Editing History of geometry (section)

=== Thales and Pythagoras ===
[[Image:Pythagorean.svg|thumb|[[Pythagorean theorem]]: ''a''<sup>2</sup>&nbsp;+&nbsp;''b''<sup>2</sup>&nbsp;=&nbsp;''c''<sup>2</sup>]]
[[Thales]] (635–543 BC) of [[Miletus]] (now in southwestern Turkey), was the first to whom deduction in mathematics is attributed. There are five geometric propositions for which he wrote deductive proofs, though his proofs have not survived. [[Pythagoras]] (582–496 BC) of Ionia, and later, Italy, then colonized by Greeks, may have been a student of Thales, and traveled to [[Babylon]] and [[Egypt]]. The theorem that bears his name may not have been his discovery, but he was probably one of the first to give a deductive proof of it. He gathered a group of students around him to study mathematics, music, and philosophy, and together they discovered most of what high school students learn today in their geometry courses. In addition, they made the profound discovery of [[commensurability (mathematics)|incommensurable lengths]] and [[irrational number]]s.