Differential Geometry

This book presents a foundation for differential geometry based not on analytic formalisms but rather on underlying geometric intuitions--basic notions such as straightness (geodesic), smooth, tangent, curvature, and parallel transport. This foundation should be accessible to anyone with a flexible geometric imagination. It may then be possible that this foundation will serve as a common starting point for the various analytic formalizations. The book will explore some of these analytical formalisms. In addition, this geometric foundation relates more directly with our actual experiences of curves and surfaces both in the physical world and in the context of computer graphics.