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A 'spatial point' is a concept used to define an exact location in space. It has no volume, area or length. Points are used in the basic language of geometry, physics, vector graphics (both 2d and 3d), and many other fields. In mathematics generally, particularly in topology, any form of ''space'' is considered as made up of ''points'' as basic elements.
A point in Euclidean geometry has no size, orientation, or any other feature except position. Euclid's axioms or postulates assert in some cases that points exist: for example, they assert that if two lines on a plane are not parallel, there is exactly one point that lies on both of them. Euclid sometimes implicitly assumed facts that did not follow from the axioms (for example about the ordering of points on lines, and occasionally about the existence of points distinct from a finite list of points). Therefore the traditional axiomatization of ''point'' was not entirely complete and definitive.
In topology, a 'point' is simply an element of the underlying set of a topological space. Similar usage holds for similar structures such as uniform spaces, metric spaces, and so on.
★ Affine space
★ Definition of Point with interactive applet
★ Points definition pages With interactive animations that are also useful in a classroom setting. Math Open Reference
★
| Contents |
| Points in Euclidean geometry |
| Points in topology |
| See also |
| External links |
Points in Euclidean geometry
A point in Euclidean geometry has no size, orientation, or any other feature except position. Euclid's axioms or postulates assert in some cases that points exist: for example, they assert that if two lines on a plane are not parallel, there is exactly one point that lies on both of them. Euclid sometimes implicitly assumed facts that did not follow from the axioms (for example about the ordering of points on lines, and occasionally about the existence of points distinct from a finite list of points). Therefore the traditional axiomatization of ''point'' was not entirely complete and definitive.
Points in topology
In topology, a 'point' is simply an element of the underlying set of a topological space. Similar usage holds for similar structures such as uniform spaces, metric spaces, and so on.
See also
★ Affine space
External links
★ Definition of Point with interactive applet
★ Points definition pages With interactive animations that are also useful in a classroom setting. Math Open Reference
★
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