PakkaPatriot (PP): nāgāḥ vājakharoṣṭravesaragavām ekaikahīnāḥ kramāt
aṣṭāviṃśatirekahīnagaṇitā rūponamantyam punaha |
teṣām sarva dhanam pṛthak ca niyamāt vācyam tvayā niścitam
kṛtsnam ca āryabhaṭapraṇītagaṇitam dṛṣṭam gurorantike || 2 ||
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PP: Hmmm, this and in most of such shlokas why is he referred to as Aryabhata? Is his name Aryabhata or Aryabhatta?
Kern: I will tell you! Arya as we all know is “the respectable one” in Sanskrit. While Bhata can be translated to a warrior, Bhatta translates closely to a scholar.
PP: So, what you are saying is Aryabhata was a respectable warrior.
Kern: Ahem, not really. He was a scholar both in math and astronomy.
PP: Then why on earth do we call him Aryabhata…
Kern: There is something called Chandas or Meter in Sanskrit where only certain alphabets fit into certain parts of the shloka. A very commonly used Chandas in most of the shlokas is Anushtup. The word Aryabhata has synced well in most of these places as opposed to Aryabhatta…
PP: (exclamation) OK…, and they started using it that widely. Fine then, let me get back to my shlokas. Well, this one sounds interesting;
षष्ट्यब्दानाम् षष्टिर्यदा व्यतीतास्त्रयश्च युगपादाः।
त्र्यधिका विंशतिरब्दास्तदेह मम जन्मनो व्यतीताः॥
Can someone please explain the meaning to me?
Aryabhata (AB): This is a shloka about me in the book I wrote, Aryabhatiya. Here I reveal my age in the form of a riddle.
PP (Curiously): A riddle, can you please translate it to me? I am sure I can solve it.
AB: Here you go… “When sixty times sixty years after three-quarters of the current maha yuga have elapsed, twenty-three years have passed since my birth”.
PP: That sounds confusing… Wait, Kaliyuga began 5122 years ago, which is 3102 BCE. For more info on Hindu Time Cycle, you can visit this link here. Since I know the concept of the time cycle, it is easier for me to calculate. Firstly, 60 times 60 years is 3600 years.
PP: So, after Satya Yuga, Treta Yuga, and Dwapara Yuga, which form the first three 3/4ths of the maha yuga, you are referring to Kaliyuga, the current one. In this yuga, when 3600 years have passed, you were just twenty-three years old. Wow, so young!
PP: If we add 3600 years to 3102 BCE, you were 23 years old when it was 499 CE. So, you were born in 476 CE.
AB: True that!
PP: Great experience talking to you…Aryabhata!
PP: Hey, wait a moment…oh no. He is gone…, now how do I find his birthplace?
Nilakantha Somayaji (NS): I am here, don’t worry.
NS: Aryabhata was born in Kerala, in the Asmaaka Region.
Parameshwaran (P): No, No! No final verdict can be given regarding his birthplace. It is also said that he wrote the book in Kusumapura, which is close to Pataliputra, which was the capital city of the then Gupta empire. Why? Some even conjecture that he was born in other parts of the south too.
PP: Oh! Alright! I am fine with any place starting from the Himalayas to Kanyakumari.
P: Absolutely. Some people also claim that he was designated as the head of a university, where he had access to an observatory, in Kusumapura.
ParmeshwarJha (PJ): Also, I strongly believe that he was an author of at least 3 books, of which unfortunately only one is surviving, that is…
PJ: Correct. This masterpiece is an astronomical treatise, a summary of Hindu Math.
PP: Amazing. Please continue… I want to know more about this masterpiece.
PJ: Of course. It consists of 121 verses of which
- 33 verses are dedicated to math giving 66 math rules
- 13 intro verses
- 25 verses on the reckoning of time and planetary models
- 50 verses on sphere and eclipse
PP: Phew. These are outstanding achievements in those days!
PJ: Not at all. We are yet to start to talk about his achievements.
PP: huh oh. Please go ahead.
PJ: His math verses cover:
- Place trigonometry
- Spherical trigonometry
- Continued fractions
- Table of sines
- Sums of powers
- Quadratic equations
Aryabhata has also used an alphabetical notation for representing 10 power 18.
He has been the first person to have used the place value system, which means he has used zero too.
PP: Obviously, without zero it is impossible to calculate 10 power 18.
PJ: He has solved algebraic problems using Kuttaka Method.
PP: These achievements are indeed extraordinary and useful.
PJ: Yes, in Bharat, no ancient mathematician has ever written a book on pure mathematics. Math has always been a part of an application and mostly this application has been astronomy or astrology.
PJ: Before I leave, let us quickly list the prominent achievements one by one.
- The value of pi = 3.1416; the value that we use even today. Even this value he calls asana or approximate.
- Two methods of computing the sine table.
- The theory of solving indeterminate equations.
- The earth is spherical and that it rotates, including calculating the period of one sidereal rotation of the earth as 23 hours, 56 minutes, and 45.1 seconds. The modern value is 23 hours 56 minutes and 45.091 seconds.
- He determined the length of the solar year that is 365 days, 6 hours, 11 minutes, 29.64 seconds, which is very close to the modern value
- He gave the correct method for calculating the celestial latitude of both superior and inferior planets.
- His book is perhaps the earliest text on astronomy to use the radian measure of 3438 units for the radius of the circle.
- He was the first to describe the true cause of lunar and solar eclipses—that they were due to the shadow of the earth and moon.
- He also said that the moon was a non-luminous body
PP: Lastly let us see what Bhaskara 1st has to say about Aryabhata in one of his shlokas…
Bhaskara, the First (B1): Yes. I will!
PP: Don’t narrate the shloka, just explain its meaning…
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.