Date: Sat, 7 Jun 2003 22:12:45 -0400 From: Ed Wall <ewall-AT-umich.edu> Subject: The dimension of a manifold Michael E and Stuart For some reason I thought this might interest you: Howard Eves _A Survey of Geometry_ (Boston: Allyn and Bacon, 1965), volume 2 page 55 reads Ideas like [circular coordinates] led to wide generalization in analytic geometry, and, in 1865, caused Plucker [two dots over the u] to develop a dimension theory. If we define a manifold of geometrical elements to be a set of geometrical elements that can be labeled with a real, continuous coordinate system, then the dimension of the manifold is the number of coordinates needed to determine a general element of the set... Although [by this definition] space is three-dimensional in points, it may be shown that it is four-dimensional in lines, and also in spheres. It is three-dimensional, however, in planes. In short, dimension depends not only on the "space," but also upon the fundamental elements that make up the space. For the first time, geometers had defined perceivable spaces of more than three dimensions. Ed Wall --- from list heidegger-AT-lists.village.virginia.edu ---
Display software: ArchTracker © Malgosia Askanas, 2000-2005