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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:appearsIn
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gptkb:religious_art
gptkb:Western_mathematics
gptkb:Albrecht_Dürer's_Melencolia_I
gptkb:Ancient_Chinese_mathematics
gptkb:Chinese_legend_of_the_Lo_Shu_turtle
gptkb:Indian_mathematics
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gptkbp:defines
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A square array of numbers where the sums of every row, column, and main diagonal are equal
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gptkbp:field
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gptkb:Mathematics
gptkb:Number_theory
Combinatorics
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gptkbp:generalizes
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gptkb:Associative_magic_squares
gptkb:Bimagic_squares
gptkb:Magic_hypercubes
gptkb:Multiplicative_magic_squares
gptkb:Pandiagonal_magic_squares
Magic tori
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gptkbp:historicalName
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gptkb:Ancient_China
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https://www.w3.org/2000/01/rdf-schema#label
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Magic Squares
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gptkbp:magicConstant
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The common sum of each row, column, and diagonal
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gptkbp:notableExample
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gptkb:Lo_Shu_Square
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gptkbp:notablePerson
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gptkb:Albrecht_Dürer
gptkb:Benjamin_Franklin
gptkb:Leonhard_Euler
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gptkbp:notation
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M(n) for order n magic square
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gptkbp:order
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The number of rows or columns in the square
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gptkbp:property
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Can be constructed for all n ≥ 3
Magic constant for order n: n(n^2+1)/2
Numbers are usually distinct positive integers
Order 1 magic square is trivial
Order 2 magic square does not exist
Order 3 is the smallest nontrivial magic square
Symmetric under rotation and reflection in some cases
All rows, columns, and main diagonals sum to the same value
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gptkbp:relatedTo
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gptkb:Magic_cubes
gptkb:Latin_squares
gptkb:Sudoku
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gptkbp:smallestOrder
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3
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gptkbp:studiedBy
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Mathematicians
Historians
Recreational mathematicians
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gptkbp:supportsAlgorithm
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gptkb:Siamese_method_for_odd_order
gptkb:Strachey's_method_for_doubly_even_order
gptkb:Conway's_LUX_method
gptkb:De_la_Loubère's_method
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gptkbp:symbolizes
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gptkb:spirituality
gptkb:state_order
gptkb:Harmony
Luck
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gptkbp:usedIn
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gptkb:art
gptkb:spirituality
Puzzle design
Mathematical recreation
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gptkbp:bfsParent
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gptkb:George_Widener
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gptkbp:bfsLayer
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6
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