The Way of Expressing, Analyzing and Calculating Space Angles in a Plane

Abstract

Based on mapping method and the principle of non-Euclidean geometry, this chapter presents a novel method for expression, analysis and calculation of space geometric angles. According to this method, a space inclined plane is mapped onto a projective plane as an image point, and a space line is mapped on the projective plane as an image line. The problem of calculating the angle between two space inclined planes is thus converted into the problem of calculating the non-Euclidean distance between their image points on the projective plane, and the problem of calculating the angle between two space inclined lines is converted into the problem of calculating non-Euclidean angle of their image lines. The problem of a rigid body rotating in the space is converted into the problem of moving and rotating in the projective plane of its image diagram. Compared with conventional ways, this method is simple and intuitive. It is a more effective approach for designing and calculating the cutting tool angles or angles in machine parts.