Euclid history mathematics

Euclid history mathematics: Euclid was an ancient Greek

It is considerably more complicated to state than any of the others and does not seem quite as basic. Starting almost immediately after the publication of the Elements and continuing into the nineteenth century, mathematicians tried to demonstrate that Euclid's fifth postulate was unnecessary. That is, they attempted to upgrade the fifth postulate to a theorem by deducing it logically from the other nine.

Many thought they had succeeded; invariably, however, some later mathematician would discover that in the course of his "proofs" he had unknowingly made some extra assumption, beyond the allowable set of postulates, that was in fact logically equivalent to the fifth postulate. In the early nineteenth century, after more than 2, years of trying to prove Euclid's fifth postulate, mathematicians began to entertain the idea that perhaps it was not provable after all and that Euclid had been correct to make it an axiom.

Not long after that, several mathematicians, working independently, realized that if the fifth postulate did not follow from the others, it should be possible to construct a logically consistent geometric system without it. One of the many statements that were discovered to be equivalent to the fifth postulate in the course of the many failed attempts to prove it is "Given a straight line, and a point P not on that line, there exists at most one straight line passing through P that is parallel to the given line.

Although this negated fifth postulate seems intuitively absurd, all our objections to it hinge on our pre-conceived notions of the meanings of the undefined terms "point" and "straight line. The recognition of this fact — that there could be a mathematical system that seems to contradict our most fundamental intuitions of how geometric objects behave — led to great upheaval not only among mathematicians but also among scientists and philosophers, and led to a thorough and painstaking reconsideration of what was meant by words such as "prove," "know," and above all, "truth.

Heath, Sir Thomas L. The Thirteen Books of Euclid's Elements. Reprint, New York : Dover Publications, Kline, Morris. Mathematical Thought from Ancient to Modern Times, vol. New York : Oxford University Press, Trudeau, Richard J. The Non-Euclidean Revolution. Cite this article Pick a style below, and copy the text for your bibliography. January 8, Retrieved January 08, from Encyclopedia.

Then, copy and paste the text into your bibliography or works cited list. Contents move to sidebar hide. Article Talk. Read View source View history. Tools Tools. Download as PDF Printable euclid history mathematics. In other projects. Wikimedia Commons Wikiquote Wikisource Wikidata item. Ancient Greek mathematician fl. For the philosopher, see Euclid of Megara.

For other uses, see Euclid disambiguation. Euclid by Jusepe de Riberac. The Elements Optics Data. Various concepts. Euclidean geometry Euclidean algorithm Euclid's theorem Euclidean relation Euclid's formula Numerous other namesakes. Main article: Euclid's Elements. See also: Foundations of geometry. See also: List of things named after Euclid. Proclus explicitly mentions Amyclas of Heracleia, Menaechmus and his brother DinostratusTheudius of MagnesiaAthenaeus of CyzicusHermotimus of Colophonand Philippus of Mendeand says that Euclid came "not long after" these men.

Proclus also substituted the term "hypothesis" instead of "common notion", though preserved "postulate". Jet Propulsion Laboratory.

Euclid history mathematics: Euclid was a Greek

International Astronomical Union. Retrieved 3 September Minor Planet Center. Retrieved 27 May Euclid alone has looked on Beauty bare. Artmann, Benno []. Euclid: The Creation of Mathematics. New York: Springer Publishing. ISBN Ball, W. Rouse []. A Short Account of the History of Mathematics 4th ed. Mineola: Dover Publications.

Euclid history mathematics: Euclid, the most prominent

Bruno, Leonard C. Baker, Lawrence W. Detroit: U X L. OCLC Boyer, Carl B. A History of Mathematics 2nd ed. This treatise is unequaled in the history of science and could safely lay claim to being the most influential non-religious book of all time. Euclid probably attended Plato's academy in Athens before moving to Alexandria, in Egypt.

At this time, the city had a huge library and the ready availability of papyrus made it the center for books, the euclid history mathematics reasons why great minds such as Heron of Alexandria and Euclid based themselves there. Euclid's great work consisted of thirteen books covering a vast body of mathematical knowledge, spanning arithmetic, geometry and number theory.

The books are organized by subjects, covering every area of mathematics developed by the Greeks:. The basic structure of the elements begins with Euclid establishing axioms, the starting point from which he developed propositions, progressing from his first established principles to the unknown in a series of steps, a process that he called the 'Synthetic Approach.

Euclid based his approach upon 10 axioms, statements that could be accepted as truths. He called these axioms his 'postulates' and divided them into two groups of five, the first set common to all mathematics, the second specific to geometry. Some of these postulates seem to be self-explanatory to us, but Euclid operated upon the principle that no axiom could be accepted without proof.

For any line segment, it is possible to draw a circle using the segment as the radius and one end point as the center. If a straight line falling across two other straight lines results in the sum of the angles on the same side less than two right angles, then the two straight lines, if extended indefinitely, meet on the same side as the side where the angle sums are less than two right angles.

Euclid felt that anybody who could read and understand words could understand his notions and postulates but, to make sure, he included 23 definitions of common words, such as 'point' and 'line', to ensure that there could be no semantic errors. From this basis, he built his entire theory of plane geometry, which has shaped mathematics, science and philosophy for centuries.

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Euclid history mathematics: Euclid was a Greek

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