Although there are major differences between the democracy of Athens and the American democracy, it served as an inspiration for democracies all around the world, including American.
First, the Athenians created a democratic system that aimed to have the participation of all citizens and the American system was designed to do the same, although the American system does not use the direct democracy system the Athenians had.
Second, the Athenian system had a bi-cameral legislative system with an Assembly and with a Council, the Assembly was made of every citizen that wanted to attend that were about 60 thousand people. The Council had 500 representatives. The US Congress takes the role of the Greek Assembly summed up with the Council but with a smaller body.
