In this post I am sharing with some very interesting numerical symmetries. I got it from varied sources but the most interesting is the book from Shakuntala Devi titled **Figuring: The Joy Of Numbers**. It’s a must read for all math lovers.

So here you go –

1 x 8 + 1 = 9

12 x 8 + 2 = 98

123 x 8 + 3 = 987

1234 x 8 + 4 = 9876

12345 x 8 + 5 = 98765

123456 x 8 + 6 = 987654

1234567 x 8 + 7 = 9876543

12345678 x 8 + 8 = 98765432

123456789 x 8 + 9 = 987654321

1 x 9 + 2 = 11

12 x 9 + 3 = 111

123 x 9 + 4 = 1111

1234 x 9 + 5 = 11111

12345 x 9 + 6 = 111111

123456 x 9 + 7 = 1111111

1234567 x 9 + 8 = 11111111

12345678 x 9 + 9 = 111111111

123456789 x 9 +10= 1111111111

9 x 9 + 7 = 88

98 x 9 + 6 = 888

987 x 9 + 5 = 8888

9876 x 9 + 4 = 88888

98765 x 9 + 3 = 888888

987654 x 9 + 2 = 8888888

9876543 x 9 + 1 = 88888888

98765432 x 9 + 0 = 888888888

Brilliant, isn’t it?

And look at this symmetry:

1 x 1 = 1

11 x 11 = 121

111 x 111 = 12321

1111 x 1111 = 1234321

11111 x 11111 = 123454321

111111 x 111111 = 12345654321

1111111 x 1111111 = 1234567654321

11111111 x 11111111 = 123456787654321

111111111 x 111111111 = 12345678987654321

In one of my earlier post named **cyclic number** you will find similar very interesting of numbers. Pay attention to the comments over there.

If you know of any other symmetry of numbers or any interesting fact about numbers, feel free to share in the comment

very nice post

I like it

Mathematics is Magic

good work……

keep it up……its of great help for students like me.

As desired by you I am sending hereith another set of numbers for your record.

Seven Multiplications and a bit more

1 x 7 + 3 = 10

14 x 7 + 2 = 100

142 x 7 + 6 = 1000

1428 x 7 + 4 = 10000

14285 x 7 + 5 = 100000

142857 x 7 + 1 = 1000000

1428571 x 7 + 3 = 10000000

14285714 x 7 + 2 = 100000000

142857142 x 7 + 6 = 1000000000

1428571428 x 7 + 4 = 10000000000

Thanks Kiran.

Surely thrs lot more coming up for you all.

Thanks

Vineet Patawari

Great Keep posting like these..

Learn Maths

Thanks brother

kiran