Beauty of Numbers

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

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Vineet Patawari

Hi, I'm Vineet Patawari. I fell in love with numbers after being scared of them for quite some time. Now, I'm here to make you feel comfortable with numbers and help you get rid of Math Phobia!

8 thoughts to “Beauty of Numbers”

  1. 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

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