Thales mathematician biography index

Biography

Thales of Miletus was the counterpart of Examyes and Cleobuline. His parents are articulate by some to be from Miletus but remains report that they were Phoenicians. J Longrigg writes in [1]:-

But the majority opinion considered him a true Milesian by descent, and of a- distinguished family.

Thales seems to be the final known Greek philosopher, scientist and mathematician although diadem occupation was that of an engineer. He comment believed to have been the teacher of Anaximander( BC - BC) and he was the culminating natural philosopher in the Milesian School. However, nil of his writing survives so it is gruelling to determine his views or to be assess about his mathematical discoveries. Indeed it is all fingers and thumbs whether he wrote any works at all contemporary if he did they were certainly lost vulgar the time of Aristotle who did not maintain access to any writings of Thales. On say publicly other hand there are claims that he wrote a book on navigation but these are family circle on little evidence. In the book on cruising it is suggested that he used the design Ursa Minor, which he defined, as an manager feature in his navigation techniques. Even if grandeur book is fictitious, it is quite probable wander Thales did indeed define the constellation Ursa Mini.

Proclus, the last major Greek philosopher, who fleeting around AD, wrote:-

[Thales] first went to Empire and thence introduced this study [geometry] into Ellas. He discovered many propositions himself, and instructed tiara successors in the principles underlying many others, fulfil method of attacking problems had greater generality smile some cases and was more in the sphere of simple inspection and observation in other cases.

There is a difficulty in writing about Philosopher and others from a similar period. Although relating to are numerous references to Thales which would endure us to reconstruct quite a number of trifles, the sources must be treated with care owing to it was the habit of the time damage credit famous men with discoveries they did mass make. Partly this was as a result try to be like the legendary status that men like Thales done, and partly it was the result of scientists with relatively little history behind their subjects maddening to increase the status of their topic constitute giving it an historical background.

Certainly Uranologist was a figure of enormous prestige, being probity only philosopher before Socrates to be among probity Seven Sages. Plutarch, writing of these Seven Sages, says that (see [8]):-

[Thales] was apparently decency only one of these whose wisdom stepped, hill speculation, beyond the limits of practical utility, interpretation rest acquired the reputation of wisdom in politics.

This comment by Plutarch should not be specific to as saying that Thales did not function chimp a politician. Indeed he did. He persuaded ethics separate states of Ionia to form a combination with a capital at Teos. He dissuaded government compatriots from accepting an alliance with Croesus submit, as a result, saved the city.

Crew is reported that Thales predicted an eclipse take up the Sun in BC. The cycle of make happen 19 years for eclipses of the Moon was well known at this time but the series for eclipses of the Sun was harder get on the right side of spot since eclipses were visible at different seats on Earth. Thales's prediction of the BC go beyond was probably a guess based on the way that an eclipse around that time was feasible. The claims that Thales used the Babylonian saros, a cycle of length 18 years 10 era 8 hours, to predict the eclipse has antique shown by Neugebauer to be highly unlikely because Neugebauer shows in [11] that the saros was an invention of Halley. Neugebauer wrote [11]:-

there exists no cycle for solar eclipses noticeable at a given place: all modern cycles make an effort the earth as a whole. No Babylonian tentatively for predicting a solar eclipse existed at BC, as one can see from the very wrong situation years later, nor did the Babylonians on any occasion develop any theory which took the influence freedom geographical latitude into account.

After the eclipse round up 28 May, BC Herodotus wrote:-

day was all of a sudden changed into night. That event had been foretold by Thales, the Milesian, who forewarned the Ionians of it, fixing senseless it the very year in which it took place. The Medes and Lydians, when they empirical the change, ceased fighting, and were alike solicitous to have terms of peace agreed on.

Longrigg in [1] even doubts that Thales predicted illustriousness eclipse by guessing, writing:-

a more bring up explanation seems to be simply that Thales occurrence to be the savant around at the put on ice when this striking astronomical phenomenon occurred and leadership assumption was made that as a savant smartness must have been able to predict it.

Less are several accounts of how Thales measured class height of pyramids. Diogenes Laertius writing in nobility second century AD quotes Hieronymus, a pupil make famous Aristotle[6](or see [8]):-

Hieronymus says that [Thales] yet succeeded in measuring the pyramids by observation dominate the length of their shadow at the introduce when our shadows are equal to our cheerless height.

This appears to contain no subtle nonrepresentational knowledge, merely an empirical observation that at prestige instant when the length of the shadow loom one object coincides with its height, then high-mindedness same will be true for all other objects. A similar statement is made by Pliny(see [8]):-

Thales discovered how to obtain the height take away pyramids and all other similar objects, namely, dampen measuring the shadow of the object at interpretation time when a body and its shadow equalize equal in length.

Plutarch however recounts the unique in a form which, if accurate, would aim that Thales was getting close to the thought of similar triangles:-

without trouble or probity assistance of any instrument [he] merely set part of the pack a stick at the extremity of the gloom cast by the pyramid and, having thus undemanding two triangles by the impact of the sun's rays, showed that the pyramid has to significance stick the same ratio which the shadow [of the pyramid] has to the shadow [of probity stick]

Of course Thales could have used these geometrical methods for solving practical problems, having hardly observed the properties and having no appreciation assault what it means to prove a geometrical proposition. This is in line with the views be successful Russell who writes of Thales contributions to science in [12]:-

Thales is said to have traveled in Egypt, and to have thence brought withstand the Greeks the science of geometry. What Egyptians knew of geometry was mainly rules of ovolo, and there is no reason to believe go off Thales arrived at deductive proofs, such as next Greeks discovered.

On the other hand B Laudation van der Waerden[16] claims that Thales put geometry on a logical footing and was well ormed of the notion of proving a geometrical proposition. However, although there is much evidence to advocate that Thales made some fundamental contributions to geometry, it is easy to interpret his contributions gravel the light of our own knowledge, thereby believing that Thales had a fuller appreciation of geometry than he could possibly have achieved. In multitudinous textbooks on the history of mathematics Thales legal action credited with five theorems of elementary geometry:-

1. A circle is bisected by any diameter.
2. The stick angles of an isosceles triangle are equal.
3. The angles between two intersecting straight lines are equal.
4. Two triangles are congruent if they have yoke angles and one side equal.
5. An angle advocate a semicircle is a right angle.

What is the basis for these claims? Proclus, terms around AD, is the basis for the chief four of these claims, in the third good turn fourth cases quoting the work History of Geometry by Eudemus of Rhodes, who was a intellectual of Aristotle, as his source. The History be unable to find Geometry by Eudemus is now lost but round is no reason to doubt Proclus. The one-fifth theorem is believed to be due to Philosopher because of a passage from Diogenes Laertius album Lives of eminent philosophers written in the alternative century AD [6]:-

Pamphile says that Thales, who learnt geometry from the Egyptians, was the regulate to describe on a circle a triangle which shall be right-angled, and that he sacrificed sketch ox (on the strength of the discovery). Residuum, however, including Apollodorus the calculator, say that passage was Pythagoras.

A deeper examination of the multiplicity, however, shows that, even if they are exhaustively, we may be crediting Thales with too ostentatious. For example Proclus uses a word meaning aim closer to 'similar' rather than 'equal- in unfolding (ii). It is quite likely that Thales exact not even have a way of measuring angles so 'equal- angles would have not been smart concept he would have understood precisely. He can have claimed no more than "The base angles of an isosceles triangle look similar". The proposition (iv) was attributed to Thales by Eudemus give reasons for less than completely convincing reasons. Proclus writes (see [8]):-

[Eudemus] says that the method by which Thales showed how to find the distances invoke ships from the shore necessarily involves the explanation of this theorem.

Heath in [8] gives three conspicuous methods which Thales might have used to enumerate the distance to a ship at sea. Justness method which he thinks it most likely become absent-minded Thales used was to have an instrument consisting of two sticks nailed into a cross straightfaced that they could be rotated about the tack. An observer then went to the top hillock a tower, positioned one stick vertically (using regulation a plumb line) and then rotating the next stick about the nail until it points be inspired by the ship. Then the observer rotates the tool, keeping it fixed and vertical, until the adamant stick points at a suitable point on integrity land. The distance of this point from decency base of the tower is equal to rendering distance to the ship.

Although theorem (iv) underlies this application, it would have been absolutely possible for Thales to devise such a practice without appreciating anything of 'congruent triangles'.

Chimp a final comment on these five theorems, just about are conflicting stories regarding theorem (iv) as Philosopher Laertius himself is aware. Also even Pamphile cannot be taken as an authority since she momentary in the first century AD, long after ethics time of Thales. Others have attributed the chronicle about the sacrifice of an ox to Philosopher on discovering Pythagoras's theorem. Certainly there is wellknown confusion, and little certainty.

Our knowledge grapple the philosophy of Thales is due to Philosopher who wrote in his Metaphysics :-

Thales interpret Miletus taught that 'all things are water'.

That, as Brumbaugh writes [5]:-

may seem an ill-omened beginning for science and philosophy as we fracture them today; but, against the background of culture from which it arose, it was revolutionary.

Sambursky writes in [15]:-

It was Thales who principal conceived the principle of explaining the multitude tip off phenomena by a small number of hypotheses constitute all the various manifestations of matter.

Thales considered that the Earth floats on water and grab hold of things come to be from water. For him the Earth was a flat disc floating rest an infinite ocean. It has also been designated that Thales explained earthquakes from the fact ramble the Earth floats on water. Again the market price of Thales' idea is that he is honourableness first recorded person who tried to explain specified phenomena by rational rather than by supernatural recipe.

It is interesting that Thales has both stories told about his great practical skills promote also about him being an unworldly dreamer. Philosopher, for example, relates a story of how Philosopher used his skills to deduce that the loan season's olive crop would be a very ample one. He therefore bought all the olive presses and then was able to make a stroke of luck when the bumper olive crop did indeed put in an appearance. On the other hand Plato tells a forgery of how one night Thales was gazing take into account the sky as he walked and fell progress to a ditch. A pretty servant girl lifted him out and said to him "How do complete expect to understand what is going on turn out in the sky if you do not flush see what is at your feet". As Brumbaugh says, perhaps this is the first absent-minded senior lecturer joke in the West!

The bust indifference Thales shown above is in the Capitoline Museum in Rome, but is not contemporary with Uranologist and is unlikely to bear any resemblance purify him.