A STUDY OF APPROXIMATE DEVELOPMENT OF SPHERICAL SURFACES

Abstract

An interesting problem in descriptive geometry is the unfolding of the non-developable surfaces of revolution. In this paper we start from the two classic methods of approximate development of a sphere: the gore method and the zone method. For each of the two methods, we study the errors of approximation. It is considered an approximate development of sphere using gore method, in 3 variants, using successively: 4 meridian (vertical) planes (resulting 8 gores), 5 meridian planes (10 gores) and 6 meridian planes (12 gores). Also for the same sphere, the approximate development is obtained using successively: 7 level planes (resulting 8 zones), 9 level planes (10 zones) and 11 level planes (12 zones). For every variant of development, the error is calculated by comparing the area of approximate development and the theoretical area of the sphere. A computerized method based on Maple procedures is used. In the paper there is also a comparison between the errors of the two methods (gore method and zone method).

Keywords

• sphere
• development
• computerized method
• errors