Description
New Age International (P) Ltd An Introduction To The Geometry Of N Dimensions by D M Y Sommerville
The present book deals with the metrical and to a slighter extent with the projective aspect. A third aspect, which has attracted much attention recently, from its application to relativity, is the differential aspect. This is altogether excluded from the present book.
In this book, a complete systematic treatise has not been attempted but rather selected certain representative topics have been discussed which not only illustrate the extension of theorems of three-dimensional geometry, but also reveal results which are unexpected and where analogy would be a faithless guide.
The first four chapters explain the fundamental ideas of incidence, parallelism, perpendicularity, and angles between linear spaces. Chapters 5 and 6 are analytical, the former projective, the latter largely metrical. In the former are given some of the simplest ideas relating to algebraic varieties and a more detailed account of quadrics, especially with reference to their linear spaces. The remaining chapters deal with polytopes and contain, especially in Chapter 9, some of the elementary ideas in analysis situs. Chapter 8 treats hyperspatial figures and the final chapter establishes the regular polytopes.
Key Features:
Some representative topics which illustrate the extension of three dimensional geometry.
No treatise on N dimensions.
Projective aspect is discussed with ideas relating to algebraic varieties and account of quadrics with reference to linear spaces.
Metrical aspects give, in addition to Cartesian formulae, some accounts and applications of the Pliicher–Grassmann coordinates of a linear space and applications to line-geometry.
Polytopes are discussed in detail leading to regular polytopes.
References are of original works.