# A NOVEL CONCEPT OF THE THEORY OF DYNAMICS OF NUMBERS AND ITS APPLICATION IN THE QUADRATIC EQUATION

#### Authors:

Prabir Chandra Bhattacharyya,

#### DOI NO:

https://doi.org/10.26782/jmcms.2024.02.00006

#### Keywords:

Cartesian Coordinate System,Imaginary Numbers,Quadratic Equation,Rectangular Bhattacharyya’s Coordinate System,Theory of Numbers,Theory of Dynamics of Numbers.,

#### Abstract

Considering the basic role of numbers in Mathematics, Science, and Technology the author developed a new structure of numbers named as ‘Theory of Dynamics of Numbers.’ According to the Theory of Dynamics of Numbers, the author defined 0 (zero) is the starting point of any number and also defined 0 (zero) as a neutral number. The numbers can move in infinite directions from the starting point 0 (zero) and back to 0 (zero). The author has defined the three types of numbers: 1) Neutral Numbers, 2) Count Up Numbers, and 3) Count Down Numbers. These three types of numbers cover the entire numbers in the number system where there is no necessity for the concept of imaginary numbers. Introducing this new concept the author solved the quadratic equation in one unknown (say x) in the form ax2 + bx + c = 0, even if the numerical value of the discriminant b2 – 4ac < 0 in real numbers without using the concept of imaginary numbers. Already the author solved the quadratic equation x2 + 1 = 0 and proved that  √ -1 = -1  by using the Theory of Dynamics of Numbers. The Theory of Dynamics of Numbers is a more powerful tool than that of the real and imaginary number system to explain the truth of nature.

#### Refference:

I. Amelia Ethan. Exploring the Use of Number Theory in Modern Cryptography: Advancements and Applications. Department of Journalism, University of Harvard. July 2023. pp 1-6.
II. A. Harripersaud, (2021). The quadratic equation concept. American Journal of Mathematicsand Statistics, (11)3, 2021, 67-71.
III. B. B. Dutta, (1929). : “The Bhakshali Mathematics”. Calcutta, West Bengal: Bulletin of the Calcutta Mathematical Society.
IV. B. B. Datta, & A. N. Singh, (1938). : “History of Hindu Mathematics, A source book”. Mumbai, Maharashtra: Asia Publishing House.
V. H. Lee Price, Frank R. Bernhart, : “Pythagorean Triples and a New Pythagorean Theorem”. arXiv:math/0701554 [math.HO]. 10.48550/arXiv.math/0701554
VI. Lucena, F. J. H., Díaz, I. A., Rodríguez, J. M. R., and Marín, J. A. M., Influencia del aula invertida en el rendimiento académico. Una revisión sistemática. Campus Virtuales, 8(1), p. 9-18, 2019.
VII. L. Nurul , H., D., (2017). : “Five New Ways to Prove a Pythagorean Theorem”. International Journal of Advanced Engineering Research and Science. Volume 4, issue 7, pp.132-137. 10.22161/ijaers.4.7.21
VIII. Makbule Gözde DİDİŞ KABAR. : A Thematic Review of Quadratic Equation Studies in The Field of Mathematics Education. Participatory Educational Research (PER)Vol.10(4), pp. 29-48, July 2023. 10.17275/per.23.58.10.4
IX. Manjeet Singh. Transformation of number system. International Journal of Advance Research, Ideas and Innovations in Technology. Volume 6, Issue 2 , 2020. pp 402-406. 10.13140/RG.2.2.33484.77442
X. M. Janani et al, : “Multivariate Crypto System Based on a Quadratic Equation to Eliminate in Outliers using Homomorphic Encryption Scheme”. Homomorphic Encryption for Financial Cryptography. pp 277–302. 01 August 2023. Springer
XI. M. Sandoval-Hernandez et al, : “The Quadratic Equation and its Numerical Roots”. International Journal of Engineering Research & Technology (IJERT). Vol. 10 Issue 06, June-2021 pp. 301-305. 10.17577/IJERTV10IS060100
XII. M. Sandoval-Hernandez, H. Vazquez-Leal, U. Filobello-Nino , Elisa De-Leo-Baquero, Alexis C. Bielma-Perez, J.C. Vichi-Mendoza , O. Alvarez-Gasca, A.D. Contreras-Hernandez, N. Bagatella-Flores , B.E. Palma-Grayeb, J. Sanchez-Orea, L. Cuellar-Hernandez. : The Quadratic Equation and its Numerical Roots’. IJERT. Volume 10, Issue 06 (June 2021), 301-305. 10.17577/IJERTV10IS060100
XIII. Peter Chew, : ‘Peter Chew Method for Quadratic Equation’ (2019). 2019 the 8th International Conference on Engineering Mathematics and Physics, Journal of Physics: Conference Series1411 (2019) 012003, IOP Publishing, 10.1088/1742-6596/1411/1/012003
XIV. Pieronkiewicz, B., & Tanton, J. (2019). Different ways of solving quadraticequations. Annales Universitatis Paedagogicae Cracoviensis Studia ad DidacticamMathematicae Pertinentia, 11, 103-125
XV. Prabir Chandra Bhattacharyya, : “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. 10.26782/jmcms.2021.11.00008
XVI. Prabir Chandra Bhattacharyya, : “AN INTRODUCTION TO THEORY OF DYNAMICS OF NUMBERS: A NEW CONCEPT”. J. Mech. Cont. & Math. Sci., Vol.-17, No.-1, January (2022). pp 37-53. 10.26782/jmcms.2022.01.00003
XVII. Prabir Chandra Bhattacharyya, : ‘A NOVEL CONCEPT IN THEORY OF QUADRATIC EQUATION’. J. Mech. Cont. & Math. Sci., Vol.-17, No.-3, March (2022) pp 41-63. 10.26782/jmcms.2022.03.00006
XVIII. Prabir Chandra Bhattacharyya. : “A NOVEL METHOD TO FIND THE EQUATION OF CIRCLES”. J. Mech. Cont. & Math. Sci., Vol.-17, No.- 6, June (2022). pp 31-56. 10.26782/jmcms.2022.06.00004
XIX. Prabir Chandra Bhattacharyya, : “AN OPENING OF A NEW HORIZON IN THE THEORY OF QUADRATIC EQUATION: PURE AND PSEUDO QUADRATIC EQUATION – A NEW CONCEPT”. J. Mech. Cont. & Math. Sci., Vol.-17, No.-11, November (2022). pp 1-25. 10.26782/jmcms.2022.11.00001
XX. Prabir Chandra Bhattacharyya, : “A NOVEL CONCEPT FOR FINDING THE FUNDAMENTAL RELATIONS BETWEEN STREAM
FUNCTION AND VELOCITY POTENTIAL IN REAL NUMBERS IN TWO-DIMENSIONAL FLUID MOTIONS”. J. Mech. Cont. & Math. Sci., Vol.-18, No.-02, February (2023) pp 1-19. 10.26782/jmcms.2023.02.00001
XXI. Prabir Chandra Bhattacharyya, : “A NEW CONCEPT OF THE EXTENDED FORM OF PYTHAGORAS THEOREM”. J. Mech. Cont. & Math. Sci., Vol.-18, No.-04, April (2023) pp 46-56. 10.26782/jmcms.2023.04.00004.
XXII. Prabir Chandra Bhattacharyya, A NEW CONCEPT TO PROVE, √− 1 = −𝟏 IN BOTH GEOMETRIC AND ALGEBRAIC METHODS WITHOUT USING THE CONCEPT OF IMAGINARY NUMBERS. J. Mech. Cont. & Math. Sci., Vol.-18, No.-9, September (2023) pp 20-43
XXIII. Sánchez, J. A. M. Investigaciones en clase de matemáticas con Geo Gebra, jornades d’Educació Matemàtica de la Comunittat Valenciana: Innovació i tecnologia en educació matemàtica. Instituto de Ciencias de la Educación, 2019.
XXIV. Sandoval-Hernandez, M. A., Alvarez-Gasca, O., Contreras-Hernandez, A. D., Pretelin-Canela, J. E., Palma-Grayeb, B. E., Jimenez-Fernandez, V. M., and Vazquez-Leal, H. Exploring the classic perturbation method for obtaining single and multiple solutions of nonlinear algebraic problems with application to microelectronic circuits. International Journal of Engineering Research & Technology, 8(9), p. 636-645, 2019.
XXV. Sandoval-Hernandez, M. A., Vazquez-Leal, H., Filobello-Nino, U., and Hernandez-Martinez, L., New handy and accurate approximation for the Gaussian integrals with applications to science and engineering. Open Mathematics, 17(1), p. 1774-1793, 2019.
XXVI. S. Mahmud, (2019). : “Calculating the area of the Trapezium by Using the Length of the Non Parallel Sides: A New Formula for Calculating the area of Trapezium”. International Journal of Scientific and Innovative Mathematical Research. volume 7, issue 4, pp. 25-27. 10.20431/2347- 3142.0704004
XXVII. T. A. Sarasvati Amma, : “Geometry in Ancient and Medieval India”. Pp. – 17. Motilal Banarasidass Publishers Pvt. Ltd. Delhi.
XXVIII. T. A. Sarasvati Amma, : “Geometry in Ancient and Medieval India”. pp. – 219. Motilal Banarasidass Publishers Pvt. Ltd. Delhi.
XXIX. Vazquez-Leal, H., Sandoval-Hernandez, M. A., Garcia-Gervacio, J. L. , Herrera-May, A. L. and Filobello-Nino, U. A., PSEM Aproximations for Both Branches of Lambert W with Applications. Discrete Dynamics in Nature ans Society, Hindawi, 2019, 15 pages, 2019.
XXX. William Robert. An Overview of Number System. RRJSMS| Volume 8 | Issue 4 |April, 2022. 10.4172/ J Stats Math Sci.8.4.002.