Bhaskara II

This article deals with the Indian mathematician Bhaskara, who lived in the 12th century; for the same mathematician of the 7th century see Bhaskara I .

Bhaskara , also Bhaskara II. , Bhaskaracharya or (older) Bhaskara Atscharja ("Bhaskara the teacher") (* 1114 with Bijjada Bida ; † 1185 ) was an Indian mathematician and astronomer. He is considered one of the most important medieval mathematicians in India.

He was born near Bijjada Bida near Bijapur in what is now the Indian state of Karnataka , was director of the astronomical observatory in Ujjain and carried on the mathematical tradition of Varahamihira and Brahmagupta . He came from a family of court scholars, otherwise little is known about him.

His main scientific works are Lilavati , which deals mainly with arithmetic and is based on the works of Brahmagupta, Sridhara and Aryabatha II, Bijaganita , a treatise on algebra (extracting roots, solving quadratic and higher equations), and the very influential astronomical work Siddhantasiromani ( 1150), which in turn comprises two parts: Goladhyaya ( sphere ) and Grahaganita (mathematics and astronomy). The astronomical work showed his knowledge of trigonometry, for example he knew the identities . It also contains the foundations of the infinitesimal calculus. This happened in connection with the observation of planetary movements from the earth. According to Bhaskara, the differential (temporal change) disappears near the maximum of a function. If a planet is still furthest or closest to earth, the midpoint equation disappears . Bhaskara concluded from this that the differential of the midpoint equation disappears for a position in between, which can be understood as the forerunner of the theorem of Rolle or the mean value theorem of differential calculus . ${\displaystyle \sin(a\pm b)=\sin(a)\cos(b)\pm \cos(a)\sin(b)}$

After the court scholar Fyzi, who translated Lilavati into Persian on behalf of the Mughal ruler Akbar in 1587, Lilavati was the name of Bhaskara's daughter. According to the legend passed down by Fyzi, Bhaskara constructed a water clock that predicted the favorable date of Lilavati's marriage, which was predicted by a horoscope, but was inadvertently blocked by a pearl from Lilavati's necklace. Since she had now missed her marriage date, according to legend, she could no longer marry and as a consolation Bhaskara wrote the mathematics textbook with her name.

Based on an idea presented in Sanskrit scripts as early as the 5th century , Bhaskara described a wheel which, he thought, would turn forever - an early perpetual motion machine . He, like so many after him, did not understand the physical impossibility of such a machine.

He had such a high reputation that his manuscripts were copied well into the 19th century. An inscription in a medieval Indian temple read: Triumphant is the famous Bhaskaracharya, whose achievements are revered by the wise and learned. A poet endowed with fame and religious merit, he is like the crest of the peacock .

literature

• Phadke, Patwardhan, Naimpally, Singh: Līlāvatī of Bhāskarācārya - A Treatise of Mathematics of Vedic Tradition . Motilal Banarsidass Pub. Delhi 2001. ISBN 81-208-1777-X
• David Pingree: Bhaskara II . In: Charles Coulston Gillispie (Ed.): Dictionary of Scientific Biography . tape 2 : Hans Berger - Christoph Buys Ballot . Charles Scribner's Sons, New York 1970, p. 115-120 .
• Francois Patte: Le Siddhantasiromani: le oeuvre mathématique et astronomique de Bhaskaracarya, Geneva, Libraire Froz 2004
• George Joseph: The crest of the peacock, Princeton UP 2011 (especially p. 377f)

Web links

• Literature by and about Bhaskara II in the catalog of the German National Library
• John J. O'Connor, Edmund F. Robertson :  Bhaskara II .. In: MacTutor History of Mathematics archive .
• Spektrum.de: Bhaskara (1114–1185) June 1, 2015

Individual evidence

1. ^ ^{A b} Joseph, Crest of the Peacock, p. 378
2. ^ Joseph, Crest of the Peacock, 2011, p. 409
3. ^ Joseph, Crest of the peacock, p. 379