1. The alliance of Nazi Germany and Fascist Italy before and during World War II. The Rome-Berlin Axis was formed 1936, when Italy was being threatened with sanctions because of its invasion of Ethiopia (Abyssinia). It became a full military and political alliance May 1939. A 10-year alliance between Germany, Italy, and Japan (Rome-Berlin-Tokyo Axis) was signed Sept 1940 and was subsequently joined by Hungary, Bulgaria, Romania, and the puppet states of Slovakia and Croatia. The Axis collapsed with the fall of Mussolini and the surrender of Italy 1943, followed by Germany and Japan 1945. 2. In mathematics, a line from which measurements may be taken, as in a coordinate axis; or a line about which an object may be symmetrical, as in an axis of symmetry; or a line about which an object or plane figure may revolve. Subject by: Russell Webb