Magic Square for odd n.pptx

Its the explanation for magic square

1. nxn Magic square for odd n Programming to create interesting Mathematical objects Programming topics for first year students Program in Scribble by creating 2D Arrays

2. row sum= column sum = diagonal sum=15 row sum= column sum = diagonal sum=65 How do we create?. Magic squares

3. 1 N=5 Fill in middle cell of the top row. Move towards right diagonal. We cross the grid 1 2 If we cross top boundary , go down to the column and fill in next number Rule 1

4. 1 3 2 Move towards right diagonal. It is unfilled . Fill it with 3 1 4 3 2 Move towards right diagonal. Boundary crossed. Go to left most cell Rule 2

5. 1 5 4 3 2 1 5 4 6 3 2 Already Filled Retrace and go down by one cell Rule 3

6. 1 5 7 4 6 3 2 1 8 5 7 4 6 3 2

7. 1 8 5 7 4 6 3 9 2 1 8 5 7 4 6 10 3 9 2

8. 1 8 5 7 4 6 10 3 11 9 2 Rule 3 15 1 8 5 16 7 14 4 6 13 10 12 3 11 9 2 Rule 4 Special rule for right top corner cell

9. 17 15 1 8 5 16 7 14 4 6 13 10 12 3 11 18 9 2 17 15 1 8 5 16 7 14 4 6 13 20 10 12 3 19 11 18 9 2

10. 17 15 1 8 5 16 7 14 4 6 13 20 10 12 3 19 21 11 18 9 2 17 15 1 8 5 16 7 14 4 6 22 13 20 10 12 3 19 21 11 18 9 2 Rule 3

11. 17 24 15 1 8 23 5 16 7 14 4 6 22 13 20 10 12 3 19 21 11 18 9 25 2

12. clear all % Fill in a odd magic squre from 1 to N^2 % In general numbers must form an Arithmetic %Progression N=7; % N must be odd A=zeros(N,N); j=1+(N-1)/2 ; % fill centre cell in the first row i =1; A( i,j )=1 for K=2:N*N i =i-1; j=j+1; % Advance towards right diagonal % putback into the matrix if gone out if and( i <1, j==N+1) i =2; j=N; end if and (j<=N , i <1) i =N; end if and ( i >0 , j>N) j=1; end if A( i,j )~=0 i =i+2; j=j-1 ; end A( i,j )=K; end A

13. How to create 4x4 magic square How to create mxm magic square where m =‘odd number’x2 3. What is determinant of odd magic squares (in relation to the magic sum and why?.) 4. What is so special about Ramanujan’s 4x4 magic square Investigate

14. Recreational mathematics Magic Square by Ramanujan

15. Magic Square by Srinivasa Ramanujan 22/12/1887 is his date of birth. See the top row Each column/sum is 139 Both Diagonal sum is 139

16. Corner sum is 139 Blue colour number sum is 139 Pink colour number sum is 139 Blue colour sum is 139 Orange colour sum is 139 Pea Green colour sum is 139 All same colour sum is 139 Blue colour sum is 139 Dark green colour sum is 139

17. Create one each with Your Date of birth How to create. See the next slide