PROJECTS
Project work in mathematics may be performed individually by a student or jointly by a group of students. These projects may be in the form of construction such as curve sketching or drawing of graphs, etc. It may offer a discussion of a topic from history of mathematics involving the historical development of particular subject in mathematics/ topics on concepts. Students may be allowed to select the topics of their own choice for projects in mathematics. The teacher may act as a fascilitator by creating interest in various topics. Once the topic has been selected, the student should read as much about the topic as is available and finally prepare the project.
PROJECT 1
ARYAB
HAT — THE MATHEMATICIAN AND ASTRONOMER
Prior to the first century A.D., there was a lot of development of mathematics in India but the nomenclature of their contributors is not known presently. One of the Indian mathematicians of ancient times about which some definite information is available is Aryabhat, and the name of his creation is Aryabhattiya.
TIME AND PLACE OF BIRTH
Aryabhat has said in his creation Aryabhattiya that he was 23 year old, when
he wrote Aryabhattiya and upto that time 3600 years of Kaliyug (dfy;qx) had
elapsed. This works out that he wrote the manuscript in 499 A.D. and his year
of birth was 476 A.D.
Aryabhat has also said in the manuscript that he has given the knowledge
attained at Kusumpur (Pataliputra) while studying. This gives the impression
that he was born at Pattliputra but according to the views of majority he was
born in South India (in Ashmak district, which is on the bank of river Godavari).
The world famous historian mathematician Dr. Bhou-Daji (Hkkm&nkth) of
Maharashtra traced the manuscript of Aryabhattiya in 1864 from South India
and published its contents.
Aryabhattiya is in Sanskrit and is divided in four major parts called 'Pads'. The
manuscript contains a total of 153 Shlokas and their distribution is given below:
1. Dashgeetika Pad (n'kxhfrdk ikn) containing 33 shlokas
2. Ganitpad (xf.kr ikn) containing 25 shlokas
3. Kalkriya Pad (dkyfØ;k ikn) containing 25 shlokas
4. Goladhyay (xksykè;k;) containing 50 shlokas
CONTRIBUTION
1. Aryabhat created a new method of enumerating numbers using Sanskrit alphabets.
According to this, he gave the following numerical values to 25 consonants
(वर्ण अक्षर)
क: 1, ख: 2, ग: 3 घ: 4, ड.: 5, च: 6, छ: 7, ज: 8, झ: 9, ञ:
10: 11, ठ: 12, ड: 13, ढ: 14
, ण: 15, त: 16, थ: 17, द: 18, ध
: 19, न: 20, प 21, फ 22, ब: 23, भ: 24, म 25, य: 30, र 40,
ल: 50 व 60 श: 70, ष: 80 स: 90 ह: 100
He gave the following values to vowels (₹)
1: 100,: 10000,: 1000000,: 100000000,: 10000000000.
: 1000000000000,: 100000000000000,: 10000000000000000
As an example, Aryabhat says that in a Mahayug (Hr), the earth revolves
around the Sun 4320000 times. According to the above numerical system,
Aryabhat has stated it as खुयुष्
: 2 x 10000 = 20000
: 30 x 10000 = 300000 jandə
: 4 x 1000000 = 4000000 CER
खुयुष = 4320000
2. Aryabhat has sumarised important principles of arithmetic, geometry and
algebra in 33 shlokas of Ganitpad only. In these shlokas, he has given
formulae for finding:
• squares and square-roots
• cubes and cube-roots
• area of squares, triangles and circles
• volume of a sphere
His most important contribution was the value of, the ratio between the
circumference and the diameter of a circle upto four places of decimals
as 3.1416. He stated that it is the approximate value of. He was the first
Indian mathematician who has stated that it is the approximate value of x.
Laboratory Manual
and solving of quadratic equations.
4. He has stated and verified Pythagoras theorem through examples.
5. Another important contribution of Aryabhat has been formation of tables
of sine and cosine functions at intervals of 3 ° 45 'each.
6. Aryabhat has also written about astronomy and astrology in his Goladhyay.
He was the first mathematician who declared that the earth revolves about
its axis and the Nakshtras are still, which was against the mythological
statements. He also described about solar and lunar eclipses and reasons
for their occurring.
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