Thales greek mathematician biography

Theaetetus c. This fact led these five solids, now called the Platonic solids , to play a prominent role in the philosophy of Plato and consequently, also influenced later Western Philosophy who associated each of the four classical elements with a regular solid: earth with the cube , air with the octahedron , water with the icosahedron , and fire with the tetrahedron of the fifth Platonic solid, the dodecahedron , Plato obscurely remarked, " The last book Book XIII of the Euclid's Elements , which is probably derived from the work of Theaetetus, is devoted to constructing the Platonic solids and describing their properties; Andreas Speiser has advocated the view that the construction of the 5 regular solids is the chief goal of the deductive system canonized in the Elements.

Eudoxus of Cnidus c. Aristarchus of Samos c. Aristarchus identified the "central fire" with the Sun, and he put the other planets in their correct order of distance around the Sun. However, Eratosthenes c. Posidonius c. Thales is known as the first Greek philosopher, mathematician and scientist. He founded the geometry of lines, so is given credit for introducing abstract geometry.

He was the founder of the Ionian school of philosophy in Miletus, and the teacher of Anaximander. Several schools were founded in Miletus, attracting scientists, philosophers, architects and geographers It is possible that Thales has been given credit for discoveries that were not really his. He is known for his theoretical as well as practical understanding of geometry.

Thales is acknowledged by a number of sources as the one who defined the constellation Ursa Minor and used it for navigation. Some believe he wrote a book on navigation, but it has never been found. Two letters and some verses of Thales are quoted by Diogenes Laertius in his Lives of the Philosophers. Much of what we know of Thales as a philosopher comes from Aristotle.

Herodotus, who lived approximately sixty years after Thales, also wrote about him, as did Eudemus, the first major historian of mathematics. It is possible and likely that his family was of the higher class, and perhaps even wealthy merchants. Some have traced the family of Thales back to an important Phoenician prince. It must be acknowledged, however, that it is possible that Thales was born in Athens and later migrated to Miletus.

This was a school of elite philosophers known to have been established in Athens in the time period attributed to the life of Thales. But Thales was bold enough to go beyond this way of thinking in favor of more logical and rational explanations. There are several accounts of how Thales measured the height of pyramids. Diogenes Laertius writing in the second century AD quotes Hieronymus, a pupil of Aristotle [ 6 ] or see [ 8 ] :- Hieronymus says that [Thales] even succeeded in measuring the pyramids by observation of the length of their shadow at the moment when our shadows are equal to our own height.

This appears to contain no subtle geometrical knowledge, merely an empirical observation that at the instant when the length of the shadow of one object coincides with its height, then the same will be true for all other objects. A similar statement is made by Pliny see [ 8 ] :- Thales discovered how to obtain the height of pyramids and all other similar objects, namely, by measuring the shadow of the object at the time when a body and its shadow are equal in length.

Plutarch however recounts the story in a form which, if accurate, would mean that Thales was getting close to the idea of similar triangles This is in line with the views of Russell who writes of Thales contributions to mathematics in [ 12 ]:- Thales is said to have travelled in Egypt, and to have thence brought to the Greeks the science of geometry.

What Egyptians knew of geometry was mainly rules of thumb, and there is no reason to believe that Thales arrived at deductive proofs, such as later Greeks discovered. On the other hand B L van der Waerden [ 16 ] claims that Thales put geometry on a logical footing and was well aware of the notion of proving a geometrical theorem. However, although there is much evidence to suggest that Thales made some fundamental contributions to geometry, it is easy to interpret his contributions in the light of our own knowledge, thereby believing that Thales had a fuller appreciation of geometry than he could possibly have achieved.

In many textbooks on the history of mathematics Thales is credited with five theorems of elementary geometry:- A circle is bisected by any diameter. The base angles of an isosceles triangle are equal. The angles between two intersecting straight lines are equal. Two triangles are congruent if they have two angles and one side equal. An angle in a semicircle is a right angle.

What is the basis for these claims? Proclus , writing around AD, is the basis for the first four of these claims, in the third and fourth cases quoting the work History of Geometry by Eudemus of Rhodes , who was a pupil of Aristotle , as his source. The History of Geometry by Eudemus is now lost but there is no reason to doubt Proclus.

Thales greek mathematician biography

The fifth theorem is believed to be due to Thales because of a passage from Diogenes Laertius book Lives of eminent philosophers written in the second century AD [ 6 ]:- Pamphile says that Thales, who learnt geometry from the Egyptians, was the first to describe on a circle a triangle which shall be right-angled, and that he sacrificed an ox on the strength of the discovery.

Others, however, including Apollodorus the calculator, say that it was Pythagoras. A deeper examination of the sources, however, shows that, even if they are accurate, we may be crediting Thales with too much.