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Bhaskara's Arithmetic Operation of Division by Zero with Application in the Foundation of the Differential Calculus


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1 Department of Mathematics, Apex Academy,Uwheru, Delta State, Nigeria
     

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This article is concerned mainly with Bhaskara's arithmetic operation of division by zero. This is the simplest of all for teaching analysis and is the most consistent and philosophical. Some mathematicians have attempted to impugn it, but when I examined their reasonings, I observed that they have done so because they have failed to comprehend the true behavior of zero. In this article I have aimed to clarify and justify Bhaskara's law of impending operations involving zero and furnish hints at the foundations upon which the arithmetic operation of division by zero rests its claims to be preferred to its fashionable rivals, the methods of infinitesimals and limits.

Keywords

Zero, Infinity, Bhaskara, Division by Zero, Law of Impending Operations, Differential Calculus
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  • Arya, S., On the Brahmagupta- Bhaskara equation, Math. Ed. 8 (1), 1991, 23-27.

  • Cajori, F., A History of Mathematics, The Macmillan Company, New York, 2nd Edition, 1919.

  • Chaudhary,B., Jha, P., Studies of Bhaskara's works in Mithila, Ganita Bharati 12 (1-2), 1990, 27-32.

  • B. Datta, The two Bhaskaras, Indian Historical Quarterly 6, 1930, 727-736.

  • R. Gupta, Bhaskara II's derivation for the surface of a sphere, Math. Education 7, 1973, A49-A52.

  • V. Madhukar Mallayya, K. Jha, Bhaskara's concept of numeration in decuple proportions earliest reference in Vedas with Yaska's 'Nirukta' throwing light on the notion of succession in enumeration : an anticipation of Peano's axioms, Ganita-Bharati 17 (1-4), 1995, 85-91.

  • U. Okoh, Euler's Constant: A Proof of its Irrationality and Trancedence by Means of Minus One Factorial, IAENG Transactions on Engineering Sciences (2015), World Scientic Publishing.

  • U. Okoh, Euler's Constant: New Insights by Means of Mimus One Factorial, (Periodical style), Proc. WCE 2014.

  • K. S. Patwardhan, S. A. Naimpally, S. L. Singh, Lilavati of Bhaskaracarya, Delhi, 2000.

  • K. Ramasubramanian and M.D. Srinivas, Studies in History of Indian Mathematics, Ed.Seshadri, Hindustan Book Agency,p. 206.

  • R. A. Rankin, An Introduction to Mathematical Analysis, Pergamon Press, Oxford, 1963. 150-184.

  • K. H. Rosen, Discrete Mathematics and Its Applications, McGraw - Hill,Inc, New York, 1994,150-167.

  • A. Sathaye, Bhaskara's Treatment of the Conception of Infinity, Ganita Bharati, Vol. 37, No 1-2(2015), pp.111-123.

  • C. Selenius, Kettenbruch theoretische Erklrung der zyklischen Methode zur Lsung der Bhaskara-Pell-Gleichung, Acta Acad. Abo. Math. Phys. 23 (10), 1963.

  • S. Sinha, Bhaskara's Lilavati, Bull. Allahabad Univ. Math. Assoc. 15, 1951, 9-16.

  • D. Somayaji, Bhaskara's calculations of the gnomon's shadow, Math. Student 18, 1950, 1-8.


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  • Bhaskara's Arithmetic Operation of Division by Zero with Application in the Foundation of the Differential Calculus

Abstract Views: 294  |  PDF Views: 1

Authors

Okoh Ufuoma
Department of Mathematics, Apex Academy,Uwheru, Delta State, Nigeria

Abstract


This article is concerned mainly with Bhaskara's arithmetic operation of division by zero. This is the simplest of all for teaching analysis and is the most consistent and philosophical. Some mathematicians have attempted to impugn it, but when I examined their reasonings, I observed that they have done so because they have failed to comprehend the true behavior of zero. In this article I have aimed to clarify and justify Bhaskara's law of impending operations involving zero and furnish hints at the foundations upon which the arithmetic operation of division by zero rests its claims to be preferred to its fashionable rivals, the methods of infinitesimals and limits.

Keywords


Zero, Infinity, Bhaskara, Division by Zero, Law of Impending Operations, Differential Calculus

References