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...
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 s...
