

International Transactions in Mathematical Sciences and Computer 8:10:45
Home Publisher_Home Order your copy LIBRARIES \| Reseach Scholar Journal subscriptions form See our subscription rates (PDF format) Login_/_Signup login Signup journal_admin

Welcome to AACS

More....

Abstract

In applied mathematics Binomial Expansion and Multinomial expansion are of great importance. In around 300 BCE Indian mathematician Pingala had derived the method of obtainng a triangular arrangement known as “Meru-Prastar” for attainment of coefficients of binomial expansion. In sixteenth century, CE it was rediscovered by French mathematician Blasé Pascal (1588-1688CE) and termed as Pascal’s triangle. This paper discusses the development of binomial expansion, multinomial expansion with its applications. The paper also emphasizes the fact that the historical roots of binomial expansion are embedded in Pingalacharya’s Meru-Prastar.

References

[1]. B Datta, A N Singh, Use of permutations and Combinations in India, revised by K

SShukla,IJHS, INSA, Vol 27, No 3 (1992), pp [231-249].

[2]. C.B.Boyer, A History of Mathematics (revised by Uta C. Mertzbach),John Wiley and Sons,

New York, 1991.

[3]. The GaÅ†itakaumudî(1356 AD) of NÄrÄyaÅ†aPaÅ†dita,translated by Parmanand

Singh,GanitaBharati, Vol. (23),No. 1-4, (2001), pp 18-82].

[4]. Ramesh Chand, A Study of Siddhant Siromani, Ph.D Thesis, GurukulKangri

Vishwavidyalaya, Haridwar, India, 1991.

[5]. J.L. Collidge, The Story of Binomial Theorem, The AmericanMathematical Monthly 56:3(1949),

pp 147-157.

[6]. Kapil Dev Dwivedi and S.L.Singh, The Prosody of Pingala, Vishwavidyalaya Prakashan,

Varanasi, 2008, pp 262-264.

[7]. R.C. Gupta, Varahmihira’s Calculation of nCr and Pascal’s Triangle,Ganita Bharati, Vol 14, No. 1-

4 (1992) pp.45-49.

[8]. R.C. Gupta, Combination Problem in Bhaskara’sLilavati, GanitaBharati,Vol.18, 1996, pp 14-20.

[9]. xq.kkdjewys] lalkj ds egkuxf.kr+K]]jktdeyizdk”ku]]ubZfYyh]] iVuk] 1992

[10]. Satya Prakash, Mathematical Physics with Classical Mechanics, Sultan Chand & Sons, New

Delhi, 2004.

[11]. K.S. Patwardhan, S.A. Naimpally and S.L. Singh, Lilavati ofBhaskaracharya, Motilal

Banarasidass Publishers Pvt. Ltd. Delhi, 2001.

[12]. M. S. Raghunathan, India and the world of Mathematics, GanitaBharati,Vol.31, No. 1-2,

2009.

[13]. S. B. Rao, Indian Mathematics and Astronomy, Jnana Deep Publication, Banglore, 1994.

[14]. V.K. Sharma and Anita Sharma, History of Development of Binomial Expansion, GanitaBharati, Vol.26, No. 1-4, 2004, 166-172.

[15]. Anita Sharma, A Study of Vedic Mathematics and its Relevance to Science and Technology, Ph. D Thesis, Gurukula Kangri Vishwavidyalaya, Haridwar 2004.

[16]. Satyadeva Sharma, Siddhant Siromani of Bhaskaracharya, ChaukhambasurbharatiPrakashan, Varanasi, 2007.

[17]. C. N. Srinivasienger, The History of Ancient Indian Mathematics, The World Press Pvt. Ltd. Calcutta, 1967.

[18]. John Stillwell, Mathematics and its History, Springer 2nd Edition, 2004, ISBN 0-387-95336-I.

[19]. Mahavira’s Ganitasarasamgrah,edt. By L. C. Jain,(1963)Ch.6,Verse 218,Publ. Jain SanskritiSanrakshakSangh,Sholapur(Maharashtra).

[20]. Eric W Weisstein, Binomial Theorem, From math World A Wolfram Web Resource http://mathworld.wolfram/Binomial Sums.html. 2010.

[21]. Stephen Wolfram, Binomial Theorem, Absolute astronomy. http://www.absoluteastronomy.com 2007

[22]. Binomial Theorem, Available athttp://mathworld.wolfram.com/classroom/BinomialTheorem.html

[23]. Yang Hui, From Wikipedia, the free encyclopedia, available athttp://en.wikipedia.org/wiki/Yang-Hui

[24]. Binomial Coefficient, Generalization to multinomial, Available athttp:/en, wikipedia.org/wiki/Binomial_Coefficient#Generalisation_to_mutinomials.

[25]. Binomial Coefficient, Pascal’s Triangle, Available at http:/en, wikipedia.org/wiki/Binomial_Coefficient#Pascal.27s_triangle.

[26]. Pascal’s Triangle. http://en.wikipedia.org/wiki/Pascal’s triangle.

International Transactions in Mathematical Sciences and ComputerJan-June 2022 Vol:15 Issue:1

History of Binomial and Multinomial Expansions

Abstract

Author

Keyword

References

Download paper