DEVELOPMENT OF MATHEMATICS

Contribution of eminent mathematicians to the development of mathematics - Aryabhatta,Brahmagupta, Baskara, Ramanujam, Euler, Euclid, Pythagoras, Gauss.

FAMOUS MATHEMATICIANS

ARCHIMEDES

Archimedes is remembered as the greatest mathematician of the ancient era. He contributed significantly in geometry regarding the areas of plane figures and the areas as well as volumes of curved surfaces. His works expected integral calculus almost 2000 years before it was invented by Sir Isaac Newton and Gottfried Wilhelm von Leibniz. He also proved that the volume of a sphere is equal to two-thirds the volume of a circumscribed cylinder. He regarded this as his most vital accomplishment. So, he desired that a cylinder circumscribing a sphere ought to be inscribed on his tomb. He found an approximate value of pi by circumscribing and inscribing a circle with regular polygons of 96 sides. His works have original ideas, impressive demonstrations and excellent computational techniques.

Some of these which have survived are:

ü on the sphere and cylinder

ü measurement of a circle

ü on conoids and spheroids

ü on spirals

ü on plane equilibriums

ü the sand reckoner

ü quadrature of the parabola

ü on floating bodies

ü stomachion

EUCLID

Euclid is the most famous mathematician of all time. "Euclid's Elements" is divided into 13 books.

ü the initial six are related to plane geometry

ü seven, eight and nine are pertaining to number theory

ü number ten is regarding Eudoxus's theory of irrational numbers

ü eleven to thirteen comprise of solid geometry

ü the last part throws light on the properties of five regular polyhedrons and an evidence that there can be maximum five of these

These Elements have an impressive clarity regarding the selection and order of the theorems and problems. There are minimum assumptions, less extraneous material and an excellent logic in the propositions. The Elements was first published in 1482.

The other works of Euclid which survive are:

ü optics

ü phenomena

ü on divisions of figures

ü data

The works of Euclid that have not survived are:

ü elements of music

ü book of fallacies

ü conics

ü porisms

ü surface loci

ARYA BHATA

The Indian mathematician and astronomer Aryabhata (476 A.D) is well known for his work. He was born at Pataliputra near Patna in Bihar. His most famous book is known as ―Aryabhrtia‖. In arithmetic, Algebra and place Geometry Aryabhata suggested humorous rules. A few important rules are enlisted below-

1. Area of triangle = base*height

2. The value of Pi =3.1456

3. Area of the circle (pi)2

4. Sum of AP =n/2[2a+(n-1)d

To sum up Aryabhata was really one of the greatest geniuses of his time in the field of mathematics and astronomy.

BRAHMAGUPTA

The ancient Indian astronomer brahmagupta is credited with having put forth the concept or zero for the fist time: brahmagupta is said to have been born in the year 598 A.D. at Bhillamala in Gujarat, western Indian. Much is known about brahmagupta’s early life, we are told that his name as a mathematician was well established when k.vyaghramukha of the chapa dynasty made him the court astronomer.

In the earlier Roman and Babylonian system of numeration, large number of characters was required to denote higher numerals. Thus enumeration and computation became unwieldy. For instance, as E the Roman system of numeration, the number thirty would have to be written as X; while as per the decimal system it would 30, further the number thirty three would be XXXIII as per roman system, would be 33 as per the decimal system. This also made computation easier.

BHASKARA

Bhashara or bhasharacharya is the most well known ancient Indian mathematician. He was born on 1114A.D. at bijjadabida in the sahyadari hill. He is famous for his book siddhantashiromani (1150 A.D). it is divided into four sections-leelavati (a book on arithmetic), bijaganita(algebra), goladnayaya(chapter on sphere- celestial globe), and granoganita (mathematics of a planets), leelavagti contains many interesting problems and was a very popular text book. He gave an example idea of what is now called ―Rolle’s theorem.‖ Unfortunately, later Indian mathematics did not take any notice of this. Five centuries, later newton and Leibnitz developed these subjects. As an astronomer bhaskara is renowned for his concept of tatakalikagati.

RAMANUJAN

Ramanujan was born in Brahmin family on December 22, 1887 at erode madras. He got his school education at kumbakoram. He won a scholarship in matriculation examination. His teachers were very much impressed by his injected and special gifted abilities in mathematics.

Hardy remarked: I had never seen anything the least like them before. A single look at them is enough to show that they could be written down by a mathematician of the highest class. His work thrown light on divergent series. Hypermetric series continued fraction, definite integrals. Partition functions, ecliptic functions the theory of numbers, fractional differentiation and highly composite numbers.