有趣的数学现象

作者：HF 发布会员：lan 版权：原创 发表日期：2011-4-10 阅读：2015次

有趣的数学现象

1×8 + 1= 9
12×8 + 2= 98
123×8 + 3= 987
1234×8 + 4= 9876
12345×8 + 5= 98765
123456×8 + 6= 987654
1234567×8 + 7= 9876543
12345678×8 + 8= 98765432
123456789×8 + 9= 987654321


1×9 + 2= 11
12×9 + 3= 111
123×9 + 4= 1111
1234×9 + 5= 11111
12345×9 + 6= 111111
123456×9 + 7= 1111111
1234567×9 + 8= 11111111
12345678×9 + 9= 111111111
123456789×9 +10= 1111111111


9×9 + 7= 88
98×9 + 6= 888
987×9 + 5= 8888
9876×9 + 4= 88888
98765×9 + 3= 888888
987654×9 + 2= 8888888
9876543×9 + 1= 88888888
98765432×9 + 0= 888888888


1×1= 1
11×11= 121
111×111= 12321
1111×1111= 1234321
11111×11111= 123454321
111111×111111= 12345654321
1111111×1111111= 1234567654321
11111111×11111111= 123456787654321
111111111×111111111=12345678987654321

 

      9 × 9 ＋ 7 = 88
      98 × 9 ＋ 6 = 888
      987 × 9 ＋ 5 = 8888
      9876 × 9 ＋ 4 = 88888
      98765 × 9 ＋ 3 = 888888
      987654 × 9 ＋ 2 = 8888888
      9876543 × 9 ＋ 1 = 88888888
      98765432 × 9 ＋ 0 = 888888888

 

      12345679 × 9  (9×1) = 111111111
      12345679 × 18 (9×2) = 222222222
      12345679 × 27 (9×3) = 333333333
      12345679 × 36 (9×4) = 444444444
      12345679 × 45 (9×5) = 555555555
      12345679 × 54 (9×6) = 666666666
      12345679 × 63 (9×7) = 777777777
      12345679 × 72 (9×8) = 888888888
      12345679 × 81 (9×9) = 999999999

 

      9 × 1  = 9   | 9 ＋ 0 = 0
      9 × 2  = 18  | 1 ＋ 8 = 9
      9 × 3  = 27  | 2 ＋ 7 = 9
      9 × 4  = 36  | 3 ＋ 6 = 9
      9 × 5  = 45  | 4 ＋ 5 = 9
      9 × 6  = 54  | 5 ＋ 4 = 9
      9 × 7  = 63  | 6 ＋ 3 = 9
      9 × 8  = 72  | 7 ＋ 2 = 9
      9 × 9  = 81  | 8 ＋ 1 = 9
      9 × 10 = 90  | 9 ＋ 0 = 9

 

      1 = 1^2
      1 + 3 = 4 = 2^2
      1 + 3 + 5 = 9 = 3^2
      1 + 3 + 5 + 7 = 16 = 4^2
      1 + 3 + 5 + 7 + 9 = 25 = 5^2
      1 + 3 + 5 + 7 + 9 + 11 = 36 = 6^2
      1 + 3 + 5 + 7 + 9 + 11 + 13 = 49 = 7^2

 

      142857·1 = 142857
      142857·2 = 285714
      142857·3 = 428571
      142857·4 = 571428
      142857·5 = 714285
      142857·6 = 857142

 

      142 + 857 = 999
      285 + 714 = 999
      428 + 571 = 999
      571 + 428 = 999
      714 + 285 = 999
      857 + 142 = 999

 

      14 + 28 + 57 = 99
      28 + 57 + 14 = 99
      42 + 85 + 71 = 99 + 99
      57 + 14 + 28 = 99
      71 + 42 + 85 = 99 + 99
      85 + 71 + 42 = 99 + 99

 

      1·7 + 3 = 10
      14·7 + 2 = 100
      142·7 + 6 = 1000
      1428·7 + 4 = 10000
      14285·7 + 5 = 100000
      142857·7 + 1 = 1000000
      1428571·7 + 3 = 10000000
      14285714·7 + 2 = 100000000
      142857142·7 + 6 = 1000000000
      1428571428·7 + 4 = 10000000000
      14285714285·7 + 5 = 100000000000
      142857142857·7 + 1 = 1000000000000
      1428571428571·7 + 3 = 10000000000000
      14285714285714·7 + 2 = 100000000000000
      142857142857142·7 + 6 = 1000000000000000
      1428571428571428·7 + 4 = 10000000000000000
      14285714285714285·7 + 5 = 100000000000000000
      142857142857142857·7 + 1 = 1000000000000000000

 

      3 2 6 + 4 5 1 = 7 7 7
      2 6 4 + 5 1 3 = 7 7 7
      6 4 5 + 1 3 2 = 7 7 7
      + + + + + +
      4 5 1 + 3 2 6 = 7 7 7
      5 1 3 + 2 6 4 = 7 7 7
      1 3 2 + 6 4 5 = 7 7 7

      3 2 6 + 4 5 1 = 7 7 7
      2 6 4 + 5 1 3 = 7 7 7
      6 4 5 + 1 3 2 = 7 7 7
      + + + + + +
      4 5 1 + 3 2 6 = 7 7 7
      5 1 3 + 2 6 4 = 7 7 7
      1 3 2 + 6 4 5 = 7 7 7
      = = = =
      7 7 7 7 7 7
      7 7 7 7 7 7
      7 7 7 7 7 7

 

      12345679×12=148148148
      12345679×15=185185185
      12345679×57=703703703

 

      12345679×10＝123456790 lose 8
      12345679×11＝135802469 lose 7
      12345679×13＝160493827 lose 5
      12345679×14＝172839506 lose 4
      12345679×16＝197530864 lose 2
      12345679×17＝209876543 lose 1

 

      12345679×243＝2999999997 2+7=9

 

      12345679×28＝345679012
      12345679×37＝456790123