In geometry, Thales' theorem (named after Thales of Miletus) states that if A, B and C are points on a circle where the line AC is a diameter of the circle, then the angle ABC is a right angle. Thales' theorem is a special case of the inscribed angle theorem. It is generally attributed to Thales, who is said to have sacrificed an ox in honor of the discovery, but sometimes it is attributed to Pythagoras.

There is nothing extant of the writing of Thales, work done in ancient Greece tended to be attributed to men of wisdom without respect to all the individuals involved in any particular intellectual constructions, this is true of Pythagoras especially. Attribution did tend to occur at a later time, Reference to Thales was made by Proclus, and by Diogenes Laertius documenting Pamphila statement that the ancient

Indian and Babylonian mathematicians knew this for special cases before Thales proved it. It's believed that Thales learned that an angle inscribed in a semicircle is a right angle during his travels to Babylon. The theorem is named after Thales because he was said by ancient sources to have been the first to prove the theorem, using his own results that the base angles of an isosceles triangle are equal, and that the sum of angles in a triangle is equal to two right angles.

Thales of Miletus ( /ˈθeɪliːz/; Greek: Θαλῆς, Thalēs; c. 624 BC – c. 546 BC) was a pre-Socratic Greek philosopher from Miletus in Asia Minor, and one of the Seven Sages of Greece. Many, most notably Aristotle, regard him as the first philosopher in the Greek tradition. According to Bertrand Russell, "Western philosophy begins with Thales." Thales attempted to explain natural phenomena without reference to mythology and was tremendously influential in this respect. Almost all of the other pre-Socratic philosophers follow him in attempting to provide an explanation of ultimate substance, change, and the existence of the world—without reference to mythology. Those philosophers were also influential, and eventually Thales' rejection of mythological explanations became an essential idea for the scientific revolution. He was also the first to define general principles and set forth hypotheses, and as a result has been dubbed the "Father of Science", though it is argued that Democritus is actually more deserving of this title.