Prabir Chandra Bhattacharyya,




Bhattacharyya’s Co-ordinate System,Cartesian Co-ordinate System,Quadratic Equation,Theory of Dynamics of Numbers,Theory of Numbers,


The basic idea of a quadratic equation is one of the most important topics in algebra. The mathematical concept for the method of solution of a quadratic equation is dependent on the advancement of the theory of numbers. The author developed a new concept regarding the method of solution of the quadratic equation based on “Theory of Dynamics of Numbers”. The author determined the inherent nature of one unknown quantity (say x) from the quadratic expression ax2+bx+c of the quadratic equation ax2+bx+c=0 by keeping the structure of the second-degree expression intact and then finding the solution of the quadratic equation using the novel concept of the Theory of Dynamics of Numbers. The author solved any quadratic equation in one unknown number (say x) of the quadratic equation in the form of ax2+bx+c=0, whether the numerical value of the discriminant is b2-4ac≥0 or b2-4ac<0, is real numbers only without using any imaginary numbers. With these new inventive concepts, the author developed new theories in the theory of quadratic equation.


I. Bhattacharyya P. C. “AN INTRODUCTION TO RECTANGULAR BHATTACHARYYA’S CO-ORDINATES: A NEW CONCEPT”. J. Mech. Cont. & Math. Sci., Vol.-16, No.-11, November (2021). pp 76-86.
II. Bhattacharyya P. C.. “AN INTRODUCTION TO THEORY OF DYNAMICS OF NUMBERS: A NEW CONCEPT”. J. Mech. Cont. & Math. Sci., Vol.-16, No.-11, January (2022). pp 37-53
III. Boyer, C. B. & Merzbach, U. C. (2011). A history of mathematics. New York: John Wiley & Sons.
IV. Cajori, F., (1919). A History of Mathematics 2nd ed., New York: The Macmillan Company.
V. Dutta, B.B. ( 1929). The Bhakshali Mathematics, Calcutta, West Bengal: Bulletin of the Calcutta Mathematical Society.
VI. Datta, B. B., & Singh, A. N. (1938). History of Hindu Mathematics, A source book. Mumbai, Maharashtra: Asia Publishing House.
VII. Gandz, S. (1937). The origin and development of the quadratic equations in Babylonian, Greek, and Early Arabic algebra. History of Science Society, 3, 405-557.
VIII. Gandz, S. (1940). Studies in Babylonian mathematics III: Isoperimetric problems and the origin of the quadratic equations. Isis, 3(1), 103-115.
IX. Hardy G. H. and Wright E. M. “An Introduction to the Theory of Numbers”. Sixth Edition. P. 52.
X. Katz, V. J. (1997), Algebra and its teaching: An historical survey. Journal of Mathematical Behavior, 16(l), 25-36.
XI. Katz, V., J. (1998). A history of mathematics (2nd edition). Harlow, England: Addison Wesley Longman Inc.
XII. Katz Victor, (2007). The Mathematics of Egypt, Mesopotamia, China, India and Islam: A source book 1st ed., New Jersey, USA: Princeton University Press.
XIII. Kennedy, P. A., Warshauer, M. L. & Curtin, E. (1991). Factoring by grouping: Making the connection. Mathematics and Computer Education, 25(2), 118-123.
XIV. Ling, W. & Needham, J., (1955). Horner’s method in Chinese Mathematics: Its root in the root extraction procedures of the Han Dynasty, England: T’oung Pao.
XV. Nataraj, M. S., & Thomas, M. O. J. (2006). Expansion of binomials and factorisation of quadratic expressions: Exploring a vedic method. Australian Senior Mathematics Journal, 20(2), 8-17.
XVI. Rosen, Frederic (Ed. and Trans). (1831). The algebra of Mohumed Ben Muss. London: Oriental Translation Fund; reprinted Hildesheim: Olms, 1986, and Fuat Sezgin, Ed., Islamic Mathematics and Astronomy, Vol. 1. Frankfurt am Main: Institute for the History of Arabic-Islamic Science 1997.
XVII. Smith, D. (1951). History of mathematics, Vol. 1. New York: Dover. Smith, D. (1953). History of mathematics, Vol. 2. New York: Dover. Stols, H. G. (2004).
XVIII. Smith, D. (1953). History of mathematics, Vol. 2. New York: Dover.
XIX. Thapar, R., (2000). Cultural pasts: Essays in early Indian History, New Delhi: Oxford University Press.
XX. Yong, L. L. (1970). The geometrical basis of the ancient Chinese square-root method. The History of Science Society, 61(1), 92-102.
XXI. http://en. wikipedia.org/wiki/Shridhara

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