Highlights of Ancient Indian Mathematics

Bringing back the much enjoyed open discussion on the Vedic Mathematics, for general public. Proceeds lessons and verse wise. For the keen student seeking a deep understanding of Vedic Mathematics! Registration necessary.

Re: Highlights of Ancient Indian Mathematics

Postby murugans61 » Wed Jan 30, 2013 5:40 pm

Hari OM Vinay ji

Thank you for highlighting the importance and usage of mathematics in day to day life of ancient India with nice examples. The other reasons for development of mathematics in our country that i can think of are:
1) In the field of agriculture one has to measure various things such as seeds, fertilizers, water quantity etc. The final output is also measured and stored or sold. Such a need for measurements is a reason for the develpoment of mathematics among common agrarian community.
2) While travelling to various places either by foot or by carts and reach destinations within time, one had to use mathematics to measure the time and distance.
As humans, identified with BMI, we are all governed by time and space and such governance leads us to various aspects of mathematics.

regards
murugan
User avatar
murugans61
 
Posts: 1409
Joined: Sun Mar 28, 2010 11:59 pm

Re: Highlights of Ancient Indian Mathematics

Postby sanjay1810 » Wed Jan 30, 2013 11:29 pm

Hari Om Vinayji,

In addition to murugan, I guess in ancient india most people were self employed which meant you have to be involved in cash transactions at a daily level. So basic mathematics like A/S/M and division was a part of every day job.

For example, a shopkeeper calculates input/output cost, profit etc. Farmers calculates cost of grain, selling price, etc etc.

So most people knew the basic mathematical operations very well.
sanjay1810
 
Posts: 0
Joined: Sat Jan 26, 2013 2:38 pm

Re: Highlights of Ancient Indian Mathematics

Postby Vinay » Fri Feb 01, 2013 7:03 pm

Hari Om All!

It seems that the 'Introduction Lesson' to the Course (which comes before Lesson 1) was not uploaded in the link. Extremely sorry from our side for the error. The Home Study Course dept of the CIF has sent an email to all the students with the pdf copy of the Intro Lesson. Once you check it out, you'll get a brief idea about the history of Indian mathematics.

Now I understand why the reply to this thread was less. Looking forward to more participation in the discussion once you go through the Intro lesson.
With Prem & Om,

Vinay Nair
Vinay
 
Posts: 26
Joined: Sat Jan 12, 2013 9:14 pm

Re: Highlights of Ancient Indian Mathematics

Postby vinay » Mon Feb 11, 2013 9:47 pm

Hari Om!

It has been quite a while that we saw some new posts. Sharing some information on India's two main contributions in the field of mathematics. Please give your thoughts/questions on the below matter.

I would urge everyone to make use of the discussion forum to share their views and put up their questions freely.

The two main discoveries that changed the course of mathematics are – the Numeral Zero and Decimal Place Value System.


ZERO AND DECIMAL PLACE VALUE SYSTEM

The concept of zero can be seen in many places in the Vedic literature. The great Sanskrit grammarian, Panini (500 BCE), mentions about zero several times in his text Ashtadhyayi. In Nyaya school of philosophy, the concept of shunya (zero) is mentioned and so is in Buddhism. Shunya is used as a symbol in Chandas Sutra of Pingala (300 BCE). Later the famous mathematician of the Classical period, Aryabhatta, writes in his text Aryabhatiya different operations by zero.

As we can see, the development of zero can be seen from being a concept of zero to the symbol or numeral zero. As of now, we cannot say which Indian mathematician can be accredited with the discovery or numeral zero or if ever there was one sole discoverer of zero. All that can be said is that it might have been during the early classical period (500 BCE - 500 CE) that the concept of zero found a numeral's form in India.

The concept of decimal place value system can also be seen in the Vedic literature like Rigveda and Taittireeya Samhita where they have given different names for the powers of 10. In Valmiki Ramayan, Valmika goes on giving the names for powers of 10 upto 10 to the power 62, (1 followed by 62 zeros) for which he gives the name Mahaukham. This he does to tell the number of monkeys in Rama's army that went in search of Sita. So, the concept of decimal place value system can be seen in such contexts in Indian literature.

It is noteworthy to see that since the Indian educational system was of oral-tradition centuries ago, they could do high level calculations even without having word numerals in the form of 1, 2, 3, 4, etc. Somewhere they knew that Base-10 system was the most suitable for counting for various reasons and hence the mention of decimal place value system in the Vedic literature.

The Babylonians were using a place value system of base 60, but it lacked zero. Only when zero came to be used as a numeral along with the decimal place value system, did calculations become very easy.

Historians, scientists and mathematicians all over the world have credited these two discoveries of zero and decimal place value system to Indian mathematicians. In the words of the famous French mathematician-astronomer Pierre-Simon Laplace, "It is India that have gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to all computations put our arithmatic in the first rank of useful inventions; and we shall appreciate the grandeur of this achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity."
vinay
 

Re: Highlights of Ancient Indian Mathematics

Postby varunv » Thu Feb 14, 2013 7:20 pm

I found some more interesting information while researching about "the history of zero" online which I submit as a reply to this thread.

Brahmagupta, around 650 AD, was the first to formalize arithmetic operations using zero. He used dots underneath numbers to indicate a zero. These dots were alternately referred to as 'sunya', which means empty, or 'kha', which means place. Brahmagupta wrote standard rules for reaching zero through addition and subtraction as well as the results of operations with zero. The only error in his rules was division by zero, which would have to wait for Isaac Newton and G.W. Leibniz to tackle.

Regards,
Varun
varunv
 

Re: Highlights of Ancient Indian Mathematics

Postby Vinay » Sun Feb 17, 2013 5:10 pm

Hari Om Varun!

Thanks for sharing the wonderful post. Really appreciate your interest in doing some research on history. Such kind of research really help us understand a subject in greater depths.

Brahmagupta (6th Cent. CE) had also given rules of using negative numbers while the appearance of negative numbers appeared in Europe somewhere in the 17th Cent. CE.

The great Sanskrit grammarian Panini (500 BCE) gives the notion of lopa, which functions as zero, in his work Astadhyayi.
Shunya (zero) appears as a symbol in Pingala's Chandas sutra (300 BCE).

Vararuchi (around 300 BCE), a great grammarian from Kerala, who is said to be the proponent of a Coding system (Katapayadi Number System, you'll see about it in detail in the last lesson of this Course), uses zero as a numeral for coding numbers using alphabets.

The Buddhists had the concept of zero in their philosophy Shunyavada and there was another school of thought in India called Nyaya philosophy which also had the notion of abhava (nothingness) in their philosophy.

By the time of Aryabhatta-I (476 CE), it is quite evident that the perfect knowledge of zero and the place value system had taken place in India. In Aryabhatiya, Aryabhatta uses zero as a number and also as a place value.

The above are based on the manuscripts that historians have come across till date. The knowledge of zero was there in India even before the numeral zero was discovered. Zero is one of the most significant discoveries by Indians in the field of mathematics.

We have uploaded on our facebook page www.facebook.com/VedicMathematicsCourse about zero and place value system. (Those of you who are on facebook can check out the page.)
With Prem & Om,

Vinay Nair
Vinay
 
Posts: 26
Joined: Sat Jan 12, 2013 9:14 pm

Re: Highlights of Ancient Indian Mathematics

Postby gkvish » Tue Feb 19, 2013 3:26 pm

Hari Om,
I am G.K.Vishwanath,GKV entering into the fore for the first time.i am sorry, for the belated appearance due to some personal exigencies.
I am actually previlaged and very happy to be in the company of brilliant individuals and a great guru who would certainly lead me to enlighten my knowledge.
After,I went into the first write up,I started reflecting back upon the Vedic Age many a thosand years back and was able to appreciate the great rishis who were able to propound Axioms phrases, called as sutras by which calculations can be effected.
I could imagine that period when when "Numbers" and the numerical system had not been in existence the only means used for explicit quantification was always a metaphorical comparison with some existing constant factor.Thus, came the need of the numbers and so they were born.Vedic Maths so evolved and progressed with the contribution of great Rishis.
gkvish
 
Posts: 0
Joined: Sat Feb 16, 2013 8:38 pm

Re: Highlights of Ancient Indian Mathematics

Postby varunv » Thu Feb 21, 2013 7:39 pm

Thank you sir for the interesting information.

The mathematical part of the "Aryabhatiya" covers algebra, arithmetic, plane trigonometry and spherical trigonometry. It also contains continued fractions, quadratic equations, sums of power series and a table of sines. This work is the first we are aware of which examines integer solutions to equations of the form by = ax + c and by = ax - c, where a, b, c are integers. Aryabhatta wrote that if 4 is added to 100 and then multiplied by 8 then added to 62,000 then divided by 20,000 the answer will be equal to the circumference of a circle of diameter twenty thousand. This calculates to 3.1416 close to the actual value Pi (3.14159).

But his greatest contribution has to be ZERO, for which he became immortal.

Regards,
Varun
varunv
 

Re: Highlights of Ancient Indian Mathematics

Postby Vinay » Thu Feb 21, 2013 11:19 pm

Hari Shri GVK and Varun!

Thank you for your valuable insights.

Varun - Numeral Zero was a contribution by Indians. We are not sure that Aryabhatta discovered zero. No mathematical text (except our school textbooks) say that it was Aryabhatta who discovered zero. The numeral zero was probably discovered during the times of Aryabhatta or even prior to him.

Regards,
With Prem & Om,

Vinay Nair
Vinay
 
Posts: 26
Joined: Sat Jan 12, 2013 9:14 pm

Re: Highlights of Ancient Indian Mathematics

Postby Vinay » Sun Apr 14, 2013 6:56 pm

Hari Om All!

Below is a continuation to the earlier posts. The matter has been taken from our facebook page www.facebook.com/VedicMathematicsCourse

Development of Mathematics in India

The birth of Mathematics in India can be traced back to the Vedas. Vedas are the storehouses of knowledge in India that contains knowledge on different sciences, mathematics, philosophy, and other subjects. Mathematical parts covered in the Vedic literature include topics like number systems, arithmetic, geometry, progression and astronomy.

The Vedas are not books written by any single author; rather it is a collection of all the knowledge that was revealed to different Rishis (seers) during their heights of contemplation and meditation. Initially, the knowledge was not available in a book-form; it was passed on from generation to the generation by word of mouth from the teacher to the student. Somewhere back in history, sage Vyasa (a great seer and visionary) took up the task to compile all the existing knowledge into four volumes – Rgveda, Yajurveda, Samaveda and Atharvaveda. The exact date of the Vedas is not known. Historians have tried giving rough estimates but it differs in view among different persons.

To study the Vedas, study of Vedangas (Veda + Anga, Anga means ‘parts of the body’) was necessary. Vedangas can be classified into six branches viz., Shiksha (phonetics), Kalpam (rituals), Vyakaranam (grammar), Chandas (Prosody), Niruktam (Etymology) and Jyotisham (Astronomy). Among these, knowledge of mathematics was covered mainly in Kalpam & Jyotisham, and also to some extent in Chandas.

Kalpam was further subdivided into four:
Srauta Sutras – dealing with rituals such as Yagas & Yagnas (sacrifices)
Grihya Sutras – rituals to be observed by a householder.
Dharma Sutras – pertaining to law and order
Sulva Sutras – dealing with guidelines of preparation of sacrificial altars (homa kundas) which also happen to be the most ancient treatises available on Geometry.

Jyotisham covered the science of astronomy (not astrology which came much later) which included mathematics. The birth of trigonometry and calculus was mainly through Jyotisham.

Mathematics (Ganitam) was never a different branch of science. It got developed as a different branch of study much later mainly from the knowledge in Sulva Sutras and Jyotisham. The ancient Indian mathematicians from the time of Aryabhatta-I (476-550 CE), gradually divided mathematics further into various branches like Arithmetic, Algebra, Trigonometry, Combinatorics, Astronomy, etc. in their treatises.
With Prem & Om,

Vinay Nair
Vinay
 
Posts: 26
Joined: Sat Jan 12, 2013 9:14 pm


Return to Vedic Mathematics

Who is online

Users browsing this forum: No registered users