I was playing around with number strings and noticed a really strange pattern. If you break consecutive numbers into groups that grow by one each time, a math magic trick happens where Pi (π) suddenly appears.
Here is how the grid starts:
* Group 1: 1
* Group 2: 2, 3
* Group 3: 4, 5, 6
* Group 4: 7, 8, 9, 10
* ...and so on.
Let's take Group 4 (7, 8, 9, 10) as an example. The size of this group is 4 numbers.
Now, pick each number in the group and find the absolute differences between it and all the other numbers in the same group, then add those differences up:
* For 7: The differences to 8, 9, and 10 are 1, 2, and 3. (1 + 2 + 3 = 6)
* For 8: The differences to 7, 9, and 10 are 1, 1, and 2. (1 + 1 + 2 = 4)
* For 9: The differences to 7, 8, and 10 are 2, 1, and 1. (2 + 1 + 1 = 4)
* For 10: The differences to 7, 8, and 9 are 3, 2, and 1. (3 + 2 + 1 = 6)
Next, take the reciprocal (1 divided by the sum) for each number, and add them all together:
* (1/6) + (1/4) + (1/4) + (1/6) = 0.8333
Finally, multiply that total by the size of the group (which is 4):
* 0.8333 × 4 = 3.3333
Here is the crazy part: As you go deeper down the grid and the groups get bigger, this final number locks directly onto Pi (3.14159...)!
* With a group size of 10, the answer is 3.1709
* With a group size of 100, the answer is 3.1418
* With a group size of 1,000, the answer is 3.14159