ARTICLETOPIC: Contributions of Euclid

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DEEPA. J Mathematics 13303008

Contributions of Euclid

Euclid of Alexandria was a Greek mathematician and philosopher living in the fourth century BC who taught at the university in Alexandria, Egypt. He became known as the father of Geometry, many years after publishing a thirteen volume work called “Euclid’s Elements”. In which he compiled and explained all the known mathematics of his time.

Euclid wrote “The Elements”, in which he made many rules that define the geometry taught in schools today. It has helped in finding the perimeters and areas of circles.

The content of the work “Elements” in the shape of 13 different books are given below:-

Book 1:- Triangles, perpendiculars, parallels, area of rectilinear figures, the Pythagorean Theorem.

Book 2:- Transformation of areas, geometric algebra.Book 3:- Circles and tangents.Book 4:- Polygons and circles, construction of regular

polygons including regular pentagon. Book 5:-Treatment of proportion.Book 6:- Idea of proportion applied to similar figures.

Book 7:- Theory of numbers, classification of numbers as even, odd, solid, perfect etc, numerical theory of proportion.

Book 8:- Study of continued proportion.Book 9:- Number theory, including a proof, that the

number of primes is infinite.Book 10:- Study of irrationals.Book 11:- Solid geometry corresponding to Book 1 for

plane geometry.Book 12:- The method of exhaustion used to show that

circles are proportional to their diameters etc.Book 13:- Regular solids.

Euclid’s Contribution in the Field of Geometry

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.

Euclid’s vital contribution was to gather, compile, organize and rework the mathematical concepts of his predecessors into a consistent whole, later to become known as Euclidean Geometry.

In Euclid’s method, deductions are made from premises or axioms. This deductive method as modified by Aristotle was as sole procedure used for demonstrating scientific certitude until the seventeenth century.

It is noteworthy that Euclid’s first geometric definition, that a point has no part. That is, has no dimensions has raised a problem in particle physics, where the electron and other fundamental particles appear to have the dimensions of just a point.

“The Data”, the only other work by Euclid in pure geometry to have survived in Greek; is closely connected with Book 1-4 of the “Elements”.

Euclid also wrote about astronomy, music and optics.

Astronomy

The name of the book is “Phaenomena”. This book of what the Greek called “Sphaeric”, intended for use by students of astronomy, survives in two recensions of which the older must be the nearer to Euclid’s own words.

Optics

“The Optica”, which is attributed to Euclid by Proclus. An elementary treatise in perspective was the first Greek word on the subject and remained the only one until Ptolemy wrote in the middle of the second century.

Music

The name of the work is “Elements of Music”. Two treatises are included in the editions of Euclid’s works.

Euclid’s “Elements” is the world’s most famous mathematical work and is also the oldest continuously used mathematical text book. Almost two and one-half millennium after Euclid’s death.

References Mathematics Education – Dr.K.Sivarajan,

Dr.K.Soman The Teaching of Mathematics – Kulbir Singh Sidhu en.wikipedia.org www.bookrags.com

Pictures

Euclid Statue of Euclid in the Oxford

University Museum of Natural History

Euclid in Rapheal’s School of Athens