Use of integral calculus for building developments of undevelopable surfaces of revolution

Abstract

Generally, students of architecture use rather simple geometric elements: planes, prisms, cylinders, etc to represent their architectural decisions with paper and card models. However, nowadays modern architects are trying to diversify the architectural environment with more complex surfaces. So, the students of architecture also try to complicate their paper models with curvilinear forms. To facilitate students' architectural modeling and to render more precise building of paper-made curvilinear surfaces, the method of constructing development of elevation view sur-faces using integral calculation has been proposed. These developments are constructed similar to the sphere development, i.e. every given surface is divided into 12 identical segments. The task is to find the full length of the main meridian and the arcs of parallels which make part of the constructed segment. The main meridian length is defined by the integral arc length formula.