MATHS HHW (Shubhang Khattar)

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The great indian mathematician-astronomer



He is the first in the line of great mathematician-astronomers from the classical age of Indian

mathematics and Indian astronomy. Aryabhata is thefather of the Hindu-Arabic or the Decimal numbersystem which has become universal today. His most

famous works are the Aryabhatiya and Arya-Siddhanta.



Aryabhata , born 476 A.D in Patliputra in Magadha is nowmodern Patna in Bihar. There are several tales of claim forhis origins. Many believe that he was born in the south of

India around the Kerala region and lived in Magadha at thetime of the Gupta rulers; time which is known as the

golden age of India. There is no evidence that he was bornoutside Patliputra and traveled to Magadha, the centre of

instruction, culture and knowledge for his studies where heeven set up a coaching institute. His first name " Arya" is

not a south Indian name while "Bhatt" (or sometimesBhatta) is a typical north Indian name. The name ispopular even today in India especially among the trader

community of north India.



He went to Kusumapura for higher studies, and that helived here for some time. Bhāskara I (was a 7th century

Indian mathematician,) identifies Kusumapura asPataliputra (modern Patna). He lived there in thedying years of the Gupta empire, the time which is

known as the golden age of India, when it was already under Hun attack in the Northeast, during the reign of

Buddhagupta and some of the smaller kings before

Vishnugupta



He wrote his famous thesis calledthe " Aryabhatta-siddhanta" morecommonly known as the" Aryabhatiya". This is the only

works to have survived to thepresent day. It containsmathematical and astronomicalhypothesis that have been

discovered to be quite accurate incontemporary mathematics



Direct details of Aryabhata's work are therefore knownonly from the Aryabhatiya. The name Aryabhatiya isdue to later commentators, Aryabhata himself may nothave given it a name.

It is also occasionally referred to as Arya-shatas-aShTa,lit., Aryabhata's 108, which is the number of verses inthe text. It is written in the very terse style typical of the sutra literature, where each line is an aid tomemory for a complex system

Thus, the explication of meaning is due tocommentators. The entire text consists of 108 verses,plus an introductory 13, the whole being divided intofour pAdas or chapters:



Gitikapada: (13 verses): large units of time—kalpa,manvantra, and yuga— which present a cosmology

different from earlier texts such as Lagadha'sVedanga Jyotisha (c. 1st century BCE). There isalso a table of sines ( jya), given in a single verse.The duration of the planetary revolutions during a

mahayuga is given as 4.32 million years.

Ganitapada (33 verses): covering mensuration

(k ṣetra vyāvahāra), arithmetic and geometricprogressions, gnomon / shadows (shanku-chhAyA), simple, quadratic, simultaneous, andindeterminate equations (kuTTaka)



Kalakriyapada (25 verses): differentunits of time and a method fordetermining the positions of planets

for a given day, calculationsconcerning the intercalary month(adhikamAsa), kShaya-tithis, and aseven-day week with names for the

days of week.

Golapada (50 verses):Geometric/trigonometric aspects of

the celestial sphere, features of theecliptic, celestial equator, node,shape of the earth, cause of day andnight, rising of zodiacal signs onhorizon, etc.

CELESTIAL SPHERE



.INNOVATIONS BY ARYABHATA INMATHEMATICS



Place value system and zero

Hindu - Arabic number system is consdered to be a

universal human language, without which mathematics,science and commerce would be almost impossible.

Aryabhatta worked on different place value notations andfinally developed the decimal place value notation and theplace holder. This method of the Indians is none otherthan our arithmetic today .



Aryabhata worked on the approximation for pi (π), andmay have come to the conclusion that π is irrational. In thesecond part of the Aryabhatiyam, he writes:

“Add four to 100, multiply by eight, and then add 62,000.By this rule the circumference of a circle with a diameter of 20,000 can be approached.“

This implies that the ratio of the circumference to thediameter is ((4 + 100) × 8 + 62000)/20000 = 62832/20000= 3.1416, which is accurate to five significant figures

Approximation of π



Aryabhata gives the area of a triangle as:“for a triangle, the result of a perpendicular with the half -side isthe area.”

Aryabhata discussed the concept of sine in his work by the nameof ardha-jya. Literally, it means "half-chord". For simplicity,

people started calling it jya. When Arabic writers translated his works, they referred it as jiba. Later in the 12th century, whenGherardo of Cremona translated these writings from Arabic intoLatin, he replaced the Arabic jiab with its Latin counterpart,sinus, which means "cove" or "bay". And after that, the sinus became sine in English.

Trigonometry



Algebra

In Aryabhatiya Aryabhata provided elegant results forthe summation of series of squares and cubes:

and



Aryabhata's work was of great influence in the Indianastronomical tradition and inf luenced several neighbouringcultures through translations.

His definitions of sine ( jya), cosine (kojya), versine (utkrama- jya), and inverse sine (otkram jya) influenced the birth of

trigonometry. Aryabhata's astronomical calculation methods were also very influential. Along with the trigonometric tables,

India's first satellite Aryabhata and the lunar crater Aryabhata arenamed in his honour. An Institute for conducting research inastronomy, astrophysics and atmospheric sciences is the

Aryabhatta Research Institute of Observational Sciences(ARIES) near Nainital, India. The inter-school Aryabhata MathsCompetition is also named after him,



Wikipedia.org

Icbse.com

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