There are times when the charm of mathematics lies in the surprising nature of its number system. There are not many words needed to demonstrate this charm. It is obvious from the patterns attained. Look, enjoy, and spread these amazing properties to your students. Let them appreciate the patterns and, if possible, try to look for an “explanation” for this. Most important is that the students can get an appreciation for the beauty in these number patterns.

NB:
denote multiplication sign
1
1 = 1
11
11 = 121
111
111 = 12
321
1
111
1
111 = 1
234
321
11
111
11
111 = 123
454
321
111
111
111
111 = 12
345
654
321
1
111
111
1
111
111 = 1
234
567
654
321
11
111
111
11
111
111 = 123
456
787
654
321
111
111
111
111
111
111 = 12
345
678
987
654
321
The Beauty in Numbers 3
1
8 + 1 = 9
12
8 + 2 = 98
123
8 + 3 = 987
1
234
8 + 4 = 9
876
12
345
8 + 5 = 98
765
123
456
8 + 6 = 987
654
1
234
567
8 + 7 = 9
876
543
12
345
678
8 + 8 = 98
765
432
123
456
789
8 + 9 = 987
654
321
Notice (below) how various products of 76,923 yield numbers in the same
order but with a different starting point. Here the first digit of the product
goes to the end of the number to form the next product. Otherwise, the
order of the digits is intact.
76
923
1 = 076
923
76
923
10 = 769
230
76
923
9 = 692
307
76
923
12 = 923
076
76
923
3 = 230
769
76
923
4 = 307
692
Notice (below) how various products of 76,923 yield different numbers
from those above, yet again, in the same order but with a different starting
point. Again, the first digit of the product goes to the end of the number
to form the next product. Otherwise, the order of the digits is intact.
76
923
2 = 153
846
76
923
7 = 538
461
76
923
5 = 384
615
76
923
11 = 846
153
76
923
6 = 461
538
76
923
8 = 615
384
Another peculiar number is 142,857. When it is multiplied by the numbers
2 through 8, the results are astonishing. Consider the following products
and describe the peculiarity.
4 Math Wonders