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'''Betweenness''' is the property of [[line]]s in certain [[geometries]], such as [[plane geometry]], which allows one to talk about when a third point is '''between''' two points.

'''Betweenness''' is the property of [[line]]s in certain [[geometries]], such as [[plane geometry]], which allows one to talk about when a third point is '''between''' two points.

Betweenness does not hold in some bizarre geometries such as [[non-Euclidean geometry]] and the [[Fano plane]]. Betweenness is equivalent to the line being a [[linear order]] of its points. The concept of betweenness was first mathematically expressed by [[David Hilbert]]<ref>http://www.libraryofmath.com/betweenness-proposition-list.html</ref>, though the concept has naturally been used imprecisely in mathematics since at least the time of [[Euclid]].

Betweenness does not hold in some bizarre geometries such as [[non-Euclidean geometry]] and the [[Fano plane]]. Betweenness is equivalent to the line being a [[linear order]] of its points. The concept of betweenness was first mathematically expressed by [[David Hilbert]]<ref>http://www.libraryofmath.com/betweenness-proposition-list.html</ref>, though the concept has naturally been used imprecisely in mathematics since at least the time of [[Euclid]].