«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*

End Date: Tuesday Mar-13-2018 18:20:15 PDT
Buy It Now for only: $58.00
MyMathLab Student Access Code

End Date: Wednesday Feb-21-2018 8:28:05 PST
Buy It Now for only: $21.95
KJV Holy Bible King James Version Black Giant Print Thumb Indexing Faux Leather

End Date: Monday Mar-5-2018 19:08:19 PST
Buy It Now for only: $29.99
The Cannabis Grow Bible: The Definitive Guide To Growing Marijuana For Recrea...

End Date: Sunday Feb-18-2018 14:10:52 PST
Buy It Now for only: $19.95
Jesus Calling - 3 Pack : Enjoying Peace in His Presence by Sarah Young Hardcover

End Date: Monday Mar-12-2018 17:47:13 PDT
Buy It Now for only: $18.72
KING JAMES VERSION HOLY BIBLE KJV Red Letter Thumb Index Black Faux Leather!

End Date: Sunday Mar-18-2018 14:18:23 PDT
Buy It Now for only: $32.95
KJV HOLY BIBLE King James Version Burgundy Giant Print Thumb Index BRAND NEW

End Date: Tuesday Mar-6-2018 14:05:27 PST
Buy It Now for only: $33.88
Bhaskara Pattelar and Other Stories

End Date: Mar-02 03:09
Buy It Now for only: US $152.57
Buy it now |
TANAPEX Madras Bhaskara Device Enable Those In Kanchi Listen 1981 Cover #32197

End Date: Mar-04 06:58
Buy It Now for only: US $15.00
Buy it now |
Bhaskara: The Last of the Varmans: Kamarupa Series by P.W. Ingty (English) Paper

End Date: Mar-01 21:55
Buy It Now for only: US $14.16
Buy it now |
Agriculture Microbiology by M. Vijaya Bhaskara Reddy (English) Paperback Book Fr

End Date: Feb-25 08:24
Buy It Now for only: US $138.76
Buy it now |

End Date: Mar-08 19:48
Buy It Now for only: US $1.99
Buy it now |
JAT C61 India 2004 FDC Bhaskara Sethupathi

End Date: Mar-07 00:26
Buy It Now for only: US $1.29
Buy it now |

Meet the Newest NOOK GlowLight 3

Start: 01 Nov 2017 | End: 31 Aug 2018

100% Anniversary of the Chore Coat at Carhartt

Start: 28 Aug 2017 | End: 01 Mar 2018

5% Off All Golf Shoes

Code: AW002

Start: 06 Jul 2017 | End: 06 Feb 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
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