A significant and increasing number of problems related to radiative heat transfer, demand accurate if not exact solutions to fourfold integral equations. In mathematical terms, this is a complex and cumbersome issue even acknowledged by famous polymaths like J. H. Lambert, since the 18^th century. The present author demonstrated and published along his research, the whole procedure for rectangular radiative emitters some 25 years ago. However, in the case of circular and curved sources, the usual analytical approach remains exceedingly difficult and not even suitable for numerical calculus. Recently, the author has elaborated on integral equations applied to fragments of spheres which usually appear in radiative heat transfer and has been fortunate to define new postulates which may solve, with required accuracy, the question of energy transfer between them. In this way not only spherical sectors but also circles, semicircles and circular sectors become affordable. As it is widely accepted, to find the exact expression for radiative exchange by virtue of integration alone is considered no mean feat. The novelty of the process developed lies in that firstly we solve the two initial sets of integrals demanded by analytical methods and then employ the exact results obtained as a kind of iterative algorithm in order to be able to provide the final solution for the remaining double integral equations. This method, has not been described by former researchers and it provides us with a considerable repertoire of scenarios for simulation of energy transmission in the void or in gaseous media. Incidentally, within the operation, new unexpected geometric forms appear and they are subject to exhaustive mathematical assessment revealing interesting findings and a plethora of applications for diverse fields such as architecture, tunnelling or space vessel construction.