Magic Square

1. Magic Square Lihui Mao

3. 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.

4. magic constant • The constant that is the sum of every row, column and diagonal is called the magic constant or magic sum

5. 5 +1 0 + 1 1 + 8 = 3 4 16 + 3 + 2 +1 3 1 3 + 1 1 + 6 + 4 = 3 4 = 1 6 + 1 0 + 7 + 1 9 + 6 + 7 + 1 2 = 3 4 4 + 15 + 14 + 1 = 3 4 34 34 34 34

6. 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???

7. magic constant • The constant that is the sum of every row, column and diagonal is called the magic constant or magic sum

8. How to make Magic Square by yourself ? When n is an odd order For a nn magic square When n is a doubly even order When n is an even but bot doubly even

9. 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

10. 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 nto 1. As shown below. Example time !

11. 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 !!!

12. 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

13. Magic Square and Cipher

16. JeovaSanctusUnus IsaacusNeutonuus!

17. Some interesting facts you don’t know Graph from Pyriamid

18. 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.

23. 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！！！

24. Q&A Time

25. Thanks for watching!