Numerical near-miss coincidences are to be expected when working with transcendental numbers. First reason is the pigeon hole observation others have made. The

Numerical near-miss coincidences are to be expected when working with transcendental numbers. First reason is the pigeon hole observation others have made. The other reason is: this is one of the properties of transcendental numbers. Roughly: one technique used in showing a number to be transcendental is you show it is not equal to any term in sequence of algebraic numbers and yet closer to them than (without equality) than any algebraic number could be. And this is something I never liked about a lot of "math puzzles." A lot of them point out some effect as surprising or esoteric when the effect is actually a specific example of something one should expect (given a developed mathematical intuition). In the end the observation is only hermetic or exotic to those who don't know math and ends up being a barrier to getting comfortable with known results and their consequences.