ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

ANCIENT INDIAN MATHEMATICS

Updated on December 4, 2010
 

ANCIENT INDIAN MATHEMATICS

Hindu mathematicians were basically number theorists, and their mathematics an appendage to Astronomy. This was because of the need to advice on the right time to sow seeds in farms or for performing of religious rituals. Naturally most of them were priests, and all mathematical principles were enunciated in the form of verse. Being purely functional, no rigorous proofs were given unlike Greek mathematics.

The difference between Hindu and Greek mathematics was also greater in its focus. While Hindu mathematics was more arithmetic oriented, Greek mathematics was geometric centered. This accounts for the refinement of numerical symbols and great advancement in algebra. The flip side was Hindu geometry was devoid of proofs and was mensuration oriented.

The growth of Hindu mathematics falls into two periods:

  1. The SULVASUTRA period starting roughly from 800 BC to 200 AD
  2. Astronomical and Mathematical period starting from 400 AD to 1200 AD

SULVASUTRAS

SULVASUTRAS, which means "Rules of the Cord" are supplements of KALPASUTRAS which explain the construction of sacrificial alters.

The main SULVASUTRAS were composed by Baudhayana (about 800 BC), Manava (about 750 BC), Apastamba (about 600 BC), and Katyayana (about 200 BC). The aims very mostly religious, but the contents of the manuals were about geometric shapes such as squares, circles, rectangles an example of which is shown below.

The rope which is stretched across the diagonal of a square produces an area double the size of the original square.

The Indian Mathematicians of the ancient era excelled in Diophantine Equations (probably erroneously credited to Diophantus , because the Vedics were adept at it long before Diophantus), algebraic equations in which only solutions in integers are permitted.

These ancient Indian mathematicians were interested in very practical aspects of mathematics, such as determining the positions of the stars, developing a PANCHANGA (calendar/almanac), and ordinary mathematics for everyday use, like measurements of land and weights etc

Some of the prominent ancient Mathematicians were:

Aryabhata I

Aryabhata wrote Aryabhatiya when he was only twenty-three years of age, and it was due to his efforts Astronomy was delinked from Mathematics. He was able to calculate the value of pi to 3.1416 and the length of the solar year to 365.3586805 days.Aryabhata wrote Aryabhatiya in Kusumapura near Pataliputra (situated in modern Bihar) which was the capital of the Gupta Empire. He was far sighted in many of his opinions. He believed that the earth was a sphere and rotated on its axis, that the shadow of the earth falling on the moon was the cause of eclipse. In fact Aryabhata was the most scientific of ancient Indian astronomers. Significantly he had another illustrious contemporary by name Varahamihira who wrote Panchasiddhantika(Five schools of Astronomy). Varahamihira focused on three different branches of astronomy as studied during the period and they were; astronomy and mathematics, astrology and horoscopy. There was however one major difference, while Varahamihira gave importance to astrology, Aryabhata emphasized astronomy.

Brahmagupta

Brahamagupta was the foremost Indian mathematician of his time. He was born possibly in 598 in Ujjain, India. Brahmagupta'smagnum opus was Brahmasphutasiddhanta (The Opening of the Universe) which he wrote in 628. The book has 25 chapters and Brahmagupta tells us in the text that he wrote it at Bhillamala which today is the city of Bhinmal. This was the capital of the lands ruled by the Gurjara dynasty. Brahmagupta became the head of an astronomical observatory at Ujjain and his second work on mathematics and astronomy was the Khandakhadyaka

Brahmagupta's understanding of the number systems went far beyond that of others of the period. He made advances in astronomy and most importantly in number systems including algorithms for square roots and the solution of quadratic equation.

In the Brahmasphutasiddhanta he defined zero as the result of subtracting a number from itself. He gave some properties as follows:-

When zero is added to a number or subtracted from a number, the number remains unchanged; and a number multiplied by zero becomes zero.

He also gives arithmetical rules in terms of fortunes (positive numbers) and debts (negative numbers):-

A debt minus zero is a debt.

A fortune minus zero is a fortune.

Zero minus zero is a zero.

A debt subtracted from zero is a fortune.

A fortune subtracted from zero is a debt.

The product of zero multiplied by a debt or fortune is zero.

The product of zero multipliedby zero is zero.

The product or quotient of two fortunes is one fortune.

The product or quotient of two debts is one fortune.

The product or quotient of a debt and a fortune is a debt.

The product or quotient of a fortune and a debt is a debt.

He wrote about quadratic equations, lunar eclipses, planetary conjunctions, and the determination of the positions of the planets. He died in the year 670 AD

Mahavira (or Mahaviracharya)

Mahavira was another great mathematician of yore. He was born around 800 AD possibly in Mysore, South India. He was a Jain and was familiar with Jaina mathematics. He wrote the book Ganita Sara Samgraha, in 850 AD, which was basically an updating of Brahmagupta's works

The nine chapters of the Ganita Sara Samgraha are:

1. Terminology

2. Arithmetical operations

3. Operations involving fractions

4. Miscellaneous operations

5. Operations involving the rule of three

6. Mixed operations

7. Operations relating to the calculations of areas

8. Operations relating to excavations

9. Operations relating to shadows

He died around the year 870 AD

Sridhara

He was born around 870 AD possibly in Bengal, India. Sridhara is known as the author of two mathematical treatises, namely the Trisatika (sometimes called the Patiganitasara ) and the Patiganita. Sridhara was one of the first mathematicians to give a rule to solve a quadratic equation. Most of the original manuscripts are no longer available, and the only source of information about him is from the works of Bhaskara II:- One rule for solving a quadratic equation is shown below

Multiply both sides of the equation by a known quantity equal to four times the coefficient of the square of the unknown; add to both sides a known quantity equal to the square of the coefficient of the unknown; then take the square root.

He died around the year 930 AD

.

http://www.malhatlantica.pt/mathis/India/Bibliografia.htm

ARYABHATA
ARYABHATA
Brahmagupta's manuscript
Brahmagupta's manuscript

Comments

Submit a Comment

  • ram_m profile imageAUTHOR

    ram_m 

    4 years ago from India

    Thank you M K Paul

  • M K Paul profile image

    M K Paul 

    4 years ago from India

    I found the hub very informative.Keep sharing.

  • ram_m profile imageAUTHOR

    ram_m 

    4 years ago from India

    Thank you Parvathy and angel

  • profile image

    parvathy and angel 

    4 years ago

    thanks for your help, thankyou .Its really great

  • ram_m profile imageAUTHOR

    ram_m 

    6 years ago from India

    Thank you Pavlo for your nice and sincere comments

  • ram_m profile imageAUTHOR

    ram_m 

    6 years ago from India

    Thank you Ajay for sharing this information

  • Pavlo Badovskyy profile image

    Pavlo Badovskyi 

    6 years ago from Kyiv, Ukraine

    I am not strong in math but your hub was interesting even for me. Voted up. Shared.

  • profile image

    ajay 

    6 years ago

    many points are missed aryabhatta only invented algebra,trignometry,gauss's formula (n)(n+1)/2, and even found the formulae for 1^2 + 2^2 + 3^2 ... n^2 = n(n+1)(2n + 1)/6

    and for 1^3 + 2^3 + 3^3 ..... n^3 = (1+2+3....n)^2 and solved indeterminate equations there all are listed in one of his books called aryabhattiayam but according to history 2 more books are written which are said to be lost or destroyed during persian invasion.

  • ram_m profile imageAUTHOR

    ram_m 

    8 years ago from India

    thanks mossesashok

  • profile image

    mossesashok 

    8 years ago

    It is very great.

  • profile image

    ghg 

    8 years ago

    kuti site

working

This website uses cookies

As a user in the EEA, your approval is needed on a few things. To provide a better website experience, hubpages.com uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at: https://hubpages.com/privacy-policy#gdpr

Show Details
Necessary
HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
LoginThis is necessary to sign in to the HubPages Service.
Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
AkismetThis is used to detect comment spam. (Privacy Policy)
HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the googleapis.com or gstatic.com domains, for performance and efficiency reasons. (Privacy Policy)
Features
Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
MavenThis supports the Maven widget and search functionality. (Privacy Policy)
Marketing
Google AdSenseThis is an ad network. (Privacy Policy)
Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
Index ExchangeThis is an ad network. (Privacy Policy)
SovrnThis is an ad network. (Privacy Policy)
Facebook AdsThis is an ad network. (Privacy Policy)
Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
AppNexusThis is an ad network. (Privacy Policy)
OpenxThis is an ad network. (Privacy Policy)
Rubicon ProjectThis is an ad network. (Privacy Policy)
TripleLiftThis is an ad network. (Privacy Policy)
Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
Statistics
Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)