Difference between revisions of "Betweenness"
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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 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> | + | Betweenness does not hold in some 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]]. |
==See also== | ==See also== | ||
Latest revision as of 03:10, July 13, 2016
Betweenness is the property of lines 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 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,[1] though the concept has naturally been used imprecisely in mathematics since at least the time of Euclid.
