Euclid

  Euclid

Euclid of Alexandria is better known as the Father of Geometry. He is one of the most prominent mathematicians of antiquity best known for his treatise The Elements. Little is known about Euclid's life, as there are only a handful of references to him. The date and place of Euclid's birth and the date and circumstances of his death are unknown. But whatever speculated data are available shows that he was born about 325 BC in Alexandria and died about 265 BC.

An Arabian author, al-Qifti (d. 1248), recorded that Euclid's father was Naucrates and his grandfather was Zenarchus, that he was a Greek, born in Tyre and lived in Damascus. But there is no real proof that this is the same Euclid. During the reign of Ptolemy I he taught at Alexandria. Ptolemy had created the great library at Alexandria, which was known as the Museum, because it was considered a house of the muses for the arts and sciences. Many scholars worked and taught there, and that is where Euclid wrote The Elements.

There is a very interesting story about Euclid---

A student who had begun to learn geometry with Euclid asked him “What shall I get by learning all these things in Geometry?” Euclid called his slave and told him to give three pence since he must make gain out of what he learns.

Euclid said to his students that --- There is no royal road to Geometry.

             A page from Euclid’s Elements

Euclid's most famous for his treatise on mathematics called The Elements. The book is a compilation of knowledge that became the centre of mathematical teaching for 2000 years. Probably no results in The Elements were first proved by Euclid. The Elements is divided into thirteen books which cover plane geometry, arithmetic and number theory, irrational numbers, and solid geometry.

Euclid organized the known geometrical ideas, starting with simple definitions, axioms; formed statements called theorems, and set forth methods for logical proofs. He began with accepted mathematical truths, axioms and postulates, and demonstrated logically 467 propositions in plane and solid geometry. One of the proofs was for the theorem of Pythagoras, proving that the equation is always true for every right triangle. The Elements was the most widely used textbook of all time. It has appeared in more than 1,000 editions since it was first printed in 1482 and is thought to have sold more copies than any book other than the Bible. Original of Euclid's Elements have not been preserved, but Arabic mathematicians obviously had a full copy as an Arabic version of The Elements appeared at the end of the 8th century BC.

 Euclid believed that we can't be sure of any axioms without proof, so he devised logical steps to prove them. There are 5 axioms and 5 postulates found in the book of Euclid. He called Axiom "Common Notions," because they were common to all sciences.

Axioms

1.    Things which are equal to the same thing are also equal to one another.

2.    If equals are added to equals, the sums are equal.

3.    If equals are subtracted from equals, the remainders are equal.

4.    Things which coincide with one another are equal to one another.

5.    The whole is greater than the part.

Postulates

1.      You can draw a straight line between any two points.

2.      You can extend the line indefinitely.

3.      You can draw a circle using any line segment as the radius and one end point as the center.

4.      All right angles are equal.

5.      Given a line and a point, you can draw only one line through the point that is parallel to the first line.

The fifth postulates later became the cause of discovery of new branch of geometry known as Non Euclidian Geometry.

Euclid's Elements is remarkable for the clarity with which the theorems are stated and proved. This wonderful book, with all its imperfections, which are indeed slight enough when account is taken of the date it appeared, is and will doubtless remain the greatest mathematical textbook of all time.

Euclid proved that it is impossible to find the "largest prime number," because if you take the largest known prime number, add 1 to the product of all the primes up to and including it; you will get another prime number. Euclid's proof for this theorem is generally accepted as one of the "classic" proofs because of its conciseness and clarity. Millions of prime numbers are known to exist, and more are being added by mathematicians and computer scientists. Mathematicians since Euclid have attempted without success to find a pattern to the sequence of prime numbers.

Although best known for its geometric results, the Elements also include number theory. It considers the connection between perfect numbers and Mersenne primes, the infinitude of prime numbers, Euclid's lemma on factorization (which leads to the fundamental theorem of arithmetic on uniqueness of prime factorizations), and the Euclidean algorithm for finding the greatest common divisor of two numbers.

Euclid also wrote Data, which contains 94 propositions, Phaenomena, concerning spherical astronomy, Caloptrics, about mirrors, Optics, the theory of perspective, and a work of music theory. In his works about optics, Euclid made light rays part of geometry, working with them as if they were straight lines. Many of the works ascribed to Euclid are no longer in existence or are incomplete.

Send your comments to

rkthakur1974@gmail.com