The examination of a map rarely provides us with its internal dynamic. Also, we have the tendency to analyze it in a static manner. The advantage that the European Union represents in abstract geostrategy comes from its diachronic polysemy. Indeed the fast evolution of its structure in the course of these last 50 years allows us to visualize in a concrete manner, topologic and isoperimetric properties. One of these important notions is connectedness. It has considerably influenced the process of enlargement from the beginning with the Benelux, since Belgium has common borders with Luxemburg and the Netherlands. This connectedness abided by the Treaty of Rome and the integration of France, Italy and Germany. At this instant it is still difficult to perceive another fundamental property that belongs to the isometric level. Yet it is already present. The entrance of Denmark confirms connectedness. As for the entrances of the United Kingdom and Ireland, they prove even more insular compactness. This was visible with Corsica, Sardinia and Sicily even if it was difficult to perceive it due to the state absorption. The entrance of Greece seems to challenge these principles but only if we do not consider maritime space. In reality, it allows to activate the first enclosure of the Mediterranean. This will be completed later on by the simultaneous entrances of Spain and Portugal. This time, apart from the existence of Yugoslavia, the enclosure of the Mediterranean is complete. Nobody can henceforth bother the European Union for acceding to it. The entrance of Sweden that creates the link between Denmark and Finland obeys the same principle. On the other side the entrance of Austria highlights the hole phenomenon on the topologic map, with the Swiss enclave. Thus the absorption of Switzerland occurs de facto and it is reinforced de jure by the recent Swiss voting regarding the extension of agreements between Switzerland and the European Union with the passing to 25 members. The entrance of ten new states in 2004 could seem confusing at first in the reading of the names catalogue. However it obeys perfectly the principles that we have highlighted. Thus Cyprus and Malta reinforce from the interior the enclosure of the Mediterranean. As for the series Estonia, Latvia, Lithuania, Poland, Slovakia, Hungary and Slovenia, it represents a related front that allows the expansion in a global manner, of the European Union’s border to the east. The case of the Czech Republic constitutes a new occurrence of the enclave notion but this time immediately absorbed. The entrance of Bulgaria and Romania in 2007, linking Greece with Hungary, completed this connectedness. In the whole of this evolution, we can henceforth promote the isoperimetric phenomenon of the absorption of borders. Indeed any enlargement has the tendency to increase the length of the borders. Yet the successive enlargements of the European Union tend to minimize this effect. Thus we have an isoperimetric phenomenon since we obtain a surface equivalent to the length of a lesser border. Moreover, on the western and Mediterranean parts, these borders are natural since they correspond to the seashore, if we exclude Yugoslavia and Norway. These principles permit us to obtain global criteria of enlargement. Thus Switzerland (enclave), Norway (natural border), Yugoslavia and Albania (enclaves and natural borders) represent candidates that respect connectedness and isoperimetry, which is far from being the case of the oriental issue.