Thales' theorem

In geometry, Thales' theorem 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, and is mentioned and proved as part of the 31st proposition, in the third book of Euclid's Elements. It is generally attributed to Thales of Miletus, who is said to have offered an ox (probably to the god Apollo) as a sacrifice of thanksgiving for the discovery, but sometimes it is attributed to Pythagoras.

History

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's statement that Thales

Indian and Babylonian mathematicians knew this for special cases before Thales proved it. It is 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 180°.

Thales

Thales of Miletus (/ˈθeɪliːz/; Greek: Θαλῆς (ὁ Μιλήσιος), Thalēs; c. 624 – c. 546 BC) was a pre-Socratic Greek philosopher, mathematician and astronomer from Miletus in Asia Minor, current day Milet in Turkey and one of the Seven Sages of Greece. Many, most notably Aristotle, regard him as the first philosopher in the Greek tradition. Aristotle reported Thales' hypothesis that the originating principle of nature and the nature of matter was a single material substance: water.

Thales attempted to explain natural phenomena without reference to mythology. 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.

In mathematics, Thales used geometry to calculate the heights of pyramids and the distance of ships from the shore. He is the first known individual to use deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. He is the first known individual to whom a mathematical discovery has been attributed.

Thales (painter)

Thales of Sicyon, was an ancient Greek painter who is mentioned with the epithet megalophyes, genius by Diogenes Laertius (i. 38), on the authority of Demetrius Magnes. In the same passage, Diogenes speaks of another Thales, as mentioned in the work of Duris on painting ; and it may be presumed, therefore, that this Thales was a painter; but whether the two were different persons, or the same person differently mentioned by Demetrius and by Duris, cannot be determined.

He is placed by a late Byzantine writer, Theodore Hyrtacenus, on a level with Pheidias and Apelles.

References

 This article incorporates text from a publication now in the public domain: Smith, William, ed. (1870). "^{article name needed}". Dictionary of Greek and Roman Biography and Mythology. 

Thales (disambiguation)

Thales was a Greek philosopher from Miletus.

Thales may also refer to: