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 ...
Read More
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.
Read Less
Add this copy of Generalized Curvatures to cart. $122.11, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2010 by Springer-Verlag Berlin and Heidelberg GmbH & Co. K.
Edition:
2010, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Publisher:
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Published:
2010
Language:
English
Alibris ID:
10540290521
Shipping Options:
Standard Shipping: $4.99
Trackable Expedited: $9.99
Two Day Air: $29.99
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
New. Print on demand Contains: Illustrations, black & white, Illustrations, color. Geometry and Computing . XI, 266 p. 107 illus., 36 illus. in color. Intended for professional and scholarly audience.
Add this copy of Generalized Curvatures to cart. $122.11, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2008 by Springer.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
New. Print on demand Sewn binding. Cloth over boards. 266 p. Contains: Unspecified, Illustrations, black & white, Illustrations, color, Figures. Geometry and Computing, 2.
