A serious technical problem that we encounter in negotiations is the lack of a uniform framework for our maps. This problem has consequences in both the issue of boundaries and the issue of borders. The repercussions are not only present in the F.I.R but in the territorial waters as well. On the technical level everything depends on the acceptance of the initial map. The traditional approach which operates under the old conditions has intrinsic cartography problems which cause dramatic conflicts with the satellite maps. Also in this framework there is the issue of digitization. Because it is not sufficient to digitize old maps with problems and say that we have passed onto the computer phase. The maps have to be satellite and the boundaries with the borders have to be calculated accordingly. Moreover, a great effort has to be made by the air force and the navy so as to have the necessary unification of our aeronautical maps, for being presented univocal abroad and in negotiations. Our methodology has to be based on the notion of the middle line, when it is necessary of course and as consequence, in the base lines as well. In this framework the hydrographic office operates in order to produce borders and it uses approximately 800 triads to construct the greatest circles. This process is not only strenuous for the technicians due to the human intervention, but it can be disputed since its complexity can easily create human errors that our adversaries will exploit in negotiations. In order to strengthen this effort, we can operate in the framework of topostrategy and use the Voronoi diagrams since via the duality, the Delaunay triangulation, we have the greatest circles as intermediate and the middle line as a final result. In other words, this new mathematical background meets the demands of cartography. Moreover, via Fortune’s algorithm, there is an efficient way of calculation with the contemporary data of computer science without having in essence problems even if tens of thousands of circles are necessary to respond to the magnitude of information that we have from the satellite maps. This is valid even in our case, where we need only the pixels that constitute the coast lines. In practice, the whole process is automatic and it is sufficient for the negotiators to agree upon the basic principles of the problem and not be bothered with its solution. This approach facilitates our internal relations between the air force and the navy as well and it allows the establishment of the unification of the aeronautical maps. We consider this the only way in order to be reliable in our negotiations on matters that concern the FIR, the borders, the territorial waters, the shelf but the E.E.Z. too. Otherwise the slightest discrepancy between us can be used against us. The legal basis of things is fundamental only it is not an argument by itself, while the mathematical substrate is directly related with justice since it causes and seeks solutions which are symmetrical for the players and in consequence righteous in the area of rights.