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My favorite constant is not irrational! It's 1/7.
Consider these:
1/7 = 0.142857142857...
2/7 = 0.285714285714...
3/7 = 0.428571428571...
4/7 = 0.571428571428...
5/7 = 0.714285714285...
6/7 = 0.857142857142...
Each of these six fractions of seven have the same six digits, in the same order, but with a different starting point. Irrational numbers do not have the market on mathematical beauty cornered.
Dit is gewoonweg prachtig

nog een:
The golden ratio gets better:
phi = (sqrt(5)+1)/2 = 1.61803398874989484820...
1/phi = 0.61803398874989484820...
phi^2 = 2.61803398874989484820...
These three numbers have the same infinite sequence of non-repeating digits, with the same starting point.