangement, a family of curves having the same topological properties as lines such that any two curves in the family either meet in a single crossing point or have no intersection. See also Configuration (geometry), an arrangement of lines and a set of points with all lines containing the same number of points and all points belonging to the same number of lines Arrangement (space partition), a partition of the plane given by overlaid curves or of a higher dimensional space by overlaid surfaces, without requiring the curves or surfaces to be flat Mathematical Bridge, a bridge in Cambridge, England whose beams form an arrangement of tangent lines to its arch Notes References ; see Example 10.14, pp. 519–520 ; see p. 6 of "Euclidean arrangements" (p. 101 of linked pdf) External links Database of Combinatorially Different Line Arrangements Discrete geometry Euclidean plane geometry