In 2007, Dr George Gheverghese Joseph from The University of Manchester said that the ‘Kerala School’ identified the ‘infinite series’- one of the basic components of calculus – in about 1350.
The discovery was wrongly credited in books to Sir Isaac Newton and Gottfried Leibnitz at the end of the seventeenth centuries.
Dr Joseph further says that there is strong circumstantial evidence that the Indians passed on their discoveries to mathematically knowledgeable Jesuit missionaries who visited India during the fifteenth century.
There was another possibility that few British scholars, during early period of British Raj, learned Sanskrit and they might have passed on these knowledge.
Most of us know the invention of zero ‘0’ by Aryabhat in India; but very few know about him or his real work in detail. Aryabhat was a famous Indian mathematician and an astronomer who lived between 476 – 550 CE. Most of his work was done towards end of 4th century CE.
He received his early education in Kusumpura, which is now known as Patna in Bihar.
He had done enormous work in mathematics and astronomy that is complied into two major works and few notes. One of the major works is known as “Aryabhatiya” that has survived the passage of time. However, his other work in astronomical computation that is known, as ‘Arya-siddhanta’ could not survive.
Aryabhatiya mainly focuses on mathematics and astronomy and it consists of 4 parts:
1. The Dasagitika Sutra: It has 33 verses that defines the basics of astronomical tables
2. Ganita – Mathematics: This section has 33 verses that give 66 mathematical rules.
3. Kalakriya – The measure of time: This section has 25 verses that describe time, its measurement and planetary models.
4. Gola – The spherics: This section has 50 verses those details on sphere and eclipses.
Here is the extract of some of his work for us to gauge the depth of knowledge that India lost over a period of time.
i. Most basic & famous example of binomial:
(a + b) ² = a² + 2ab + b²
a X b = (a+b)2 – (a2 – b2)
ii. Value of Pi:
abhi svav Rushtim madey ays yudhyato raghveeriva pravaNe samsrutaya: | indro yad vajree dhRuSHamANo andhasA behind valasya paridheemriva trita: ||
paridhi m. circumference Paridhih +iva+ tritah. Paridhih means circumference, iva means like or for example, tritah means by 3. Thus, like circumference by three.
chaturadhikam śatamaṣṭaguṇam dvāṣaṣṭistathā sahasrāṇām ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ. ”
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 the diameter is:
((4 + 100) × 8 + 62000)/20000
= 3.14159265 i.e. the value of π is correct to 8 places
iii. The value of pie upto
गोपीभाग्य मधुव्रातः श्रुंगशोदधि संधिगः |
खलजीवितखाताव गलहाला रसंधरः ||
gopeebhaagya maDhuvraathaH shruMgashodhaDhi saMDhigaH
khalajeevithakhaathaava galahaalaa rasaMDharaH
ga-3, pa-1, bha-4, ya -1, ma-5, Dhu-9, ra-2, tha-6, shru-5, ga-3, sho-5, dha-8, Dhi -9, sa-7, Dha- 9, ga-3, kha-2, la-3, jee-8, vi-4, tha-6, kha-2, tha-6, va-4, ga-3, la-3, ha-8, la-3, ra-2, sa-7, Dha-9, ra-2
π = 3.1415926535897932384626433832792…
iv. Measurement of earth:
About the circumference of the earth, Aryabhat measured as 4 967 yojanas (1 yojana = 5 miles) and its diameter as 1 5811/24 yojanas.
5 x 1 5811/24
And, today it is measured as 24 902 miles (using all the advanced equipment, technologies)
Sine differences: The rules says each sine-difference reduced by quotients of all the previous differences and itself by the first difference.
d2 (sin x)
————– = – Sin x
For example, check the numbers – 51, 37, 22, 7
v. Earth and planetary light:
Aryabhat has mentioned that the Moon and planets shine by reflected sunlight.
vi. Rotation of earth:
In his golapada stanza 9, he wrote:
He also mentioned the unconventional discovery about the rotation of the heavens was due to the axial rotation of the Earth on daily basis; that apparently was accepted much later by the West.
Acknowledging Aryabhat’s contribution in mathematics and astronomy, India honored him by naming its first satellite as ‘Aryabhat.’
If the Indian government takes interest in teaching ancient languages and investing into ancient scientific scriptures, it can build stronger scientific base in future. Apparently, it was believed that Germans learned Sanskrit to rediscover Indian scientific and technological advancement in aeronautical field and they succeeded in building an advanced plane. That knowledge was eventually taken by NASA scientists after World War II and used in their research.
- J. J. O’Connor and E. F. Robertson, Aryabhata the Elder, MacTutor History of Mathematics archive
- Understanding (Third Edition). New York: W.H. Freeman and Company. p. 70. ISBN 0-7167-4361-2
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