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

5 +1 0 + 1 1 + 8 = 3 4

9 + 6 + 7 + 1 2 = 3 4

4 + 15 + 14 + 1 = 3 4

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343434 34

= 1 6 + 1 0 + 7 + 1

1 3 + 1 1

+ 6 + 4 = 3 4

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

When n is a doubly even order

When n is an even but bot doubly even

For a nn magic square

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.

• 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.

No example!!! , example is your homework

Magic Square and Cipher

S O E U

A T

U N

C S A S

V U N J

J E O V

A S

A N

C T U S

U N U S

JeovaSanctusUnus

IsaacusNeutonuus!

Some interesting facts you don’t knowGraph 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/10001.4-8.shtml

• http://www.math.wichita.edu/~richardson/mathematics/magic%20squares/even-ordermagicsquares.html

• http://www.murderousmaths.co.uk/books/bkmm1x5s.htm

• Wiki！！！

Q&A Time

• Thanks for watching!