The Golden Ratio of Curves

The royal Egyptian cubit has the curve embedded into it because that value of 1.718 which is Euler minus one is actually a curve of linear value. A pizza cut into six slices will have an arc for each slice that is pi over six meters right or 1.718 feet and will have a radius of exactly one meter. If I take an exact pendulum that is one meter in length and I swing it exactly 30 degrees of arc it will take precisely one second to traverse each direction of that 30 degree arc. It's just all those that kind of thing just makes me wonder how what creates this reality.