ABSTRACT

A.D. Alexandrov is considered by many to be the father of intrinsic geometry, second only to Gauss in surface theory. That appraisal stems primarily from this masterpiece--now available in its entirely for the first time since its 1948 publication in Russian.

Alexandrov's treatise begins with an outline of the basic concepts, definitions, and r

chapter I|56 pages

BASIC CONCEPTS AND RESULTS

chapter II|34 pages

GENERAL PROPOSITIONS ABOUT INTRINSIC METRICS

chapter IV|36 pages

THE ANGLE

chapter V|40 pages

CURVATURE

chapter VIII|24 pages

OTHER EXISTENCE THEOREMS

chapter IX|40 pages

CURVES ON CONVEX SURFACES

chapter X|24 pages

AREA

chapter XI|28 pages

THE ROLE OF SPECIFIC CURVATURE

chapter XII|16 pages

GENERALIZATION