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Difference between revisions of "Point space"

From Online Dictionary of Crystallography

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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.
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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''.
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Objects in point space are described by means of a coordinate system referred to a 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.
 
The point space used in crystallography is a Euclidean space, ''i.e.'' an affine space where the scalar product is defined.
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==See also==
 
==See also==
* [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]]
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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)
  
 
[[Category:Fundamental crystallography]]
 
[[Category:Fundamental crystallography]]

Revision as of 13:04, 16 May 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 a 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