Mathematics

Aryabhatta - Great Indian Mathematician

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Table of Contents

1. Who is Aryabhatta?
2. Works of Aryabhatta
3. Summary
4. FAQs

24 September 2020                

Read time: 3 minutes

Who is Aryabhatta?

Aryabhatta means the noble warrior. He mentions his period on the Earth in one of the parts of his work, Kalakriya, which is a part of Aryabhateeya.

 He says :

When sixty-times sixty years have elapsed,

then twenty plus three years have passed since my birth

Sixty times sixty years means 3600 years; it corresponds to 499 AD. It follows that Aryabhatta was born in 476 AD.

There is no biography or pictures available of Aryabhatta or for that matter of any Indian astronomer or Mathematician. The information we have today is gathered from his critics and commentators like Brahmagupta and Bhaskara I, who mentions Pandurangasvami, Latadeva and Nishanku, as pupils of Aryabhatta.

The pictures of Aryabhatta pervading the internet, as well as his statue, are merely artists’ imaginations.


Works of Aryabhatta

Aryabhateeya is a book written by Aryabhatta. It’s the earliest datable text available in complete form. There were many other Mathematicians and scientists before him. 

In Aryabhateeya, Aryabhatta says:

I entered into the ocean of knowledge, with my intellect as a boat and lifted up gems.

In other words, he mentions that there have been other literature from which he has culled out the most relevant information in his work Aryabhateeya.

The phrase Kusumapure abhyaarcitam gnaanam (knowledge respected in Kusumapura), in Aryabhateeya, hints that he lived in Kusumapura and is writing about the knowledge revered in Kusumapura (Pataliputra or Patna). In other words, he does not claim that he has discovered any of the theories mentioned in Aryabhateeya.

So, Aryabhateeya is a magnum opus written by Aryabhatta. This book is essentially a compilation of all the work done by the Astronomers and Mathematicians before Aryabhatta.

Aryabhateeyam is divided into four parts:

Aryabhateeyam is divided into four parts:

Gītīkāpāḍa, contains 13 shlokas. 

Aryabhateeya begins with an introduction called the "Dasageethika" or "Ten Stanzas."

This is an introduction to Aryabhateeya, and it contains the following:

  • Invocation to Brahman “Cosmic spirit" in Hinduism. He was a scientist, but not an atheist. Almost every jyotisha who followed him begins his work with a salutation to his favourite God.
  • The numeration system used in work like the astronomical constants and the sine table.
  • Overview of astronomical findings.

Ganitapada records the following:

  • The first ten decimal places.
  • Algorithms for obtaining square and cubic roots, using the decimal number system.
  • Geometric measurements—employing \(62,832/20,000 (= 3.1416)\) for \(\pi\).
  • Properties of similar right-angled triangles and two intersecting circles.
  • Using the Pythagorean Theorem, constructed a table of sines. And that second-order sine difference is proportional to sine.
  • Mathematical series, quadratic equations.
  • Calculating the compound interest (involving a quadratic equation),
  • Proportions (ratios)
  • The solution of various linear equations is among the arithmetic and algebraic topics included.
  • Aryabhatta’s general solution for linear indeterminate equations, which Bhaskara I called kuttakara (“pulveriser”), consisted of breaking the problem down into new problems with successively smaller coefficients—essentially the Euclidean algorithm and related to the method of continued fractions.

Representation of numbers by Aryabhatta

The Hindu-Arabic numeral system was introduced in India around the 6th and the 7th century AD, the Arab traders took this to Europe, and the acceptance of this system happened only by the 12th century AD. So, how did Aryabhatta represent numbers?

Aryabhatta used a unique system of representing numbers in Aryabhateeya. He gave numerical values to the 33 consonants of the Indian alphabet to represent \(1, 2, 3, ... , 25, 30, 40, 50, 60, 70, 80, 90, 100.\) The higher numbers are denoted by these consonants, followed by a vowel to obtain \(100, 10000,...\)This system allows numbers up to 10^ 18 to be represented with an alphabetical notation. This proves that Aryabhatta was also familiar with numeral symbols and the place-value system. This supposition is based on the following two facts: first, the invention of his alphabetical counting system would have been impossible without zero or the place-value system; secondly, he carries out calculations on square and cubic roots which are impossible if the numbers in question are not written according to the place-value system and zero.

 

Aryabhatta was also familiar with numeral symbols

Kalakriyapada was about astronomy in this he discussed:

  • Planetary motion along the ecliptic.
  • Units of time, eccentric and epicyclic models of planetary motion.
  • Gives the time unit for a year, months and days based on movements of celestial bodies.
  • Divides History also astrologically.
  • Gave rules for computing the longitudes of planets using eccentrics and epicycles.

Golapada dealt with Geometric/ trigonometric aspects of the Earth.

  • Elliptical equator, celestial equator
  • Solar and Lunar eclipses are shadows of the Moon on Earth and Earth on the Moon, respectively.
  • Stated that the Sun is the only source of light and not just planets, but even the stars only reflect sunlight.
  • Node, the shape of the Earth
  • Cause of day and night
  • Zodiacal signs on the horizon, etc.

Aryabhatta used the metaphor of a kadamba-pushpa-grantha to explain how people and creatures in all parts of the world believe they are standing on top of the world.

Aryabhatta used the metaphor of a kadamba-pushpa-grantha

He introduced another metaphor, for Earth’s rotation: consider a boat-rider on the Ganga, who feels trees on the shore pass him by; whereas, in reality, it is the boat that is moving.

Similarly, Aryabhatta suggested, the Earth rotates, and like trees on a riverbank, the stars seem to revolve around it. But it was only a metaphor, not a proof.

Unlike today, Mathematics was not taught to schoolchildren. Mathematics and Astronomy were pursued by specialists.

Arithmetic symbols familiar to us like \(+ - \times ÷ =\) were only introduced in fifteenth-century Europe.

Mathematics was not expressed in shlokas.

Aryabhatta gives two-line slokas like this:

त्रिभुजस्य फल शरीरं समदलकोटी भुजार्ध संवर्गः

Tribhujasya phala shareeram samadalakoti bhujaardha samvargah.

Bhuja means Arm. Tribhuja means three-armed or Triangle.

Translation “Multiplication (Samvargah) of perpendicular (Samadalakoti) and a half (ardha) the base (Bhuja) results (phala) in Triangle’s (Tribhuja-sya) area (Shareeram).”

The entire work is written in verse and is so complex in some parts that it was referred to as Aryabatta’s sutras. It was impossible to understand Aryabhateeyam without bhashyaas (commentaries).


Summary

Aryabhatta ranks with Archimedes, Euclid, Isaac Newton and Leonard Euler as one of the greatest mathematicians of the world. The Classical Era Of Aryabhatta is considered as a golden period of Astronomy and Mathematics. The mathematics set forth by Aryabhatta is mostly practical, not theoretical: its primary purpose is astronomy. His book Aryabhateeya is a magnum opus, a masterpiece of brevity and eloquence.


Frequently Asked Questions (FAQs)

What did aryabhatta discover?

There is no discovery attributed to Aryabhatta. However, he compiled the discoveries of the Mathematicians before him.

Who invented zero aryabhatta or brahmagupta?

Evidence suggests that Aryabhatta knew about “zero”. This is evident from the algorithms for decimals and a thorough knowledge of place value. Brahmagupta came many years after Aryabhatta. Hence it is evident that both already knew about zero.

When was aryabhatta born?

He was born in 476 AD.

Where was aryabhatta born?

There is no evidence to suggest where Aryabhatta was born. But in his work, he mentions the knowledge of people in Kusumapura, which is modern-day Patna.

When did aryabhatta die?

He passed away in 550 AD.


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