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Topic: Crossing number

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	Point in Polygon Winding Number Inclusion
		The point is outside when this "crossing number" is even; otherwise, when it is odd, the point is inside.
		If this number is even, then the point is outside; otherwise, when the crossing number is odd, the point is inside.
		However, the validity of the crossing number method is based on the "Jordan Curve Theorem" which says that a simple closed curve divides the 2D plane into exactly 2 connected components: a bounded "inside" one and an unbounded "outside" one.
	geometryalgorithms.com /Archive/algorithm_0103/algorithm_0103.htm (2662 words)

	Crossing number - Wikipedia, the free encyclopedia
		Tables of prime knots are traditionally indexed by crossing number, with a subscript to indicate which particular knot out of those with this many crossings is meant (this sub-ordering is not based on anything in particular, except that torus knots are listed first).
		The crossing number cr(G) of a graph G is the lowest number of crossings of a planar diagram of the graph G.
		In general, determining the crossing number of a graph is hard; Garey and Johnson showed in 1983 that it is an NP-hard problem.
	www.wikipedia.org /wiki/Crossing_number (842 words)

	Crossing number (Site not responding. Last check: 2007-10-20)
		A knot 's crossing number is simply the lowest number of crossings of any diagram of the knot.
		Knots (to be precise prime knot s are traditionally indexed by crossing number, with a subscript to indicate which particular knot out of those with this many crossings is meant (this sub-ordering is not based on anything in particular).
		A cattle crossing or deer crossing is a location along a road where cattle or deer, respectively, frequently cross from one side to the other.
	www.serebella.com /encyclopedia/article-Crossing_number.html (550 words)

	98-29: Which Crossing Number Is It Anyway? (Site not responding. Last check: 2007-10-20)
		The crossing number of $G$ is the minimum number of crossing points in any drawing of $G$.
		the odd-crossing number) of $G$ is the minimum number of pairs of edges that cross (resp.
		We also prove that the largest of these numbers (the crossing number) cannot exceed twice the square of the smallest (the odd-crossing number).
	dimacs.rutgers.edu /TechnicalReports/abstracts/1998/98-29.html (186 words)

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