ARYABHATA

Contents

• Introduction
• Place of Birth
• His Works
• His Inventions
• The Zero
• Pi (π)
• Trigonometry
• Rotation of the Earth
• Sidereal Astronomy
• Solar and Lunar Eclipses
• His Commentators
• Brahmagupta
• Bhaskara I
• Bhaskara II

Introduction

Aryabhata was one of the greatest mathematicians and astronomers of Ancient India whose works are still referred to by the modern scholars. He is mostly known for his contribution in the field of astronomy as the head of an astronomical observatory in Ujjain, the leading communication network centre of Gupta dynasty.

Aryabhata set a stepping stone towards the advancement of astronomy in India which is a matter of utmost pride and gratitude. Such is the influence of this great scientist in the genre of astronomy, that the first satellite launched by India (19^th April 1975) was named after Aryabhata. Simultaneously, the International Astronomical Union has named a lunar crater after him. The residue of a lunar impact crater situated in the eastern Mare Tranquillitatis is named Aryabhata to pay homage to the scientist.

Place of Birth

There is controversy over Aryabhata’s date and place of birth; however,  historians have archived his year and place of birth as 476 A.D. at Ashmaka or Kusumapura in India. It is also believed that he was born at Ashmaka, in present Maharashtra, but later his family moved to a small town of Kusumapura located in the present Bihar. Again, official records state that Aryabhata lived till the year 550 A.D. while many historians claim his year of death as 629 A.D.

His Works

Aryabhata was a revered scholar and teacher of his times. It is most probable that he was the Vice Chancellor of the Nalanda University as he is being referred to as Kulapa or Kulapati (vice chancellor) by many of his commentators including Brahmagupta and Bhaskara II. His works include –

I.        Aryabhatiya in 499 A.D.  (A compendium of mathematics and astronomy)

II.        Aryabhata-siddhanta  (Astronomical computations)

Aryabhatia is a synopsis on Hindu mathematics till the date of Aryabhata and is called the Indian Mathematical literature of all times. He composed this text when he was only 23 years of age. The plethora of subjects covered in the book includes complex computations of Indian astronomy, trigonometry (spherical and plane), algebra and arithmetic. Through Aryabhatia, Aryabhata attempted to make clear the concept of eclipse forecasting and celestial movements. In fact, before the invention of Gregorian calendar the Indian calendric system was based on Aryabhatiya.

While nothing has been mentioned about the date of composition of Aryabhata-siddhanta, the prose is best known for Aryabhata’s astronomical computation endorsed by his contemporary Varahamihira (505–587 A.D.) – the well known astrologer, mathematician, astronomer and one of the Navaratnas (nine jewels) at the court of celebrated monarch Yashodharman Vikramaditya of Malwa. Aryabhata-siddhanta is based on the ancient text Surya Siddhanta, one of the most primitive philosophies on archeoastronomy of the Hindus, the original author of which is anonymous.

His Inventions

The Zero – Aryabhata was always ahead of his times and envisioned the importance of the ‘zero’ quite before his contemporaries. It was Aryabhata who first introduced to the world the concept of ‘zero’; however, he did not document his invention properly. His other discoveries include the extensive usage of triangles and spheres in mathematical theories. He also bestowed his knowledge of numerical notation method in alphabetical system.

Pi (π) – In the words of Aryabhata, the estimation of the value of Pi is derived as: “Add four to one hundred, multiply by eight and then add sixty-two thousand. The result is approximately the circumference of a circle of diameter twenty thousand. By this rule the relation of the circumference to diameter is given.” Thus, he estimated the value of Pi (π) as 3.1416 which helped in solving high level indeterminate equations.

Trigonometry – Aryabhata’s contribution in the field of trigonometry is tremendous as he became the foremost calculator of the sines formulae for angles greater than 90°, by providing a table of sine differences.  Many scholars argue that Aryabhata molded the base of trigonometry with his definitions on sine, cosine, and inverse sine. He also introduced the logic of versine (versine = 1 – cosine) in trigonometry.

Rotation of the Earth – Prior to the findings of Aryabhata, it was believed that all celestial bodies revolved around the motionless earth present at the centre of the universe. However, it was Aryabhata who first put forward in his theory of epicycles, that it is earth that rotates around its axis while the stars, on the other hand, are fixed in space.

Sidereal Astronomy – Aryabhata calculated earth’s one sidereal rotational period as 23 hours, 56 minutes 4.1 seconds which is very near to the modern accurate calculation of 23 hours, 56 minutes 4.091 seconds. Hence, the time calculated by Aryabhata for each sidereal year stood at 365 days 6 hours 12 minutes 30 seconds, which is very close to the precise current value of 365 days 6 hours 9 minutes 10 seconds – merely 3 minutes and 20 seconds shorter than the one set by Aryabhata.

Solar and Lunar Eclipses – One of the milestone achievements of Aryabhata in the field of astronomy was his explanations on the solar and the lunar eclipses. He maintained that planet orbits are elliptical and that the reflection of the sun causes the moon and the planets to shine. Thus, he stood out against his contemporaries who believed that eclipses were induced by pseudo-planetary demons Rahu and Ketu. Through his forward vision, Aryabhata clarified that eclipses can only occur due to intersection of either earth-moon or earth-sun orbital planes at lunar nodes.

His Commentators

Brahmagupta – Brahmagupta (598 – 668 AD) who later became the head of the Ujjain astronomical observatory composed Brahmasphuta-siddhanta in 628 A.D. which was substantially based on Aryabhatiya. In his yet another work Khandakhadyaka (665 A.D), – significantly based on Aryabhata-siddhanta – he elucidated how his philosophy and calculations differed from that of Aryabhata. Unfortunately, the original version of Aryabhata-siddhanta was lost soon after Brahmagupta released his commentary.

Bhaskara I – Bhaskara I (600-680 A.D.), the famous mathematician from Vallabhi in Saurashtra was also a commentator of Aryabhatia. Bhaskara I wrote his prose in Sanskrit in which he estimated the function of sine and emphasized on Hindu decimal system (using a circle for zero). He wrote his commentary in 629 A.D. around a decade after the composition of Aryabhatia.

When Bhaskara I wrote the commentary on Arybhatiya, he wrote about this great mathematician-astronomer:

“Aryabhata is the master who, after reaching the furthest shores and plumbing the inmost depths of the sea of ultimate knowledge of mathematics, kinematics and spherics, handed over the three sciences to the learned world.”

Bhaskara II – Bhaskara II (1114 – 1185 AD) who contributed extensively to the astronomical developments during 12^th Century is also said to have been the head of Ujjain astronomical observatory. His work Siddhanta Shiromani also reflects heavily on Aryabhata’s findings. Siddhanta Shiromani is divided into four parts and includes Arithmatic (Lilavati), Bijaganita (Algebra), Grahaganita (Mathematics of the planets 365-Day Year) and Goladhyaya (Astronomy and Spheres).

Several works of Aryabhatya is also translated in various different neighboring languages. His works have greatly influenced the scientific theories of different ancient cultures particularly their translations in the times of Islamic Golden Age around 820 A.D. His astronomical and mathematical theories were well cited by ancient Persian mathematicians including Al-Khwarizmi and Al-Biruni. The inland popularity of Aryabhata’s texts is evident from their translations in Tamil, Telugu and Malayalam languages.