The structure of descriptive geometry of the four- -dimensional Lobachevski space

Andrzej Bieliriski
1988 Demonstratio Mathematica  
Dedicated to the memory of Professor Edward Otto 1.Intloduction In the following article we shall present the method of developing geometry of four-dimensional space of Lobachevski (L^) realized in the three-dimensional Euclidean space complemented with an improper point. In order to attain this result the space L^ should be mapped by means of rectilinear projection onto the surface of the hyperhorysphere embedded in the space L^. Then the fact that on the hyperhorysphere three-dimensional
more » ... ee-dimensional Euclidean geometry is realized enables us to obtain the solution of the problems concerning space L^ in the 3 three-dimensional Moebius space (M ). The examples of the constructions of common elements, belonging of the elements, and mensural constructions will be presented below. Definition 1. The hyperhorysphere is defined as a surface spread over the hyperpencil of parallel lines with the improper vertex for which the line linking it to points is -1193 -Unauthenticated Download Date | 7/27/18 8:59 PM
doi:10.1515/dema-1988-0427 fatcat:2gwtu3g2qbdqvmzksvmdfmm42y