Point space - Revision history

BrianMcMahon: Added German and Spanish translations (U. Mueller)

2017-11-17T09:53:51Z

Added German and Spanish translations (U. Mueller)

BrianMcMahon: Style edits to align with printed edition

2017-05-16T13:04:16Z

Style edits to align with printed edition

MassimoNespolo: /* See also */

2017-04-10T16:25:50Z

‎See also

BrianMcMahon at 17:17, 7 February 2012

2012-02-07T17:17:59Z

MassimoNespolo at 16:39, 27 February 2007

2007-02-27T16:39:34Z

New page

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==
* Chapter 8.1 in the ''International Tables for Crystallography Volume A''
* [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]]

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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.''		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.
+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''.
+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.
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 ==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]]
+* [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]]