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Betweenness (other)
Betweenness is a noun derived from the proposition between. It may refer to: * The ternary relation of intermediacy or betweenness, a feature of ordered geometry. * Betweenness problem - an algorithmic problem. The input is a collection of ordered triples of items; the task is to decide whether there is a single total order such that such that, for each of the given triples, the middle item in the triple appears in the output somewhere between the other two items. * Betweenness centrality - a measure of centrality in a graph, based on shortest paths. The betweenness centrality of a vertex is the number of shortest paths that pass through the vertex. * Metric betweenness - given a metric ''d'', a point ''y'' is said to be ''between'' ''x'' and ''z'' if all three points are distinct, and d(x,y)+d(y,z)=d(x,z). See convex metric space. See also * Between (other) * In Between (other) {{Disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordered Geometry
Ordered geometry is a form of geometry featuring the concept of intermediacy (or "betweenness") but, like projective geometry, omitting the basic notion of measurement. Ordered geometry is a fundamental geometry forming a common framework for affine, Euclidean, absolute, and hyperbolic geometry (but not for projective geometry). History Moritz Pasch first defined a geometry without reference to measurement in 1882. His axioms were improved upon by Peano (1889), Hilbert (1899), and Veblen (1904). Euclid anticipated Pasch's approach in definition 4 of ''The Elements'': "a straight line is a line which lies evenly with the points on itself". Primitive concepts The only primitive notions in ordered geometry are points ''A'', ''B'', ''C'', ... and the ternary relation of intermediacy 'ABC''which can be read as "''B'' is between ''A'' and ''C''". Definitions The ''segment'' ''AB'' is the set of points ''P'' such that 'APB'' The ''interval'' ''AB'' is the segment ''AB'' and it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |