«Science History»
Bhaskara I

Bhaskara I

Born: about 600 in (possibly) Saurastra (modern Gujarat state), India
Died: about 680 in (possibly) Asmaka, India

We have very little information about Bhaskara I's life except what can be deduced from his writings. Shukla deduces from the fact that Bhaskara I often refers to the Asmakatantra instead of the Aryabhatiya that he must have been working in a school of mathematicians in Asmaka which was probably in the Nizamabad District of Andhra Pradesh. If this is correct, and it does seem quite likely, then the school in Asmaka would have been a collection of scholars who were followers of Aryabhata I and of course this fits in well with the fact that Bhaskara I himself was certainly a follower of Aryabhata I.

There are other references to places in India in Bhaskara's writings. For example he mentions Valabhi (today Vala), the capital of the Maitraka dynasty in the 7th century, and Sivarajapura, which were both in Saurastra which today is the Gujarat state of India on the west coast of the continent. Also mentioned are Bharuch (or Broach) in southern Gujarat and Thanesar in the eastern Punjab which was ruled by Harsa for 41 years from 606. Harsa was the preeminent ruler in north India through the first half of Bhaskara I's life. A reasonable guess would be that Bhaskara was born in Saurastra and later moved to Asmaka.

Bhaskara I was an author of two treatises and commentaries to the work of Aryabhata I. His works are the Mahabhaskariya , the Laghubhaskariya and the Aryabhatiyabhasya . The Mahabhaskariya is an eight chapter work on Indian mathematical astronomy and includes topics which were fairly standard for such works at this time. It discusses topics such as: the longitudes of the planets; conjunctions of the planets with each other and with bright stars; eclipses of the sun and the moon; risings and settings; and the lunar crescent.

Bhaskara I included in his treatise the Mahabhaskariya three verses which give an approximation to the trigonometric sine function by means of a rational fraction. These occur in Chapter 7 of the work. The formula which Bhaskara gives is amazingly accurate and use of the formula leads to a maximum error of less than one percent. The formula is

sin x = 16x (π - x)/[5π2 - 4x (π - x)]
and Bhaskara attributes the work as that of Aryabhata I. We have computed the values given by the formula and compared it with the correct value for sin x for x from 0 to π/2 in steps of π/20.
x = 0formula = 0.00000sin x = 0.00000error = 0.00000
x = π/20formula = 0.15800sin x = 0.15643error = 0.00157
x = π/10formula = 0.31034sin x = 0.30903error = 0.00131
x = 3π/20formula = 0.45434sin x = 0.45399error = 0.00035
x = π/5formula = 0.58716sin x = 0.58778error = -0.00062
x = π/4formula = 0.70588sin x = 0.70710error = -0.00122
x = π/10formula = 0.80769sin x = 0.80903error = -0.00134
x = 7π/20formula = 0.88998 sin x = 0.89103error = -0.00105
x = 2π/5formula = 0.95050sin x = 0.95105error = -0.00055
x = 9π/20formula = 0.98753sin x = 0.98769error = -0.00016
x = π/2formula = 1.00000sin x = 1.00000error = 0.00000
In 629 Bhaskara I wrote a commentary, the Aryabhatiyabhasya , on the Aryabhatiya by Aryabhata I. The Aryabhatiya contains 33 verses dealing with mathematics, the remainder of the work being concerned with mathematical astronomy. The commentary by Bhaskara I is only on the 33 verses of mathematics. He considers problems of indeterminate equations of the first degree and trigonometric formulae. In the course of discussions of the Aryabhatiya , Bhaskara I expressed his idea on how one particular rectangle can be treated as a cyclic quadrilateral. He was the first to open discussion on quadrilaterals with all the four sides unequal and none of the opposite sides parallel.

One of the approximations used for π for many centuries was √10. Bhaskara I criticised this approximation. He regretted that an exact measure of the circumference of a circle in terms of diameter was not available and he clearly believed that π was not rational.

In [11], [12], [13] and [14] Shukla discusses some features of Bhaskara's mathematics such as: numbers and symbolism, the classification of mathematics, the names and solution methods of equations of the first degree, quadratic equations, cubic equations and equations with more than one unknown, symbolic algebra, unusual and special terms in Bhaskara's work, weights and measures, the Euclidean algorithm method of solving linear indeterminate equations, examples given by Bhaskara I illustrating Aryabhata I's rules, certain tables for solving an equation occurring in astronomy, and reference made by Bhaskara I to the works of earlier Indian mathematicians.

Article by: J J O'Connor and E F Robertson

November 2000
MacTutor History of Mathematics
Search All Ebay* AU* AT* BE* CA* FR* DE* IN* IE* IT* MY* NL* PL* SG* ES* CH* UK*
KJV Holy Bible King James Version Black Giant Print Thumb Indexing Faux Leather

End Date: Sunday Jun-10-2018 5:31:28 PDT
Buy It Now for only: $13.30
The Subtle Art of Not Giving a F*ck by Mark Manson A Counterintuitive Approach,,

End Date: Monday Jun-4-2018 23:43:04 PDT
Buy It Now for only: $11.97
Think and Grow Rich by Napoleon Hill (2012, Hardcover)

End Date: Monday Jun-11-2018 23:29:51 PDT
Buy It Now for only: $12.55
Trump: The Art of the Deal by Donald Trump (New Papaerback Book)

End Date: Friday Jun-15-2018 1:39:01 PDT
Buy It Now for only: $11.90
Medical Medium: Secrets Behind Chronic and Mystery Illness by Anthony William

End Date: Wednesday May-30-2018 14:14:56 PDT
Buy It Now for only: $12.22
F.U. Money: Make as Much Money as You Damn Well Want and Live Your Life as You D

End Date: Wednesday Jun-20-2018 20:19:17 PDT
Buy It Now for only: $7.99
The Story of the Last Black Cargo: Barracoon by Zora Neale Hurston(2018, eBooks)

End Date: Monday Jun-18-2018 1:35:12 PDT
Buy It Now for only: $7.99
The Keto Reset Diet by Mark Sisson (2017, eBooks)

End Date: Saturday Jun-16-2018 20:04:07 PDT
Buy It Now for only: $4.98
TANAPEX Madras Bhaskara Device Enable Those In Kanchi Listen 1981 Cover #32197

End Date: Jun-08 11:43
Buy It Now for only: US $15.00
Buy it now |

End Date: Jun-04 04:49
Buy It Now for only: US $1.99
Buy it now |
India MNH 2004 Bhaskara Sethupathy

End Date: Jun-05 12:02
Buy It Now for only: US $1.34
Buy it now |
Aphorisms of Siva : The Siva Sutra With Bhaskara's Commentary, the Varttika, ...

End Date: Jun-11 23:25
Buy It Now for only: US $29.09
Buy it now |
Cointegration: For the Applied Economist by B. Bhaskara Rao.

End Date: Jun-12 07:25
Buy It Now for only: US $107.77
Buy it now |
Rudyard Kipling's India K. Bhaskara Rao 1967 First Edition OU Press

End Date: May-28 20:40
Buy It Now for only: US $15.99
Buy it now |
Rudyard Kipling's India by K. Bhaskara Rao/Nice 1967 Un. of OK 1st ed. HB-DJ

End Date: Jun-23 20:38
Buy It Now for only: US $15.00
Buy it now |

Home Textile Clearance 20% Off + Extra 20% Off


Start: 19 Oct 2017 | End: 18 Mar 2018

Free 5 Year Warranty on most mattresses & beds

Start: 11 Apr 2017 | End: 01 Apr 2018

10% Off Newsletter Sign Ups at Moda Operandi!

Start: 12 Sep 2017 | End: 01 Apr 2018

Search All Amazon* UK* DE* FR* JP* CA* CN* IT* ES* IN* BR* MX
Booking.com B.V. is based in Amsterdam in the Netherlands. Ready for some statistics? Our 1,534,024 properties, including 860,482 holiday rentals, are located in 123,105 destinations in 229 countries and territories, and are supported internationally by 198 offices in 70 countries.
2013 Copyright © Techhap.com Mobile version 2015 | PeterLife & company
Skimlinks helps publishers monetize editorial content through automated affiliate links for products.
Terms of use Link at is mandatory if site materials are using fully or particulary.
Were treated to the site administrator, a cup of coffee *https://paypal.me/peterlife