The Unreasonable Influence of Geometry by Doug Muder Introduction In a world of flux and change, Euclidean geometry maintained its structure for more than 2, years. Over time, this apparent changelessness made Euclidean geometry the poster child of Reason.
Version for printing Euclid of Alexandria is the most prominent mathematician of antiquity best known for his treatise on mathematics The Elements.
The long lasting nature of The Elements must make Euclid the leading mathematics teacher of all time. However little is known of Euclid's life except that he taught at Alexandria in Egypt. Proclusthe last major Greek philosopher, who lived around AD wrote see [ 1 ] or [ 9 ] or many other sources: This man lived in the time of the first Ptolemy; for Archimedeswho followed closely upon the first Ptolemy makes mention of Euclid, and further they say that Ptolemy once asked him if there were a shorted way to study geometry than the Elements, to which he replied that there was no royal road to geometry.
He is therefore younger than Plato 's circle, but older than Eratosthenes and Archimedes ; for these were contemporaries, as Eratosthenes somewhere says.
In his aim he was a Platonist, being in sympathy with this philosophy, whence he made the end of the whole "Elements" the construction of the so-called Platonic figures.
There is other information about Euclid given by certain authors but it is not thought to be reliable. Two different types of this extra information exists.
The first type of extra information is that given by Arabian authors who state that Euclid was the son of Naucrates and that he was born in Tyre.
It is believed by historians of mathematics that this is entirely fictitious and was merely invented by the authors. The second type of information is that Euclid was born at Megara.
This is due to an error on the part of the authors who first gave this information. In fact there was a Euclid of Megarawho was a philosopher who lived about years before the mathematician Euclid of Alexandria.
Get the CBSE Class 9th Mathematics chapter 5, Introduction to Euclid's Geometry: Important questions and topics to prepare for Class 9 Mathematics Examination, Euclid, a Greek mathematician, wrote the book "Elements, " which presented the basic principles for what is now known as Euclidian geometry. Euclid established the system of postulates and proofs still in use today in geometry. The geometry that we all know from high school is Euclidean geometry, which goes back to the book Elements of Geometry written by Euclid in about BC, just after the time of Alexander the Great. But Euclid did not invent his geometry, he collected and systematized the geometry that was already known in .
It is not quite the coincidence that it might seem that there were two learned men called Euclid. In fact Euclid was a very common name around this period and this is one further complication that makes it difficult to discover information concerning Euclid of Alexandria since there are references to numerous men called Euclid in the literature of this period.
Returning to the quotation from Proclus given above, the first point to make is that there is nothing inconsistent in the dating given. However, although we do not know for certain exactly what reference to Euclid in Archimedes ' work Proclus is referring to, in what has come down to us there is only one reference to Euclid and this occurs in On the sphere and the cylinder.
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 ]: 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. 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.Geometry: Euclid’s Elements Essay - Most of geometry is based on two main constructions, circles and straight lines.
In geometry, there are many different tools used for construction such as the compass, the straightedge, carpenter’s square, and mirrors. Fact 4 In the Elements, Euclid inferred the values of what is now called Euclidean geometry from a minor set of axioms. Euclid also wrote works on spherical geometry, perception, conic sections, number theory and rigor.
Fact 5 "Euclid" is a Greek word, meaning "Good Glory". Elements presents all of the Greek geometrical knowledge of Euclids day in a logical fashion.
These books give us a little insight into Euclid and were designed and are used as learning tools. Including theorems and constructions of plane geometry, solid geometry theory of proportions, incommensurable, commensurable, number theory, and the basis for what is known as geometrical algebra.
Theorems One and Two, with important Definitions and Postulates.
Translated by Alex Pearson. Euclid's 23 Definitions for plane geometry: The definitions begin the Elements. 1. A point is that of which there is no part. 2. A line is a widthless length. 3. A line's ends are points. DOWNLOAD AN EPITOME OF THE FIRST THREE BOOKS OF EUCLIDS ELEMENTS OF GEOMETRY FOR THE CADETS OF H M S BRITANNIA an epitome of the pdf An epitome (/ Éª Ëˆ p Éª t É™m iË’ /; Greek: á¼’Ï€Î¹Ï„Î¿Î¼Î®, from á¼’Ï€Î¹Ï„ÎÎ¼Î½ÎµÎ¹Î½ epitemnein meaning.
Both Lincoln and Thomas Jefferson admired and read Euclid’s Elements as a way to improve the mind and promote an individual’s ability to think and reason logically. For me, a former high school geometry teacher and Civil War buff, this was a thrilling realization, a moment of epiphany.