AN ESTIMATOR OF MOMENT OF INERTIA OF MAGIC SQUARE ARRAY OF MASSES

Authors

  • Babangida Ibrahim Babura
    Federal University Dutse image/svg+xml
  • Aliyu Ibrahim Kiri
    Departmentt of Mathematics, Bayero University Kano
  • Aminu Tukur Muhammad
    Department of Science Laboratory Technology, College of Science and Technology, Jigawa State Polytechnic, Dutse Jigawa State, Nigeria

Keywords:

Magic square, moment of inertia, kinetic energy, axis

Abstract

The classical definition of magic square of order  is a square array of consecutive natural numbers from 1 to  such that the raw, column and diagonal sum add up to the same number. When the magic square entries are considered as an array of masses of a rigid body, it is established that its moment of inertia is a function of  This work consider a more general magic array of masses of a rigid body to establish its inertial moment as a function of the magic sum and the central entry of the array. The paper further discusses the advantage of this development.

Dimensions

Cross, D. C. (1966). 3149. The Magic of Squares. The Mathematical Gazette, 50(372), 173. https://doi.org/10.2307/3611960

Eperson, D. B. (1962). 3026. Magic Squares. The Mathematical Gazette, 46(357), 219. https://doi.org/10.2307/3614021

Holmes, R. (1970). 230. The Magic Magic Square. The Mathematical Gazette, 54(390), 376. https://doi.org/10.2307/3613858

Kashimbila, M. (2003). Principles of Mechanics for Scientists and Engineers.

Loly, P. (2004). 88.30 The invariance of the moment of inertia of magic squares. The Mathematical Gazette, 88(511), 151–153. https://doi.org/10.1017/S002555720017456X

Martin, R. J. (2014). Magic Square Designs. In Wiley StatsRef: Statistics Reference Online. https://doi.org/10.1002/9781118445112.stat05050

Mayoral, F. (1996). Semi-Magic Squares and Their Orthogonal Complements. The Mathematical Gazette, 80(488), 308. https://doi.org/10.2307/3619564

Ward, J. E. (1980). Vector Spaces of Magic Squares. Mathematics Magazine, 53(2), 108. https://doi.org/10.2307/2689960

Published

02-11-2022

How to Cite

AN ESTIMATOR OF MOMENT OF INERTIA OF MAGIC SQUARE ARRAY OF MASSES. (2022). FUDMA JOURNAL OF SCIENCES, 6(5), 66-70. https://doi.org/10.33003/fjs-2022-0605-997

Issue

Vol. 6 No. 5 (2022): FUDMA Journal of Sciences - Vol. 6 No. 5

Section

Research Articles
Copyright & Licensing

FUDMA Journal of Sciences

How to Cite

AN ESTIMATOR OF MOMENT OF INERTIA OF MAGIC SQUARE ARRAY OF MASSES. (2022). FUDMA JOURNAL OF SCIENCES, 6(5), 66-70. https://doi.org/10.33003/fjs-2022-0605-997