Surprising Number Patterns

Dear my lovely students,

What do you feel about mathematics? Do you think that mathematics is difficult? Why?

Meanwhile, maybe, some students say that mathematics is fun.

Well…..

I think we have to appreciate all the opinions. But, now, I will show that mathematics is fun. I have some amazing with mathematics. And I hope it will change all the frights to the full of fun.

Actually, there are times/multiplications 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. Let you appreciate the patterns and, if possible, try to look for an “explanation” for this. Most important is that you can get an appreciation for the beauty in these number patterns.

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

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

Well…..

What do you say about the patterns above? I think it will be better if you would like to give some comments, ok?