Titlebook: Exploring Curvature; James Casey Textbook 1996 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden 1996 Gaussian curvatu

Malaise

Gaussian Curvature,r. We learned that this variation is governed by Euler’s formula (15.30). In the present chapter, a completely different approach is taken, which is not based at all on the curvature of curves. Here, we study a brilliant idea of Gauss’s, which will enable us to define a unique value of . at each point on a smooth surface.

Connotation

,Levi-Civita (1873–1941), Christoffel (1829–1901), Beltrami (1835–1900), and others. During the closing decades of the 19th century, a powerful school of mathematics developed at the University of Padua. It was here that Levi-Civita came into contact with modern geometry.

爱哭

atopic

省略

High Data Rate Transmitter CircuitsWe now discuss the concept of a mapping (or function). The usefulness of this idea for the mathematical sciences can hardly be exaggerated.

机构

adroit

abysmal

Palliation

Black Holes and Accretion EfficiencyIn this chapter, we describe a particular way of moving a vector along a given curve on a surface. It provides an especially revealing means of exploring the non-Euclideanness of the surface.

锡箔纸

Basic Operations,We start out by performing some geometrical operations that can be easily done on objects located in ordinary three-dimensional space. You will need a ruler and a piece of string (or a tape measure) for measuring lengths, and a protractor for measuring angles.