I'm a musician, not a smith. Ruler is fine. It's quite transparent. Even though they have various lengths for length unit such as centimeter, e.g. a diameter of my glass: one ruler says it's 7.2 cm, another ruler says it's 7.25 cm. But that's okay for phew.
You didn't measure the outer circumference with a measuring tape because you are a musician?
So instead, you just totally eyeballed the measurement but cutting notches into a strip of paper? because you are a musician?
And you also think you are qualified to demonstrate experiments that are mathematically proven to be fallacious? Is that also because you are a musician?
But let's pretend your inaccurate measurement are about right anyway, for musical fun. The difference between 7.2cm and 7.25cm is just under .7%. The difference between pi and 3.17157 is about .95%. So how do you have any confidence at all in what you measured? Is that also because you're a musician?
What kind of music do you make?