See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/272680672 SOME PROBLEMS ON LILAVATI GANITHAM Conference Paper · February 2015 CITATIONS READS 0 16,928 2 authors, including: Dr Bhavanari Satyanarayana Acharya Nagarjuna University 191 PUBLICATIONS 285 CITATIONS SEE PROFILE Some of the authors of this publication are also working on these related projects: THE CONCEPT "PRIME" IN DIFFERENT ALGEBRAIC SYSTEMS View project GOOD DEEDS View project All content following this page was uploaded by Dr Bhavanari Satyanarayana on 23 February 2015. The user has requested enhancement of the downloaded file. co. (Comp.).Paper presentation “SOME PROBLEMS .D. who wrote the first work with full and systematic use of the decimal number system. and a Scientist (1114-1185 A. Bhaskara was the leading mathematician of 12th century. Bhavanari Satyanarayana AP scientist Awardee. He is not only a famous Mathematician. he not only used . FEB. which was the leading mathematical centre of ancient India of that time. Andhra Pradesh and Prof. 1 SOME PROBLEMS ON LILAVATI GANITHAM By Bhavanari Satya Gnyana Sri IIyr B.Tech. Lilavati (“The Beautifiul”) (arithmetic) and Bijaganita (“seed counting”) (algebra). In his mathematical works. Bhaskara – II is also called as Bhaskaracharya or Bhaskara.LILAVATI GANITAM – 12TH CENTURY (by SATYA GNYANA SRI BHAVANARI) MERISTELLA COLLEGE. VIJAYAWADA ON 2015-02-21 NBHM SPONSORED NATIONAL CONFERENCE ON WOMEN IN MATHEMATICS WITH SPECIAL REFERENCE TO LILAVATI. particularly. 2015.II became head of the astronomical observatory at Ujjain. As an astronomer Bhaskara wrote about planetary positions and eclipses.in Introduction: Lilavati is the daughter of Bhaskara – II. Bhaskara . 20-21. Guntur DT.. a famous mathematician of ancient India during 12th Century. 2009 Acharya Nagarjuna University Andhra Pradesh Bhavanari2002@yahoo. but also an excellent Astronomer. Science) Vignan’s Nirula of Science and Technology for Women Palakaluru. FEB.II anticipated the modern convention of signs . ∞ . and evidently was the first to gain some understanding of the meaning of division by zero. 2 the decimal system but also compiled earlier problems from Brahmagupta and others.LILAVATI GANITAM – 12TH CENTURY (by SATYA GNYANA SRI BHAVANARI) MERISTELLA COLLEGE. Bhaskara .II mentioned in his Beejaganitha that. VIJAYAWADA ON 2015-02-21 NBHM SPONSORED NATIONAL CONFERENCE ON WOMEN IN MATHEMATICS WITH SPECIAL REFERENCE TO LILAVATI. 20-21.Paper presentation “SOME PROBLEMS . 2015. Bhaskara . Bhaskara’s notable work is Siddhantasiromani (“Head Jewel of Accuracy”) He wrote siddhanta Shiromani at the age of 36 in 1150 A. ∞. screaming. One problem related to quadratic equation and another problem related to cubic equation. and this work (consisting of about 1450 verses) has divided into four parts: 1) Lilatvati (ARITHMETIC) has 278 verses.D. Another 12 were on the hill. How many monkeys were there in that group? . 3) Goladhyaya (sphere/celestial globe) has 451 verses. The first part Lilavati contains simple problems of Arithmetic. 2) Bijaganit (ALGEBRA) has 213 verses.. and 4) Grahaganit (mathematics of the planets) has 501 verses. THE PROBLEMS: Problem-1(SOLVING A QUADRATIC EQUATION IN ONE VARIABLE) The eighth part of a group of monkeys. In this conference. we wish to discuss two simple problems of Arithmetic from Siddanta Siromani. squared was skipping in the forest. 2015. FEB. Then. . VIJAYAWADA ON 2015-02-21 NBHM SPONSORED NATIONAL CONFERENCE ON WOMEN IN MATHEMATICS WITH SPECIAL REFERENCE TO LILAVATI.Paper presentation “SOME PROBLEMS . 20-21.LILAVATI GANITAM – 12TH CENTURY (by SATYA GNYANA SRI BHAVANARI) MERISTELLA COLLEGE. 3 Solution: Let be the number of monkeys in the group. we get . Multiplying by 64. we get . Adding (32)2 on both sides. . . So. . Here || || Hence both negative and positive signs have to be taken. . . So. . . Thus. which when multiplied by 12 and increased by the cube of the number is equal to the sum of 35 and six times the square of the number? Solution: Let be the number. we have . Oh learned man. ! . Can you give me the number. The ancient Indian Mathematicians were not very successful in solving cubic and quadratic equations. Problem-2 (An EQUATIONS OF THIRD DEGREE). Then. Bhaskara-II has provided the following example related to a cubic equation. . 2015.LILAVATI GANITAM – 12TH CENTURY (by SATYA GNYANA SRI BHAVANARI) MERISTELLA COLLEGE. VIJAYAWADA ON 2015-02-21 NBHM SPONSORED NATIONAL CONFERENCE ON WOMEN IN MATHEMATICS WITH SPECIAL REFERENCE TO LILAVATI. FEB. 20-21.Paper presentation “SOME PROBLEMS . 4 . we get . . Subtracting 8 from both sides. . . That is. . Hence. . . . . [6] K. Britannica. 2010 SGS College. Pages 172-173.02. Acknoledgements: The authors thank the Organizers of the National Conference for giving us the opportunity of presenting this paper in the Conference on 2015.com/EBchecked/topic/64067/Bhaskara.P. Satyanarayana “Number and Infinity Concepts in Vedas” (Survey Article).mcs. Jaggaiahpet. 2012 (by T K Puttaswamy).aspx [3] http://www-history.st-and. Pages 50- 53.net/Biography/Bhaskara.biography. Elsevier. Vijayawada. Proceedings of the One day National Seminar on Algebra.21. [5] Bhavanari Satyanarayana and K. 2011 (200th Birth Anniversary of Evariste Galois). Satyanarayana and Bhavanari Satyanarayana “A Prospective Theme of Mathematics” (Survey Article).ac. Proceedings of the National Seminar on Present Trends in Mathematics and its Applications (Sponsered by UGC). . References: [1] http:// ww. KBN College. A.uk/Biographies/BHaskara_ II. November 11th and 12th. 25 Oct. Krishna Dt.II . Andhra Predesh.II [2] http://www.studyhelpline.html [4] Book: Mathematical Achievements of pre-modern Indian Mathematicians. February 20-21. 2015. Paper presentation “SOME PROBLEMS ...National Seminar on GEOMETRICAL CONCEPTS IN SULVA SUTRAS.LILAVATI GANITAM – 12TH CENTURY (by SATYA GNYANA SRI BHAVANARI) MERISTELLA COLLEGE. December 18-19. [9] Bhavanari Satyanarayana “Some Problems from Bijaganitha of Bhaskara-II” (An invited talk). NBHM Sponsored National Conference on WOMEN IN MATHEMATICS WITH SPECIAL REFERENCE TO LILAVATI. Tirupati. National Work Shop on “Mathematics Flavour in Vedas and Shastras” (On the Occasion of 125th Birth Anniversary of Srinivasa Ramanujam). Andhra Pradesh. India. 5 [7] Bhavanari Satyanarayana “Some Mathematical Concepts in Ancient Sanskrit Works” (An invited talk). Tirupathi.P. December 21-22. 2013.P. Sri Venkateswara Vedic University. 2015. Sri Venkateswara Vedic University. 2014. National Conference on Mathematics and Astronomy of Bhaskara-II. 2012. Tirupathi. A.P. Maris Stella College. FEB. December 27-28. Sri Venkateswara Vedic University. Vijayawada. [10] Bhavanari Satyanarayana “Some Problems from Algebra of Bhaskaracharya” (An invited talk). VIJAYAWADA ON 2015-02-21 NBHM SPONSORED NATIONAL CONFERENCE ON WOMEN IN MATHEMATICS WITH SPECIAL REFERENCE TO LILAVATI.. A. [8] Bhavanari Satyanarayana “On Geometrical Concepts in Ancient Sanskrit Works” (An invited talk). 20-21. A. View publication stats .