Part 2: Structure of number Pi

Here we have calculated, how often the figures 0 to 9 occur in the number Pi, if we increase the number of positions in Pi always by a factor 10.

That means, we start with 10 positions, then we take 100 up to

The table had to be divided into 2 parts.

  • In the first row the figures 0 to 9 are shown.
  • In the first column of the first part is shown, how many positions of Pi are calculated.
  • In the table is then shown, how often a figure is contained in Pi
  • in the last row each column is summed up 10 million positions

Results:

  • We see, that the 4 is most often contained in Pi
  • 2 and 3 occur each 103 times up to position 1000
  • 2 and 6 occur each 1021 up to position 10 000
  • 3 and 4 occur each 100230 up to position 10 000 000

Is that just a chance  or a hint, that there exists a structure in Pi, which we can describe with a mathematical equation ?

These results may change, if we increase the number of positions, which we take into account.

part 1 of table

 positions 0 1 2 3 4
10 2 1 2 1
100 8 8 12 12 10
1000 93 116 103 103 93
10000 968 1026 1021 975 1012
100000 9999 10137 9908 10026 9971
1000000 99959 99757 100026 100230 100230
10000000 999440 999333 1000306 999965 1001093
Sum 1110467 1110379 1111377 1111313 1112410

part  2 of table should be added to the right side of part 1

5 6 7 8 9
2 1 1
8 9 7 13 13
97 94 95 100 106
1046 1021 969 948 1014
10026 10028 10025 9978 9902
100359 99548 99800 99985 100106
1000466 999337 1000206 999814 1000040
1112004 1110038 1111102 1110838 1111182
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