Actions

Difference between revisions of "Point space"

From Online Dictionary of Crystallography

 
(Added German and Spanish translations (U. Mueller))
 
(3 intermediate revisions by 2 users not shown)
Line 1: Line 1:
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.
+
<font color="red">Punktraum</font> (''Ge''). <font color="green">Espacio puntual</font> (''Sp'').
  
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.
+
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.
 
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==
 
==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)
* [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]]

Latest revision as of 09:53, 17 November 2017

Punktraum (Ge). Espacio puntual (Sp).


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