There is an upward trend in the digits of . I just found it using Maple.
X := [0, 1, 2, 3, 4, 5, 6, 7, 8]: Y := [3, 1, 4, 1, 5, 9, 2, 6, 5]: LinearFit([1, n], X, Y, n); 2.20000000000000+.450000000000000*n
Here the digits are enumerated beginning with the th, which is . The regression line predicts that the th digit of is approximately .
But maybe my data set is too small. Let’s throw in one more digit; that ought to be enough. Next digit turns out to be , and this hurts my trend. The new regression line has smaller slope, and it crosses the old one at .
But we all know that can be easily changed to . The old “professor, you totaled the scores on my exam incorrectly” trick. Finding a moment when none of the -obsessed people are looking, I change the decimal expansion of to . New trend looks even better than the old: the regression line became steeper, and it crosses the old one at the point .
What, again? Is this a coincidence? I try changing the th digit to other numbers, and plot the resulting regression lines.
All intersect at the same spot. The hidden magic of is uncovered.
(Thanks to Vincent Fatica for the idea of this post.)