Konstruksi Persegi Ajaib dengan Entri Bilangan Bulat

Authors

DOI:

https://doi.org/10.26594/jmpm.v6i2.2228

Keywords:

Algoritma, Bilangan Bulat, Persegi Ajaib

Abstract

Persegi ajaib adalah kotak-kotak persegi berisi bilangan berbeda yang disusun sedemikian rupa sehingga jumlah bilangan-bilangan pada baris, kolom, dan diagonal adalah sama. Penelitian ini membahas tentang pola dan algoritma untuk menyusun persegi ajaib berukuran m x m dari rangkaian m^2 bilangan bulat berurutan. Konstruksi algoritma dibagi menjadi tiga kasus, yaitu: algoritma persegi ajaib ordo ganjil (2j + 1) x (2j + 1), algoritma persegi ajaib ordo genap (4j) x (4j), dan algoritma persegi ajaib ordo genap (4j + 2) x (4j + 2) dengan j = 1, 2, ..., m.

Author Biographies

Ulil Albab Mu'min, Institut Pertanian Bogor

Sekolah Pascasarjana Jurusan Matematika Terapan Institut Pertanian Bogor

Bib Paruhum Silalahi, Institut Pertanian Bogor

Department of Mathematics, IPB University

Dr. Ir. Bib Paruhum Silalahi, M.Kom

References

Adetokunbo, P., Al-Shuhail, A. A., & Al-Dossary, S. (2016). 3D Seismic Edge Detection Using Magic Squares and Cubes. Interpretation, 4(3), T271–T280.

Andrews, W. S. (1917). Magic Squares and Cubes. USA: Open Court Publishing.

Ashhab, S. (2012). Special Magic Squares of Order Six and Eight. International Journal of Digital Information and Wireless Communications, 1(4), 769–781.

Baksalary, O. M., Trenkler, D., & Trenkler, G. (2018). On Most Perfect Magic Square of Order Four. Linear and Multilinear Algebra, 1–13.

Berndt, B. C., & Brualdi, R. A. (2010). Introductory Combinatorics. Beijing: China Machine Press.

Dean, A. (2017). The Magic Square of Olocin Ozzaniugnas. Early Music, 45(4), 599–611.

Gafoor, K. A., & Kurukkan, A. (2015). Why High School Students Feel Mathematics Difficult? An Exploration of Affective Beliefs. UGC Sponsored National Seminar on Pedagogy of Teacher Education Trends and Challenges, 1–6.

Gupta, B. (2019). Algorithm for Doubly Even Magic Square. International Advanced Research Journal in Science, Engineering and Technology, 6(3), 112–117.

Kislenko, K., Grevholm, B., & Lepik, M. (2007). “Mathematics is Important but Boring”: Students Beliefs and Attitudes Towards Mathematics. Mathematics Educational Research Journal., 11(1), 39–53.

Kunwar, R. (2020). Math mania : Meaning , Problems and Ways of Effective Teaching and Learning Mathematics at Basic Level Education in Nepal. International Journal of Science and Research, 9(8), 1136–1141.

Namakshi, N., Bhattacharyya, S., Starkey, C., & Linker, J. M. (2015). Mystical Magic Square. National Council of Teachers of Mathematics, 20(6), 372–377.

Sahni, M., & Ojha, D. B. (2012). Magic Square and Cryptography. Journal of Global Research in Computer Science, 3(12), 15–17.

Sallows, L. (2011). Geometric Magic Squares. The Mathematical Intelligencer, 33(4), 25–31. https://doi.org/10.1007/s00283-011-9229-0

Sesiano, J. (2019). Magic Squares: Their History and Construction from Ancient Times to AD 1600. Geneva: Springer.

Wallis, W. D., & George, J. C. (2017). Introduction to Combinatorics. London: CRC Press.

Downloads

Published

2021-09-15