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- Payer en toute sécurité
- Toujours un magasin près de chez vous
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Format
Description
The central object of this book is the measure of geometric quantities describing N a subset of the Euclidean space (E, ), endowed with its standard scalar product. Let us state precisely what we mean by a geometric quantity. Consider a subset N S of points of the N-dimensional Euclidean space E, endowed with its standard N scalar product. LetG be the group of rigid motions of E . We say that a 0 quantity Q(S) associated toS is geometric with respect toG if the corresponding 0 quantity Q[g(S)] associated to g(S) equals Q(S), for all g?G . For instance, the 0 diameter ofS and the area of the convex hull ofS are quantities geometric with respect toG . But the distance from the origin O to the closest point ofS is not, 0 since it is not invariant under translations ofS. It is important to point out that the property of being geometric depends on the chosen group. For instance, ifG is the 1 N group of projective transformations of E, then the property ofS being a circle is geometric forG but not forG, while the property of being a conic or a straight 0 1 line is geometric for bothG andG . This point of view may be generalized to any 0 1 subsetS of any vector space E endowed with a groupG acting on it.
Spécifications
Parties prenantes
- Auteur(s) :
- Editeur:
Contenu
- Nombre de pages :
- 266
- Langue:
- Anglais
- Collection :
- Tome:
- n° 2
Caractéristiques
- EAN:
- 9783540737919
- Date de parution :
- 13-06-08
- Format:
- Livre relié
- Format numérique:
- Genaaid
- Dimensions :
- 157 mm x 236 mm
- Poids :
- 521 g
