Information about euclid mathematicians

At the time, Euclid the philosopher and Euclid the mathematician were wrongly considered the same person, so this painting includes mathematical objects on the table. Most of these, and the finest of them, are novel. And when we discovered them we realized that Euclid had not made the synthesis of the locus on three and four lines but only an accidental fragment of it, and even that was not felicitously done.

The oldest extant direct citations to the Elements in works whose dates are firmly known are not until the 2nd century AD, by Galen and Alexander of Aphrodisias ; by this time it was a standard school text. This deductive method, as modified by Aristotlewas the sole procedure used for demonstrating scientific certitude "truth" until the seventeenth century.

At the time of its introduction, Elements was the most comprehensive and logically rigorous examination of the basic principles of geometry. It survived the eclipse of classical learning, which occurred with the fall of the Roman Empirethrough Arabic translations. Elements was reintroduced to Europe in c.

Information about euclid mathematicians: Euclid (flourished c. bce, Alexandria, Egypt)

Over time, it became a standard textbook in many societies, including the United Statesand remained widely used until the mid-nineteenth century. Much of the information in it still forms a part of many high school geometry curricula. Axiomatic Systems To understand Euclid's Elements, one must first understand the concept of an axiomatic system.

Mathematics is often described as being based solely on logic, meaning that statements are accepted as fact only if they can be logically deduced from other statements known to be true. What does it mean for a statement to be "known to be true? However, there must be some set of statements, called axioms, that are simply assumed to be true.

Without axioms, no chain of deductions could ever begin. Thus even mathematics begins with certain unproved assumptions. Ideally, in any axiomatic system, the assumptions are of such a basic and intuitive nature that their truth can be accepted without qualms. Yet axioms must be strong enough, or true enough, that other basic statements can be proved from them.

Information about euclid mathematicians: Euclid of Alexandria is

Definitions are also part of an axiomatic system, as are undefined terms certain words whose definitions must be assumed in order for other words to be defined based on them. The obvious conclusion, therefore, is that all is well with the argument of Proclus and this was assumed until challenged by Hjelmslev in [ 48 ]. He argued that the reference to Euclid was added to Archimedes ' book at a later stage, and indeed it is a rather surprising reference.

It was not the tradition of the time to give such references, moreover there are many other places in Archimedes where it would be appropriate to refer to Euclid and there is no such reference. Despite Hjelmslev's claims that the passage has been added later, Bulmer-Thomas writes in [ 1 ]:- Although it is no longer possible to rely on this reference, a general consideration of Euclid's works For further discussion on dating Euclid, see for example [ 8 ].

This is far from an end to the arguments about Euclid the mathematician. The situation is best summed up by Itard [ 11 ] who gives three possible hypotheses. They all contributed to writing the 'complete works of Euclid', even continuing to write books under Euclid's name after his death.

Information about euclid mathematicians: Euclid (/ˈjuːklɪd/; Ancient Greek:

The 'complete works of Euclid' were written by a team of mathematicians at Alexandria who took the name Euclid from the historical character Euclid of Megara who had lived about years earlier. It is worth remarking that Itard, who accepts Hjelmslev's claims that the passage about Euclid was added to Archimedesfavours the second of the three possibilities that we listed above.

We should, however, make some comments on the three possibilities which, it is fair to say, sum up pretty well all possible current theories. There is some strong evidence to accept i. It was accepted without question by everyone for over years and there is little evidence which is inconsistent with this hypothesis. It is true that there are differences in style between some of the books of the Elements yet many authors vary their style.

Again the fact that Euclid undoubtedly based the Elements on previous works means that it would be rather remarkable if no trace of the style of the original author remained. Even if we accept i then there is little doubt that Euclid built up a vigorous school of mathematics at Alexandria. He therefore would have had some able pupils who may have helped out in writing the books.

However hypothesis ii goes much further than this and would suggest that different books were written by different mathematicians. Other than the differences in style referred to above, there is little direct evidence of this. Although on the face of it iii might seem the most fanciful of the three suggestions, nevertheless the 20th century example of Bourbaki shows that it is far from impossible.

Of course if iii were the correct hypothesis then Apolloniuswho studied with the pupils of Euclid in Alexandria, must have known there was no person 'Euclid' but the fact that he wrote Euclid did not work out the syntheses of the locus with respect to three and four lines, but only a chance portion of it Nevertheless the mathematicians who made up the Bourbaki team are all well known in their own right and this may be the greatest argument against hypothesis iii in that the 'Euclid team' would have to have consisted of outstanding mathematicians.

So who were they? We shall assume in this article that hypothesis i is true but, having no knowledge of Euclid, we must concentrate on his works information about euclid mathematicians making a few comments on possible historical events. Euclid must have studied in Plato's Academy in Athens to have learnt of the geometry of Eudoxus and Theaetetus of which he was so familiar.

None of Euclid's works have a preface, at least none has come down to us so it is highly unlikely that any ever existed, so we cannot see any of his character, as we can of some other Greek mathematicians, from the nature of their prefaces. Pappus writes see for example [ 1 ] that Euclid was Although being an amazing work in the history of mathematics, it still has its critics.

For instance, On Divisions of Figures was a work that focused on geometrical figures. His work Catoptrics was about mathematical theories of mirrors.