Replication property for magic squares
This paper is an exposition of Daniel B. Shapiro's article A Replication Property for Magic Squares , published in Mathematics Magazine, Volume 65, Number 3, June 1992. A matrix A is said to have the Replication Property if its derived matrix A' equals a constant matrix plus a shifted vers...
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oai:animorepository.dlsu.edu.ph:etd_bachelors-170712021-12-02T04:34:08Z Replication property for magic squares Angeles, Antonio S. Ramirez, Almario D., III This paper is an exposition of Daniel B. Shapiro's article A Replication Property for Magic Squares , published in Mathematics Magazine, Volume 65, Number 3, June 1992. A matrix A is said to have the Replication Property if its derived matrix A' equals a constant matrix plus a shifted version of A. This study presents a solution in finding m x n matrices that possess the Replication Property by using the concepts of matrices, complex numbers and vector spaces. The paper also shows that any array with the replication property is a linear combination of blow-ups of certain squares of sizes 1 x 1, 3 x 3 and 12 x 12. 1999-01-01T08:00:00Z text https://animorepository.dlsu.edu.ph/etd_bachelors/16558 Bachelor's Theses English Animo Repository |
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This paper is an exposition of Daniel B. Shapiro's article A Replication Property for Magic Squares , published in Mathematics Magazine, Volume 65, Number 3, June 1992. A matrix A is said to have the Replication Property if its derived matrix A' equals a constant matrix plus a shifted version of A. This study presents a solution in finding m x n matrices that possess the Replication Property by using the concepts of matrices, complex numbers and vector spaces. The paper also shows that any array with the replication property is a linear combination of blow-ups of certain squares of sizes 1 x 1, 3 x 3 and 12 x 12. |
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text |
| author |
Angeles, Antonio S. Ramirez, Almario D., III |
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Angeles, Antonio S. Ramirez, Almario D., III Replication property for magic squares |
| author_facet |
Angeles, Antonio S. Ramirez, Almario D., III |
| author_sort |
Angeles, Antonio S. |
| title |
Replication property for magic squares |
| title_short |
Replication property for magic squares |
| title_full |
Replication property for magic squares |
| title_fullStr |
Replication property for magic squares |
| title_full_unstemmed |
Replication property for magic squares |
| title_sort |
replication property for magic squares |
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Animo Repository |
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1999 |
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https://animorepository.dlsu.edu.ph/etd_bachelors/16558 |
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1772835121060118528 |