Topic
Siamese method
About: Siamese method is a research topic. Over the lifetime, 2 publications have been published within this topic receiving 2 citations.
Papers
1 Feb 2015
TL;DR: In this article, a numerical construction of associative magic squares based on Bree's Orthogonality Criterion is presented, which replicates the known algorithms, e.g., the Siamese method and the Pyramid method.
Abstract: A magic square of order n consists of the numbers 1 to n^2 placed such that the sum of each row, column and principal diagonal equals the magic sum n(n^2 +1)/2. In addition, an odd ordered magic square is associative or self-complementary if diagonally opposite elements have the same sum (n^2 +1)/2. The magic square is said to be regular Greco-Latin if it can be decomposed as a sum of a pair of Latin squares. Here, a numerical construction of associative magic squares based on Bree's Orthogonality Criterion is presented. This construction method replicates the known algorithms, e.g., the Siamese method and the Pyramid method. Duplications are identified, and this leads to a count of the unique regular Greco-Latin associative magic squares of prime order.
1 citations
Journal Article•
TL;DR: In this paper, a goal programming model is developed to construct a magic square of any kind, which is an m x m square array of numbers consisting of the first m 2 distinct positive integers arranged such that the sum of numbers in every row, every column, and every diagonal is the same number known as the magic total (or magic constant).
Abstract: In this paper, we develop a goal programming model that can be used to construct a magic square of any kind. A magic square is an m x m square array of numbers consisting of the first m 2 distinct positive integers arranged such that the sum of numbers in every row, every column, and every diagonal is the same number known as the magic total (or magic constant). The commonly used method for constructing magic squares are the Siamese method and Lozenge method for odd order square, the LUX method for singly even order square, and the cross diagonals method for doubly even order square. None of these methods uses a mathematical formula in the construction of the magic squares but uses the rule of thumb. The model developed in this paper is tested on the 3 x 3 magic square and is found to work perfectly well.
1 citations
Performance Metrics
| Year | Papers |
|---|---|
| 2015 | 1 |
| 2013 | 1 |