History of Indian Mathematics

[KoH]

You are saying they used π since 800 BC in India and I don't deny that! I only say that pi is not the invention by Indians first when it is known to Agyptians in 1700 BC already. You must know that 1700 BC is 900 years earlier than 800 BC! Or do you want to deny it?

... It's not a logical thinking ...

Who said you that Indian Civilisation didn't exist before 1700 B.C ??
Harrapa and Indus Valley cities were said to be the one of the most anciant cities until that they discoverd the Dwarka underwater city in Gujarat which is estimitated to 7500 B.C , do you know that my srilankan bro ?

It is not myth but reality.

My srlinkan bro,
what is not a logical thinking?
I said that the egyptians had the knowledge of pi = 3.16... arrounf 1700 BC. It is found on papyrus of that time. This also means that they had already invented writing too.
The matter about pi the vedic moron SRS is talking about is from 800 BC. This Indian pi =3,003 was also not that "accurtae" as of that egyptian.
This only shows that
i) Indians were late in "inventing" pi (later than the Egyptians)
ii) Indians were not accurate with the pi (than the Egyptians)
iii) Indians invented their own pi

Bearing the knowledge about pi has nothing to do with a society that can be called a civilisation, my dear srilankan bro!

[KoH]

Bill Gates, when asked if Indian were not allowed to work in his Company. in USA, he would move to India.

No! He will not move to India! His company will move to India, if ever! Do you think that Bill Gates will feel comfortable if he wants to walk through an Indian city?
And if he ever moves to India he will probably come as a deity like Alexander turned Skantha!

So Foriegners have the skill to develop it and market commercially, but the basic is from India.
uppuma

Of course! They are only good as coolies and very happy that they have an earning and work until death assuming that everything is their fate. Not without a reason there is a caste system in India! If the Indians are born to serve others rather than make the use of their own knowledge then it had to be so! And if the rare knowledge is also kept unknown for the majority then they will always be th coolies. In the past, the present and very well also in the future! India is a country that does not change the time, the system and the fate!

[Eelavar]

"Bearing the knowledge about pi has nothing to do with a society that can be called a civilisation, my dear srilankan bro!"

What I tried to say is that a civilisation should forcebily know Pi...Otherwise we cannot talk about civilisation...

Pi is not an "invention"...
Nobody can invent Pi, because Pi already exists, and can't be invented...

Pi number is more a conception than an invention..

Pre computer calculations of
Mathematician Date Places Comments Notes


1 Rhind papyrus 2000 BC 1 3.16045 (= 4(8/9)2)
2 Archimedes 250 BC 3 3.1418 (average of the bounds)
3 Vitruvius 20 BC 1 3.125 (= 25/8)
4 Chang Hong 130 1 3.1622 (= 10)
5 Ptolemy 150 3 3.14166
6 Wang Fan 250 1 3.155555 (= 142/45)
7 Liu Hui 263 5 3.14159
8, Zu Chongzhi 480 7 3.141592920 (= 355/113)
9 Aryabhata 499 4 3.1416 (= 62832/2000)
10 Brahmagupta 640 1 3.1622 (= 10)
11 Al-Khwarizmi 800 4 3.1416
12 Fibonacci 1220 3 3.141818
13 Madhava 1400 11 3.14159265359
14 Al-Kashi 1430 14 3.14159265358979
15 Otho 1573 6 3.1415929
16 Viète 1593 9 3.1415926536
17 Romanus 1593 15 3.141592653589793
18 Van Ceulen 1596 20 3.14159265358979323846
19 Van Ceulen 1596 35 3.1415926535897932384626433832795029
20 Newton 1665 16 3.1415926535897932
21 Sharp 1699 71
22 Seki Kowa 1700 10
23 Kamata 1730 25
24 Machin 1706 100
25 De Lagny 1719 127 Only 112 correct
26 Takebe 1723 41
27 Matsunaga 1739 50
28 von Vega 1794 140 Only 136 correct
29 Rutherford 1824 208 Only 152 correct
30 Strassnitzky, Dase 1844 200
31 Clausen 1847 248
32 Lehmann 1853 261
33 Rutherford 1853 440
34 Shanks 1874 707 Only 527 correct
35 Ferguson 1946 620

Computer calculations of
Mathematician Date Places Type of computer

Ferguson Jan 1947 710 Desk calculator
Ferguson, Wrench Sept 1947 808 Desk calculator
Smith, Wrench 1949 1120 Desk calculator
Reitwiesner et al. 1949 2037 ENIAC
Nicholson, Jeenel 1954 3092 NORAC
Felton 1957 7480 PEGASUS
Genuys Jan 1958 10000 IBM 704
Felton May 1958 10021 PEGASUS
Guilloud 1959 16167 IBM 704
Shanks, Wrench 1961 100265 IBM 7090
Guilloud, Filliatre 1966 250000 IBM 7030
Guilloud, Dichampt 1967 500000 CDC 6600
Guilloud, Bouyer 1973 1001250 CDC 7600
Miyoshi, Kanada 1981 2000036 FACOM M-200
Guilloud 1982 2000050
Tamura 1982 2097144 MELCOM 900II
Tamura, Kanada 1982 4194288 HITACHI M-280H
Tamura, Kanada 1982 8388576 HITACHI M-280H
Kanada, Yoshino, Tamura 1982 16777206 HITACHI M-280H
Ushiro, Kanada Oct 1983 10013395 HITACHI S-810/20
Gosper Oct 1985 17526200 SYMBOLICS 3670
Bailey Jan 1986 29360111 CRAY-2
Kanada, Tamura Sept 1986 33554414 HITACHI S-810/20
Kanada, Tamura Oct 1986 67108839 HITACHI S-810/20
Kanada, Tamura, Kubo Jan 1987 134217700 NEC SX-2
Kanada, Tamura Jan 1988 201326551 HITACHI S-820/80
Chudnovskys May 1989 480000000
Chudnovskys June 1989 525229270
Kanada, Tamura July 1989 536870898
Chudnovskys Aug 1989 1011196691
Kanada, Tamura Nov 1989 1073741799
Chudnovskys Aug 1991 2260000000
Chudnovskys May 1994 4044000000
Kanada, Tamura June 1995 3221225466
Kanada Aug 1995 4294967286
Kanada Oct 1995 6442450938
Kanada, Takahashi Aug 1997 51539600000 HITACHI SR2201
Kanada, Takahashi Sept 1999 206158430000 HITACHI SR8000



P.S: This list is not forcebily correct, because we don't know if man before 2000 BC found the value of Pi.
We must not conlcude that because we have not written proofs that man never found the value of Pi before.
In the Indian text the Sulba Sutras the ratio for the area is given as 3.088 while the ratio for the circumference is given as 3.2.

[Uppuma]

Friends, have a look at the following site :


VEDIC MATHEMATICS NEWSLETTER
ISSUE No. 23
Vedic Mathematics is becoming increasingly popular as more and more people are introduced to the beautifully unified and easy Vedic methods. The purpose of this Newsletter is to provide information about developments in education and research and books, articles, courses, talks etc., and also to bring together those working with Vedic Mathematics. If you are working with Vedic Mathematics - teaching it or doing research - please contact us and let us include you and some description of your work in the Newsletter. Perhaps you would like to submit an article for inclusion in a later issue or tell us about a course or talk you will be giving or have given.

If you are learning Vedic Maths, let us know how you are getting on and what you think of this system.
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This issue’s article is taken from a longer article by Andrew Nicholas. The full article can be viewed at www.vmacademy.com
INDIA’S SYSTEM OF MENTAL MATHEMATICS

THE VEDIC IDEAL

In the vedic system, the work is done mentally. This stems from the tradition being an oral one.

In practice, today, the initial problem or question is usually written down and the answer or solution also. The work being done mentally, a one-line answer results. This is the vedic ideal.

BACKGROUND
But what is this word ‘vedic’? It refers to an ancient period in India’s history. Tradition has it that the system of the vedas covered all branches of knowledge. Originally an oral tradition, it began to be written down around 1600 or 1700BC, according to western scholars. Over the next thousand years four vedas, as they were called, were recorded - rig-veda, yajur-veda, sama-veda and atharva-veda.

An appendix to this last contained a section headed ‘Ganita Sutras’, i.e. mathematical formulae, or principles. In the nineteenth century scholars began to look at it, but could make no sense of what they found there: statements such as, ‘In the reign of King Kamsa, famine, pestilence, and insanitary conditions prevailed.’

Then a brilliant south Indian scholar, Shri Bharati Krishna Tirthaji (1884-1960), began a detailed investigation. He concluded that the above statement about King Kamsa was a cryptic form of the decimal fraction for 1/17, using letters to represent single-digit numbers, much as we might use the letter A to represent 1, and B to represent 2, etc.

Having obtained one clue, further investigation led him to conclude that the whole of mathematics is based on 16 sutras, and he finally wrote 16 volumes on the topic.

Then events intervened. He was virtually forced into becoming a Shankaracharya. Hindu India has four of these top religious leaders - a bit like having four Popes.

The upshot was that he left his beloved vedic mathematics alone for many years. Returning to the subject in the 1950‘s, it emerged that the 16 volumes had been lost. On realising this, he decided to re-write them all, and began by writing a book intended to introduce the whole series. Ill health stopped him from getting any further, and he died in 1960. This introductory book is now all that we have by him. It was first published in 1965.

DIFFERENT IDEAS ABOUT NUMBER

Western version

When measuring weight, the bigger the number, the greater the weight. Similarly for temperature, length, electric current etc. We are used to the idea that larger numbers are weightier.

Vedic version

In the vedic system, numbers are viewed differently. An analogy is telephone numbers, which we don’t associate with quantity. They are patterns of digits acting as addresses.

Similarly, when working to a base of ten (as we normally do), the vedic system deals with the single-digit numbers 1, 2, 3, 4, up to 9, together with the zero, arranged in different patterns. For example, we don’t divide by 52, we divide by 5, and take account of the 2 afterwards. This shift of focus eliminates the heaviness, or weight, associated with the common view of numbers. The vedic mathematician considers a number such as 52 as 5 and 2 in succession.

IS VEDIC MATHEMATICS CURRENTLY USED IN INDIA?

CAN YOU TELL US ABOUT DEVELOPMENTS THERE?

To answer the first question first, yes and no. It is used there to some extent. Here is a brief account of the developments.

Tirthaji died in 1960

‘Vedic Mathematics’ was published in 1965

Before going to India in 1981 I wrote to all Indian universities to find out what more was known about the subject. About 30% of them replied. No one could tell me anything more about it. Evidently the subject was being neglected. However, one or two letters pointed me to Tirthaji’s last residence and ashram in Nagpur. Visiting there, I was invited to return the following year to teach a fortnight’s course.

These days, the subject can be taught in schools, alongside the conventional system. Where this is done, I am told, the pupils have no problem with learning the two approaches side-by-side - the western and the vedic.

There is also a passionate debate raging about the status of Tirthaji’s system. Some argue that it is historically accurate, despite the lack of normal historical evidence. Others argue that, lacking evidence for its historical validity, it should be dismissed - despite the fact that, mathematically, it works.

My view (which I am not alone in holding) is that it is a reconstruction. At present we are unable to say for sure that it is historically accurate - nor to prove that it is not. This is because we are dealing with an oral tradition, and it is no surprise that written evidence may not be available.

WHAT IS THE POTENTIAL OF THE SYSTEM?

Tirthaji points out that it normally takes about 16 years to go from first steps in mathematics to a Degree in the subject. (e.g. from age 5 to age 21). But he states that with the vedic system the course in its entirety could be done in about two years! Of course, at present we don’t have all the material that’s needed available.

Needless to say, however, this would benefit everybody - not least those who are not interested in mathematics and would prefer to spend less time on it!

I think, myself, that once vedic mathematics begins to win general acceptance it will lead people to question other academic disciplines. Are rapid methods available in other subjects? If so, are they being used, and if not can they be developed?
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NEWS
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New course in london

Following the successful recent course at Imperial College another introductory course is to take place at the Regency Hotel, Queen’s Gate, London, SW7 5AG, on five Mondays from 29th April 2002. Time: 7.00 to 8.30 pm. Course fee: 30 pounds (20 pounds, students and concessions). Enquiries: tel. 020 8688 2642. Topics covered: Squares and Cubes, pi and the Vedic numeral code, Easy Calculus, Fibonacci within Nature, Mathematics and Mind.

BUSINESS APPLICATION OF A VM SUTRA

“Business India” has published an interesting article by Chetan Dalal entitled “Practical application of Vedic mathematics – Vedic mathematics has certain visual solutions which could be applied in problem solving”. This is on the application of Anurupye Shunyam Anayat (zero value of one of the variables in Simultaneous equations where the other variables are in perfect proportion to constants) illustrated in an Insurance claim. The article ends:

“This illustration . . . emphasizes on the simplicity of the tenets of the sutras of vedic mathematics. Perhaps research and intensive study of vedic scriptures might reveal even more advanced applications. What is illustrated above is a very elementary application of the sutra. The depth and richness of the vedic knowledge is beyond description. Greater research and more teamwork in sharing of ideas and interpretation may provide revolutionary results.”

It would be good to see more such applications of the Vedic Sutras.

MULTIPLICATION ON THE FINGERTIPS

A lot of interest was taken in the article in the last newsletter. Mr. Carlos Javier Maya from Mexico has given an idea for doing multiplications of 2 digit by 2 digit on the hands when the multiplier is 19. Mrs Sharma is developing the methods further and is currently conducting a series of courses on Vedic Mathematics.

Dr Abhijit Das in Mumbai, India, has also been researching this area, but without using fingers. We hope to have an article by him for the next newsletter.

COSMIC CALCULATOR COURSE NOW AVAILABLE

As stated in the last newsletter this Vedic Maths course, that covers the National Curriculum for England and Wales, can now be obtained. In India you can purchase whatever you need from Motilal Banarsidass shops and presumably from other bookshops.

The ISBN’s are as follows:

Full set: 81-208-1871-7

Book 1: 81-208-1862-8

Book 2: 81-208-1863-6

Book 3: 81-208-1864-4

Teachers Guide: 81-208-1865-2

Answer Book 1: 81-208-1866-0


To purchase the course in the UK contact:

Motilal Books, PO Box 324, Borehamwood, WD6 1NB

Tel: 0208 905 1244

Mailto:info@mlbduk.com

Price 39.75 pounds



For the USA contact:

THE SACRED SCIENCE INSTITUTE who have the books on order.

Address: PO Box 3617, Idyllwild, CA 92549-3617

http://www.sacredscience.com

mailto:institute@sacredscience.com

Tel: +1 (909) 659-8181

Fax: +1 (909) 659-8383

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WORKSHOPS IN INDIA
If you want to know about Vedic Mathematics Workshops or research in India send an email to Mr R. P. Jain at mlbd@vsnl.com

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CORRESPONDENCE

Email:

First of all I am thankful to those who are behind this effort of rejuvenating vedic science or mathematics.

I have learned very few mathema-tactics when I was giving some scholarship exams in 4 th standard. These were taught to me by my Nanny at that time. I could score 99/100 in that exam. and much of it due to use of vedic maths. But afterwards I never pursued it. I have done engineering and after so much of years have passed now I have decided to study vedic maths from scratch. I have done tutorials from your site and they are simply best to add my interest. So please subscribe me as student and pls. guide me what next I should do.
****************************
Your comments about this Newsletter are invited.

If you would like to send us details about your work or submit an article for inclusion please let us know on news@vedicmaths.com

Previous issues of this Newsletter can be copied from the Web Site: www.vedicmaths.org

Issue 1: An Introduction

Issue 2: "So What's so Special about Vedic Mathematics?"

Issue 3: Sri Bharati Krsna Tirthaji: More than a Mathematical Genius

Issue 4: The Vedic Numerical Code

Issue 5: "Mathematics of the Millennium"- Seminar in Singapore

Issue 6: The Sutras of Vedic Mathematics

Issue 7: The Vedic Square

Issue 8: The Nine Point Circle

Issue 9: The Vedic Triangle

Issue 10: Proof of Goldbach's Conjecture

Issue 11: Is Knowledge Essentially Simple?

Issue 12: Left to Right or Right to Left?

Issue 13: The Vinculum and other Devices

Issue 14: 1,2,3,4: Pythagoras and the Cosmology of Number

Issue 15: A Descriptive Preparatory Note on the Astounding Wonders of Ancient

Indian Vedic Mathematics

Issue 16: Vedic Matrix

Issue 17: Vedic Sources of Vedic Mathematics

Issue 18: 9 by 9 Division Table

Issue 19: “Maths Mantra”

Issue 20: Numeracy

Issue 21: Only a Matter of 16 Sutras

Issue 22: Multiplication on the Fingertips


To subscribe or unsubscribe to this Newsletter simply send an email to that

effect to news@vedicmaths.com

Please pass a copy of this Newsletter on (unedited) to anyone you think may

be interested.

Editor: Kenneth Williams

Visit the Vedic Mathematics web site at
http://www.vedicmaths.org
mailto:news@vedicmaths.com
uppuma

[Eelavar]

Please try this one.

http://www.vedamu.org/Mathematics/vedicmathematics.asp

[karuvaadu]

What I tried to say is that a civilisation should forcebily know Pi...Otherwise we cannot talk about civilisation...

It aches my eyes to read what you write thus I better ignore your posts in future. It is very wrong to say that you can not call a civilisation as civilisation without the knowledge of pi!
But for what purpose did a civilisation need pi if not for wheel making first? With the knowledge of pottery the mankind aquired the next knowledge called the wheel. With the aquiring of wheel knowledge they had the need to know about pi. Do you want to say that Inkas, Mayas and Aztekes are not civilisations? They did not know about wheels!

Pi is not an "invention"...
Nobody can invent Pi, because Pi already exists, and can't be invented...

This word invention you are riding of is put into quotation marks by KoH! pi is nothing else than the circumference devided by the diameter of a circle, in other words the wheel. You for sure have seen bullock carts, precisely the wheels of these carts. These wheels are made of wood and coverd with flat iron aginst wearing down. And this was the start of calculating pi. I don't want to say that the ancient egyptions used bullock carts but who knows.

Pi number is more a conception than an invention..

The religion and God is a conception but for sure not science! Or do you want to say that E=mc2 is a concept? Or the center of gravity, elctricity etc? Firs someone must have invented the wheel prior to pi.

....

P.S: This list is not forcebily correct, because we don't know if man before 2000 BC found the value of Pi.
We must not conlcude that because we have not written proofs that man never found the value of Pi before.
In the Indian text the Sulba Sutras the ratio for the area is given as 3.088 while the ratio for the circumference is given as 3.2. [/tscii]

The mankind used 3 X radius + a bit before they calculated with pi. Even without c2 = a2 +b2 they knew how to calculate it: A triangle with an 90 degree angle has one side of the length 3, the other side 4 and the third side 5! Try it! The mankind was not at all dummy, only we are dummy because we are using calculators and computers and don't know about 1 X 1. And we are also kept dummy because the knowledge was available to certain people only, the so called the caste of the priests in Egypt as well as in India!

This discussion only started because I denied the SRS' claim that the Indians aquired the knowledge of pi up to 32 digits ca. 800 BC which is definitely not true!

I would suggest you, my dear srilankan bro, try to understand first before you start to think! What you read and how you read is not important but the understanding. Only then you'll gain logical thinking before you assess me illogical.

[indian224080]

Please try this one.

http://www.vedamu.org/Mathematics/vedicmathematics.asp

Good Link EElavar.
Please continue.

[SRS]

But for what purpose did a civilisation need pi if not for wheel making first? With the knowledge of pottery the mankind aquired the next knowledge called the wheel. With the aquiring of wheel knowledge they had the need to know about pi. Do you want to say that Inkas, Mayas and Aztekes are not civilisations? They did not know about wheels!

Rv. Dinakaran has taught you well indeed, but not about your own history. Wheels? Pi has many, many uses beyond wheels. The ancient Indians had advanced spacecraft (read Ramayana). Pi is a concept, as someone has already pointed out. The practical application is not at all necessary. What practical application does infinity have? Pure math is justified on its own terms.

[SRS]

By the way, I am of the opinion that the "wheel" was "invented" without any knowledge of pi. A rolling wheel simply represents one type of motion. People must have observed rolling objects and then concieved of a wheel. The dimensions of the circular wheel need not necessarily have been calculated using pi, especially considering that pi is an irrational number - the concern was only with constructing a functional wheel and not the abstract properties of a perfect circle.

[karuvaadu]

But for what purpose did a civilisation need pi if not for wheel making first? With the knowledge of pottery the mankind aquired the next knowledge called the wheel. With the aquiring of wheel knowledge they had the need to know about pi. Do you want to say that Inkas, Mayas and Aztekes are not civilisations? They did not know about wheels!

Rv. Dinakaran has taught you well indeed, but not about your own history. Wheels? Pi has many, many uses beyond wheels. The ancient Indians had advanced spacecraft (read Ramayana). Pi is a concept, as someone has already pointed out. The practical application is not at all necessary.

Ramayana? Do you believe in Homer's Odyssee? Jules Verne? Ron Hobbard?
Who flew away with Seetha? Raavanan or Raman? Who was Indian? Raavanan or Raman? Who was Lankan? Now tell me who had the knowledge of advanced spacekraft? Indian or Lankan?

What practical application does infinity have? Pure math is justified on its own terms.

The practical application of infinity is the existence of God, isn't it?
"All is this, All is that
All from All
All remains ... " I read somewhere and smashed that book of theroies against the wall!

By the way, I am of the opinion that the "wheel" was "invented" without any knowledge of pi.

Did I say something else?
From my point of view, the wheel was invented for the use of making pots! The same technology is still in use!