I always thought there was a connection between geometry and the math and physical constants. Once I was thinking about Einstein's equivalence principle between gravity and acceleration and his elevator-in-space argument. He claimed that there is no experiment that the man in the elevator could do to determine if he was in a gravity field or accelerating rocket. It occurred to me that all he had to do was wait because the rocket could not accelerate at 9.81 m/s forever. So I did the math lightspeed/acceleration of gravity = 30559883.59 sec = 353.7023 days for 86,400 sec/day or 96.9% of a year to get to c. Just a coincidence, they say.

Look at a chart of sin(x) + sin(x/2) + sin(x/3) + sin(x/5) + sin(x/7) + sin(x/11) + sin(x/13) + sin(x/17) + sin(x/19) + sin(x/23) + sin(x/29) + sin(x/31) + sin(x/37) + sin(x/43), you can find a local peak close to practically any number; the chart is effectively entirely composed of peaks.

It's extremely unsurprising that you would find peaks near mathematically relevant numbers, since there are peaks near any number whatsoever. You could pick ten random numbers out of a hat and fine tune those to 99.999%+ accuracy as well using the same scaling procedure.