Beautiful Mathematical Patterns

I once wrote those down in the corner of a notebook. I don’t even remember when or where I first discovered them.

Today I tried to google them in order to figure out whether they had a dedicated name and if I could find more. I was rather surprised to discover they often come with religious references…

Anyways, here they are:

• 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

• 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

• 3 x 37 = 111
  6 x 37 = 222
  9 x 37 = 333
  12 x 37 = 444
  15 x 37 = 555
  18 x 37 = 666
  21 x 37 = 777
  24 x 37 = 888
  27 x 37 = 999