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Item Details
| Title:
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GENERALIZED CURVATURES
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| By: |
Jean-Marie Morvan |
| Format: |
Paperback |
| List price:
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£109.99 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
3642093000 |
| ISBN 13: |
9783642093005 |
| Publisher: |
SPRINGER-VERLAG BERLIN AND HEIDELBERG GMBH & CO. KG |
| Pub. date: |
28 October, 2010 |
| Edition: |
1st ed. Softcover of orig. ed. 2008 |
| Series: |
Geometry and Computing 2 |
| Pages: |
277 |
| Synopsis: |
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. |
| Illustrations: |
71 black & white illustrations, 36 colour illustrations, biography |
| Publication: |
Germany |
| Imprint: |
Springer-Verlag Berlin and Heidelberg GmbH & Co. K |
| Returns: |
Returnable |
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