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Magic Square
Lihui Mao
Definition
• a magic square is an arrangement of distinct
numbers (i.e. each number is used once),
usually integers, in a square grid, where the
numbers in each row, and in each column, and
the numbers in the forward and backward
main diagonals, all add up to the same
number.
magic constant
• The constant that is the sum of every row,
column and diagonal is called the magic
constant or magic sum
16 + 3 + 2 +1 3 = 3 4
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5 +1 0 + 1 1 + 8 = 3 4
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9+6 +7+12=34
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4 + 15 + 14 + 1 = 3 4
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34 34 34 34
magic constant
• The constant that is the sum of every row,
column and diagonal is called the magic
constant or magic sum
• Q!!!: What’s the formula of magic constant???
magic constant
• The constant that is the sum of every row,
column and diagonal is called the magic
constant or magic sum
How to make Magic Square
by yourself ?
When n is an odd order
For a n×n
magic square
When n is a doubly even order
When n is an even but bot doubly even
Method for constructing a magic square of odd order
• 1. diagonally up and to the right when you
can,
2. down if you cannot.
• Example time
A method of constructing a magic square of doubly even
order
• Double even number n= 4p (e.g. 4, 8, 12),
where p is an integer.
• 1. Go left to right through the square counting
and filling in on the diagonals only.
2. Then continue by going left to right from the
top left of the table and fill in counting down from n
to 1. As shown below.
Example time !
A method of constructing a magic square of other
even order
• Double even number n= 4p+2 (e.g. 4, 8, 12),
where p is an integer and p≠ 0.
• 1. make a magic square with order n, where n = n-2,
and add every number with 2n-2
• 2. fill the rest grid with the rest number
• Example time !!!
A method of constructing a magic square of other
even order
• Double even number n= 4p+2 (e.g. 4, 8, 12),
where p is an integer and p≠ 0.
No example!!! , example is your homework
Magic Square and Cipher
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JeovaSanctusUnus
IsaacusNeutonuus!
Some interesting facts you don’t know
Graph from Pyriamid
• In Dan Brown’s the Lost Symbol, application of
magic square means the transition from chaos
to order. In other words, number every
elements in grids with Franklin’s Square, and
come out with the graph after ordering them,
in order to make disordered graphs
meaningful.
Reference
• http://www.math.hmc.edu/funfacts/ffiles/100
01.4-8.shtml
• http://www.math.wichita.edu/~richardson/m
athematics/magic%20squares/evenordermagicsquares.html
• http://www.murderousmaths.co.uk/books/bk
mm1x5s.htm
• Wiki！！！
Q&A Time
• Thanks for watching!