What is 142857?

You may have noticed that my website domain contains a secret number: 142857. What does it mean?
It’s the most widely known cyclic number, which is the first six digits of the result of 1÷7, multiplied by 2,3,4,5 or 6, the answer is a cyclic permutation of itself.

For example:
1 × 142857 = 142857
2 × 142857 = 2857 14
3 × 142857 = 42857 1
4 × 142857 = 57 1428
5 × 142857 = 7 14285
6 × 142857 = 857 142
7 × 142857 = 999999

Is that amazing? And it’s not the end!

8 × 142857 = 1 14286 (Not cycle? Please notice that 1+6=7!)
9 × 142857 = 12857 13 (Again, 1+3=4)
10 × 142857 = 1428570
11 × 142857 = 157 1427
12 × 142857 = 17 14284
13 × 142857 = 1857 141
14 × 142857 = 1999998
15 × 142857 = 2 142855
16 × 142857 = 22857 12

Unfortunately, this is the end of the magic number’s journey, as 17 × 142857 = 2428569.

I learnt this interesting number from a Korean comic called “Fantasy Math War”. My parents like to buy books and encourage me to read. When they took me to Shanghai Library, I used to sit in the children’s section and watch this comic. This comic told me a lot of interesting mathematical theories and developed my interest in mathematics, I would say it helped me a lot.