1 / 20

# Magic Squares - PowerPoint PPT Presentation

Magic Squares!!!. By John Burton. What Are Magic Squares?. A Magic Square is a grid (or matrix) containing numbers from 1 to n (where n is any number), and where every row, column and diagonal adds to the same number The most basic example is the 1 x 1 square, shown below.

Related searches for Magic Squares

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Magic Squares' - RexAlvis

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Magic Squares!!!

By John Burton

A Magic Square is a grid (or matrix) containing numbers from 1 to n (where n is any number), and where every row, column and diagonal adds to the same number

The most basic example is the 1 x 1 square, shown below

One of the most famous magic squares is that of Albrecht Dürer. It was created in 1514 and is shown below

16

3

2

13

5

10

11

8

9

6

7

12

4

15

14

1

Dürers Square

As you can see from the square, the total of each row, column, diagonal and small square is 34.

You can also see that the year it was made (1514) appears in the square

Here is the year

8

1

6

The total for each row, column etc. is 15

3

5

7

4

9

2

The total for each row, column here is 50

Magic squares can be made to work in several ways. A 3x3 magic square is made in a different way to a 4x4 magic square

For example, magic squares can be constructed in the following way:

To construct 4 x 4 magic squares, we need the following basic squares:

These squares identify where the numbers (these can be any numbers) go

B1

B2

B3

B4

B5

B6

B7

From these squares, (any) numbers are chosen and put into the following formula:

9B1+7B2+6B3+7B4-B5+2B6+3B7

The numbers are then put into a magic square, corresponding with were the 1s’ are, in the above basic squares

Constructing the Dürer magic square

Start in the bottom right corner of the grid, and count along, but only put the numbers you count on the diagonal lines.

i.e. follow the path marked out below, putting numbers on the diagonals

16

13

10

11

6

7

4

1

As you can see, these numbers lie on the diagonal lines

Constructing the Dürer magic square 2

Next, starting at the bottom left, count backwards from 16, putting the numbers in the blank spaces.

16

13

3

2

5

10

11

8

6

7

9

12

4

1

15

14

Constructing the Dürer magic square 3

As you can see, the Dürer magic square has now been constructed

16

3

2

13

5

10

11

8

9

6

7

12

4

15

14

1

To find out what the magic total is, we can use a formula, which will tell us the total of the rows, columns, diagonals etc.

The formula is ½n(n²+1)

Where n is the number of rows

To derive the formula for the magic square, we must first assign the magic total. Let’s call this x.

We must then assign the number of rows (i.e. the size of the square). As you may have gathered, this will be called n

We can write this out as

1+2+3+4+…+n²=n.x

From Pure maths, this can be written as:

n^2

=

n.x

i=1

From pure maths, we know that the formula for this series is:

n.x= ½n²(n²+1)

We then divide both sides by n, to get:

x= ½n(n²+1)

This formula only works for magic squares, which contain integers (i.e. whole numbers, no decimals)

My own magic square

http://digilander.libero.it/ice00/magic/general/MagicSquare.html

http://www.mrexcel.com/tip069.shtml

http://www.MarkFarrar.co.uk/msqhst01.htm

Aside from magic squares, there are also a number of magic shapes you could go onto study

• Magic cubes

• Magic stars

• Magic circles

• Magic word squares

The list goes on!!!