A new class of pandiagonal squares

Loly, P. D.; Steeds, M. J.

doi:10.1080/00207390512331325950

Cited by 4 publications

(2 citation statements)

References 7 publications

(12 reference statements)

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“…The Square Tool can create non-Magic Squares, since the diagonals, horizontals, or verticals are not necessarily equal to one another. Loly and Steeds (2005) [7] says that there are an interesting class of purely pandiagonal, i.e. non-magic squares, counting number squares of orders (row / column dimension) that exist and many patterns can be discovered while observing them.…”

Section: Connections To Magic Squaresmentioning

confidence: 99%

Investigating Numeric Relationships Using an Interactive Tool: Covering Number Sense Concepts for the Middle Grades

Su¹,

Marinas²,

Furner³

2010

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This article investigates intriguing number patterns utilizing an emerging technology called the Square Tool. Middle School math teachers will find the Square Tool useful in making connections and bridging the gap from the concrete to the abstract. Pattern recognition helps students discover mathematical concepts. With the development of puzzles, games, and computer programs, students learn and practice the skills that are created in the mathematics classrooms. By studying patterns that exist within different number arrangements, consistencies are observed among them. Middle School students will investigate various mathematics relationships found in numbered squares including multiples, factors, ratios of comparative numbers, and other mathematical concepts

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Section: Connections To Magic Squaresmentioning

confidence: 99%

Investigating Numeric Relationships Using an Interactive Tool: Covering Number Sense Concepts for the Middle Grades

Su¹,

Marinas²,

Furner³

2010

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“…In pandiagonal squares, the broken diagonals (n consecutive elements parallel to the main diagonals under tiling as indicated below) have the same sum as the main diagonals, but need not even be semi-magic squares (Loly & Steeds 2005).…”

Section: ð1:1þmentioning

confidence: 99%

Enumerating the bent diagonal squares of Dr Benjamin Franklin FRS

2006

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All 8th order Franklin bent diagonal squares with distinct elements 1, …, 64 have been constructed by an exact backtracking method. Our count of 1, 105, 920 dramatically increases the handful of known examples, and is some eight orders of magnitude less than a recent upper bound. Exactly one-third of these squares are pandiagonal, and therefore magic. Moreover, these pandiagonal Franklin squares have the same population count as the eighth order ‘complete’, or ‘most-perfect pandiagonal magic’, squares. However, while distinct, both types of squares are related by a simple transformation. The situation for other orders is also discussed.

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