Ancient greeks were very sophisticated, with authors like Socrates and Platos, they contributed much knowledge of what we know today from other sources such as the Arabs and the Romans.
Pythagoras studied triangular numbers (based on patterns of dots in triangular shapes) and also perfect numbers (integers that are the sum of their proper positive divisors). Although the Pythagorean Theorem has his name, it may have been discovered by the Indians and Babylonians much earlier in time. Some scholars believe Pythagoras and/ or his student were among the first Greeks to actually prove the theorem. A wierd fact is that Pythagoras and his followers worshiped numbers like God. Although that seems a little odd, modern day mathematicians often debate if the creation of math was from the human mind or simply just part of the universe.
Example:
Suppose Homer wants to catch a stationary bus. Before he can get there, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there. Before traveling a fourth, he must travel one-eighth; before an eighth, one-sixteenth; and so on.
