Indian mathematics

[yudhamanyu]

Indian mathematics and the numeral system is the forerunner of modern science , technology and mathematics.



We have to be grateful to the Indians for teaching us how to count without which no worthwhile scientific discovery could have been made.

-----Albert Einstein



It is a fact that before the advent of the Indian numeral system and algebra in Europe , the Roman numeral system was used , which could not have been used for cumbersome scientific calculations. They are even today counting 1 , 2 , 3 , etc to zero, after Sanskrit figures.

It was Indian mathematics, which provided the base for the growth of European science and technology to its present standards.

If it weren't for Indian mathematics, Europe would still would have been using the Roman numeral system, and in all probability , would still have been in the Dark Ages as well.

A scientific temperament existed in India, as can be understood by this quote of the Buddha 2500 years ago ...

Believe nothing, merely because you have been told it, or because it is traditional or because you yourselves have imagined it. Do not believe what your teacher tells you merely out of respect for your teacher. But whatever after due consideration and analysis you find to be conducive to the good , the benefit, the welfare of all beings, that doctrine , believe and cling to and take it as your guide.
- Buddha

[Agnideva]

Namaste Yudhamanyu,

What you say is quite true. The numerals we use today called "Arabic" numerals are actually Indian numerals, that came to Europe by way of the Arabs.



Before the arrival of the Indian numerals in Europe, letters of the alphabet were used as numerals (the Roman numerals). The same is true for Hebrew, where the letters of the alphabet stood for different numbers. In Hebrew, I'm told, the number fifteen is curiously written as 9+6 because writing 10+5 would spell the name of God (YHWH)

Also the numeral 0 (zero) came from India originally. Europe in the middle ages didn't have the zero. And since there was no zero, the year before 1 AD was called 1 BC.

Thought I'd share these interesting tidbits

Regards,
A.

[Jigar]

Namaste,
The decimal (base ten or occasionally denary) numeral system has ten as its base. It is the most widely used numeral system, probably because humans have 5 digits on each hand.


Alternative notations

Some cultures use other numeral systems, including the Maya, who use a vigesimal system (using all twenty fingers and toes), some Nigerians who use several duodecimal (base 12) systems, the Babylonians, who used sexagesimal (base 60), and the Yuki, who reportedly used octal (base 8).

Computer hardware and software systems commonly use a binary representation, internally. This binary representation is sometimes presented in the related octal or hexadecimal systems. Binary values are converted to the equivalent decimal values for presentation to and manipulation by humans.

Maste Nam,
Jigar

[saidevo]

Namaste.

Some cultures use other numeral systems, including the Maya, who use a vigesimal system (using all twenty fingers and toes), some Nigerians who use several duodecimal (base 12) systems, the Babylonians, who used sexagesimal (base 60), and the Yuki, who reportedly used octal (base 8).

It is interesting to study the Sanskrit and English terms for these bases:
No......Sanskrit....................English
10 .... dashamá ................. decimal
12 .... dvaadashá .............. duodecimal
20 .... vimshatitamá ........... vigesimal
60 .... sastitamá ................ sexagesimal
8 ..... astamá ................... octal
2 ..... dvitiiya ................... binary (dual)

Other numbers that appear like phonemes or start with same sounds, between Sanskrit and English include:
No......Sanskrit....................English
3 ..... tritiiya .................... three, (tri-)
5 ..... pañcamá ................. penta
7 ..... saptamá ................. septa
9 ..... navamá .................. nine
100 .... shatatamá ............. centum

Members may add more. Incidentally, the Sanskrit term 'paraardhatamá' stands for the number 100,000,000,000,000,000th, the highest in the series!

[saidevo]

Some Details on the History of Indian Mathematics
The Decimal System in Harappa

In India a decimal system was already in place during the Harappan period, as indicated by an analysis of Harappan weights and measures. Weights corresponding to ratios of 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, and 500 have been identified, as have scales with decimal divisions. A particularly notable characteristic of Harappan weights and measures is their remarkable accuracy. A bronze rod marked in units of 0.367 inches points to the degree of precision demanded in those times. Such scales were particularly important in ensuring proper implementation of town planning rules that required roads of fixed widths to run at right angles to each other, for drains to be constructed of precise measurements, and for homes to be constructed according to specified guidelines. The existence of a gradated system of accurately marked weights points to the development of trade and commerce in Harappan society.

Mathematical Activity in the Vedic Period

Arithmetic operations (Ganit) such as addition, subtraction, multiplication, fractions, squares, cubes and roots are enumerated in the Narad Vishnu Purana attributed to Ved Vyas (pre-1000 BC). Examples of geometric knowledge (rekha-ganit) are to be found in the Sulva-Sutras of Baudhayana (800 BC) and Apasthmaba (600 BC) which describe techniques for the construction of ritual altars in use during the Vedic era. It is likely that these texts tapped geometric knowledge that may have been acquired much earlier, possibly in the Harappan period. Baudhayana's Sutra displays an understanding of basic geometric shapes and techniques of converting one geometric shape (such as a rectangle) to another of equivalent (or multiple, or fractional) area (such as a square). While some of the formulations are approximations, others are accurate and reveal a certain degree of practical ingenuity as well as some theoretical understanding of basic geometric principles. Modern methods of multiplication and addition probably emerged from the techniques described in the Sulva-Sutras.

Pythagoras - the Greek mathematician and philosopher who lived in the 6th C B.C was familiar with the Upanishads and learnt his basic geometry from the Sulva Sutras. An early statement of what is commonly known as the Pythagoras theorem is to be found in Baudhayana's Sutra: The chord which is stretched across the diagonal of a square produces an area of double the size.

Panini and Formal Scientific Notation

Ingerman in his paper titled Panini-Backus form finds Panini's notation to be equivalent in its power to that of Backus - inventor of the Backus Normal Form used to describe the syntax of modern computer languages. Thus Panini's work provided an example of a scientific notational model that could have propelled later mathematicians to use abstract notations in characterizing algebraic equations and presenting algebraic theorems and results in a scientific format.

For the complete article with much more details, check:
History of Mathematics in India at (http://india_resource.tripod.com/mathematics.htm)

and several other articles in this search link: http://www.google.co.in/search?as_q=...s=&safe=images

[Jigar]

Namaste,
So could someone explain me how the Lakh system comes into this decimal system they use? To my understanding, 1 Lakh is 10,000-99,999 in value, right? How does that work?

Swas Tik Hai,
Jigar

[Agnideva]

Namaste Jigar,

Namaste,
So could someone explain me how the Lakh system comes into this decimal system they use? To my understanding, 1 Lakh is 10,000-99,999 in value, right? How does that work?

Lakh and crore from the sanskrit terms laksha and koti are measures, not ranges.

1 lakh = 100000 (hundred thousand)
1 crore = 100 lakhs = 10000000 (ten million)

It's as simple as that.

Here's a table I pulled off a website about the ancient measures:

Number / Sanskrit / English

1 / ekam / one
10 / dasham / ten
100 / shatam / hundred
1 000 / sahasra/ thousand
10 000 / dasha-sahasra / ten thousand
100 000 / laksha / hundred thousand
1 000 000 /dasha-laksha / million
10 000 000 / koti / ten million
100 000 000 / dasha-koti / hundred million
1 000 000 000 / abja / billion
10 000 000 000 / kharva / ten billion
100 000 000 000 / nikharva / hundred billion
1 000 000 000 000 / padma / trillion
10 000 000 000 000 / mahapadma / ten trillion
100 000 000 000 000 / shankhu / hundred trillion
1 000 000 000 000 000 / jaladhi / quadrillion
10 000 000 000 000 000 / antya / ten quadrillion
100 000 000 000 000 000 / madhya / hundred quadrillion
1 000 000 000 000 000 000 / parardha / quintillion

OM Shanti,
A.

[Jigar]

Namaste,

Namaste Jigar,
Lakh and crore from the sanskrit terms laksha and koti are measures, not ranges.
1 lakh = 100000 (hundred thousand)
1 crore = 100 lakhs = 10000000 (ten million)
It's as simple as that.

OM Shanti,
A.

But why do they put the kama in a different place? it should be 100,000 not 1,00,000?

Maste Nam,
Jigar

[Agnideva]

Namaste Jigar,

But why do they put the comma in the wrong place it should be 100,000 not 1,00,000?

Hehe . The commas are for emphasis. Our emphasis is on the hundred in hundred thousand; their emphasis is on the one in one lakh. In the Indian system, after the unit, ten and hundred position, all others numbers would be separated by commas in twos.

For example, if one were to write the lifetime of Brahmā (the Creator) in the western system one would write:

311,040,000,000,000

In the Indian system one would write:

31,10,40,00,00,00,000

Go ahead, translate this number using the ancient count system from that table above .

A.