 by Joanna Hung

# some research on MATHEMATICS

(for Primary Students or above)

The following table shows the square of a sequence of consecutive numbers. You can find that there is an interesting recurring pattern of the last digit of the product, i.e. 0,1,4,9,6,5,6,9,4,1.

Do you know why? Think about it and I am sure that you can find out the answer easily.

 0 X 0 = 0 1 X 1 = 1 2 X 2 = 4 3 X 3 = 9 4 X 4 = 16 5 X 5 = 25 6 X 6 = 36 7 X 7 = 49 8 X 8 = 64 9 X 9 = 81 10 X 10 = 100 11 X 11 = 121 12 X 12 = 144 13 X 13 = 169 14 X 14 = 196 15 X 15 = 225 16 X 16 = 256 17 X 17 = 289 18 X 18 = 324 19 X 19 = 361 20 X 20 = 400 21 X 21 = 441 22 X 22 = 484 23 X 23 = 529 24 X 24 = 576 25 X 25 = 625 26 X 26 = 676 27 X 27 = 729 28 X 28 = 784 29 X 29 = 841 30 X 30 = 900 31 X 31 = 961 32 X 32 = 1024 33 X 33 = 1089 34 X 34 = 1156 35 X 35 = 1225 36 X 36 = 1296 37 X 37 = 1369 38 X 38 = 1444 39 X 39 = 1521 40 X 40 = 1600 41 X 41 = 1681 42 X 42 = 1764 43 X 43 = 1849 44 X 44 = 1936 45 X 45 = 2025 46 X 46 = 2116 47 X 47 = 2209 48 X 48 = 2304 49 X 49 = 2401 50 X 50 = 2500 51 X 51 = 2601 52 X 52 = 2704 53 X 53 = 2809 54 X 54 = 2916 55 X 55 = 3025 56 X 56 = 3136 57 X 57 = 3249 58 X 58 = 3364 59 X 59 = 3481

23 JANUARY, 1999

Please click to see the comment and relationship with magic square. What has been will be again, what has been done will be done again; there is nothing new under the sun.--Ecclesiastes 1:9 