On multiplication theorems for magic squares
In this paper, we present, prove, and illustrate a Composition Theorem for Magic Squares.Let M and N be magic squares of orders p and q, respectively. For k = 1,2..., q2, letMk = M + (k - 1) p2 Jpwhere Jp = p x p matrix of all 1's. Form the array Nm of order pq obtained by replacing each entry...
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| Main Authors: | , |
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| Format: | text |
| Language: | English |
| Published: |
Animo Repository
1995
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| Subjects: | |
| Online Access: | https://animorepository.dlsu.edu.ph/etd_bachelors/16240 |
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| Institution: | De La Salle University |
| Language: | English |
| Summary: | In this paper, we present, prove, and illustrate a Composition Theorem for Magic Squares.Let M and N be magic squares of orders p and q, respectively. For k = 1,2..., q2, letMk = M + (k - 1) p2 Jpwhere Jp = p x p matrix of all 1's. Form the array Nm of order pq obtained by replacing each entry of N by Mk. Then Nm is a magic square of order pq.Using this composition theorem, we can compose the approximate magic square N = 14 32 with anu p x p matrix M to form a magic square of order 2p. |
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