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2009•Unpublished venueRequires access

When a Magic Square Is Not Square

Seymour S Block, Santiago A Tavares

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Abstract

Abstract The magic triangle shown in Figure 6.1 is presented by Mochalov [105]. It is constructed with the numbers 1, 2, 3, ... , 9. The four magic triangles shown in Figure 6.2 are constructed with the numbers 1, 2, 3, 4, 5, and 6. Each triangle has a different magic number, as can be verified by adding each number along each side of each triangle. When is a square nota square? When itis a rectangle? After all, a rectangle is a square that has grown too much in one dimension. If we can have magic squares, why notmagic rectangles? A magic rectangle is defined as an array of rc integers, where r is the number of rows and c the number of columns, with the following properties (Jelliss [103], Nakamura [106]):

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What this paper is about

Abstract The magic triangle shown in Figure 6.1 is presented by Mochalov [105]. It is constructed with the numbers 1, 2, 3, ... , 9. The four magic triangles shown in Figure 6.2 are constructed with the numbers 1, 2, 3, 4, 5, and 6. Each triangle has a different magic number, as can be verified by adding each number along each side of each triangle. When is a square nota square? When itis a rectangle? After all, a rectangle is a square that has grown too much in one dimension. If we can have magic squares, why notmagic rectangles? A magic rectangle is defined as an array of rc integers, where r is the number of rows and c the number of columns, with the following properties (Jelliss [103], Nakamura [106]):

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Available abstract

Abstract The magic triangle shown in Figure 6.1 is presented by Mochalov [105]. It is constructed with the numbers 1, 2, 3, ... , 9. The four magic triangles shown in Figure 6.2 are constructed with the numbers 1, 2, 3, 4, 5, and 6. Each triangle has a different magic number, as can be verified by adding each number along each side of each triangle. When is a square nota square? When itis a rectangle? After all, a rectangle is a square that has grown too much in one dimension. If we can have magic squares, why notmagic rectangles? A magic rectangle is defined as an array of rc integers, where r is the number of rows and c the number of columns, with the following properties (Jelliss [103], Nakamura [106]):

Key concepts: Magic square, Rectangle, Square (algebra), Combinatorics, Mathematics, Row, MAGIC (telescope), Dimension (graph theory)

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