Mathematics Dictionary
Sample of Magic Square
Magic Squre : Use number 1 to 16 to make a magic square
Following procedures are based on a Chinese Poiem. The first use of the magic square in the West was the magic square of order 4 shown in the Duerer's Malancholia (The British Museum) In 1514. Magic square in order 3 or 5 or 7 can be found in Computer Mathematics by Dr K. G. Shih. It also given in MD2002 program 01 10.
Step 1 :
Arrange the number as shown in this Figure.
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
16 2 3 4
5 6 7 8
9 10 11 12
13 14 15 1
Step 2 :
Exchange the top left corner number 1 with bottom right corner number 16 as shown in this figure
Step 3 :
Exchange the top right corner number 4 with bottom leftt corner number 13 as shown in this figure
16 2 3 13
5 6 7 8
9 10 11 12
4 14 15 1
16 2 3 13
5 11 7 8
9 10 6 12
4 14 15 1
Step 4 :
Exchange inner top left corner number 6 with inner bottom right corner number 11 as shown in this figure
Step 5 :
Exchange inner bottom left corner number 10 with inner top left corner number 7 as shown in this figure. Now the sum of each row or each column or each diagonal will be the same. The sum of the elements in any row of in any column or in any digonal is 34. This magic pattern is given in MD2002 program 11 08.
16 2 3 13
5 11 10 8
9 7 6 12
4 14 15 1
Reference

  • On internet : Magic circle - Use 1 to 33 to make 4 circles and 4 diameters
  • MD2002 : Magic square of order 7 - Program 01 10
  • MD2002 : Magic square of order 4 - Program 11 08
Show Room of MD2002 Contact Dr. Shih Math Examples Room
Copyright © Dr. K. G. Shih. Nova Scotia, Canada.
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