# Difference between revisions of "Point space"

### From Online Dictionary of Crystallography

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==See also== | ==See also== | ||

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* [http://www.iucr.org/iucr-top/comm/cteach/pamphlets/22/index.html Matrices, Mappings and Crystallographic Symmetry], teaching pamphlet No. 22 of the [[International Union of Crystallography]] | * [http://www.iucr.org/iucr-top/comm/cteach/pamphlets/22/index.html Matrices, Mappings and Crystallographic Symmetry], teaching pamphlet No. 22 of the [[International Union of Crystallography]] | ||

[[Category:Fundamental crystallography]] | [[Category:Fundamental crystallography]] |

## Revision as of 16:25, 10 April 2017

A mathematical model of the space in which we live is the **point space**. Its elements are points. Objects in point space may be single points; finite sets of points like the centres of the atoms of a molecule; infinite discontinuous point sets like the centres of the atoms of an ideal crystal pattern; continuous point sets like straight lines, curves, planes, curved surfaces, etc.

Objects in point space are described by means of a coordinate system referred to point chosen as the origin O. An arbitrary point P is then described by its coordinates *x*, *y*, *z*.

The point space used in crystallography is a Euclidean space, *i.e.* an affine space where the scalar product is defined.

Crystal structures are described in point space. The vector space is a dual of the point space because to each pair of points in point space a vector in vector space can be associated.

## See also

- Matrices, Mappings and Crystallographic Symmetry, teaching pamphlet No. 22 of the International Union of Crystallography