Computed Tomography and Nuclear Magnetic Resonance with Mathematical Applications
Glen A. Hagemann and Joseph R. Cummins
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Lesson #3
Method B: Variation of the staircase method
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1. Place the number 1 in the box horizontally to the right of the center box.
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2. Fill in the sequence by advancing diagonally upward to the right until a number is placed outside the magic square. When a number is placed outside the magic square, place it into its corresponding position inside.
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3. When a move is blocked, place the number two boxes horizontally to the right of its predecessor.
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Although, there are 880 ways to organize the natural numbers 1 through 16 only two lesson plans are included. The other 878 can be explored on your own.
Method A:4 x 4 magic square
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1. The natural numbers 1,2,3, . . . ,16 are used in the 4 x 4 magic square.
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2. Beginning in the top left hand corner cell, place the numbers in consecutive order until all cells are filled.
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3. Leave all the numbers in their current locations except those in the corner to corner diagonals.
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4. Reverse the order of the numbers in the corner to corner diagonals.
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5. Check the sums of each row, column and corner to corner diagonal. They should all equal 34.
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Method B.: 4 x 4 magic square
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1. The natural numbers 1,2,3, . . . ,16 are used in the 4 x 4 magic square.
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2. A complement is defined as a pair of numbers that are equidistant from the center box. To determine the complement, add the first and last numbers in the sequence. ( 1 + 16 = 17 ), therefore, the complement equals seventeen.
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3. Place the natural numbers 1 through 16 in consecutive order beginning with the top left-hand corner cell.
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4. The numbers in the corner to corner diagonals remain the same but all remaining pairs of complementary numbers are to “switch” locations.
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5 Check the sums of each row column, and corner to corner diagonal. They should all equal 34.
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