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Difference between revisions of "Point space"

From Online Dictionary of Crystallography

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<font color="red">Punktraum</font> (''Ge''). <font color="green">Espacio puntual</font> (''Sp'').
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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.''
  

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