What more can I explain? Even Mike don't dare to explain pi.
How about why anyone should doubt the known value of pi or why anyone should take your value seriously?
I have provided a derivation of pi, with you not objecting to any step.
If you think some part of it is wrong, explain exactly what.
That means pointing out exactly what step you disagree with.
It's the calculation of radius as well as the angle, which has nothing to do with anything in an arch length.
This shows you either have no idea what you are talking about or are just spouting crap.
The angle has almost everything to do with the arc length.
Of course the series method with wrong assumption of arch length position. I've mentioned it repeatedly.
The series is only indirectly related to the arc length.
If you object to the series, the one you have to object to is that used in my derivation. That is the series expansion for (1-x^2)^(-1/2).
But you can easily test that expansion.
Again, the expansion is:
(1-x^2)^(-1/2)=sum((((2*n)!/((2^(2*n))*((n!)^2)))*x^(2*n)) from n=0 to infinity, which holds while |x|<1, and x!=0, as that requires the first term being slightly different as you would otherwise get 0^0, but noting that would simply be no number there at all, it still works.
For example, using x=0.5, x^2=0.25. 1-x^2=0.75=3/4. (3/4)^(-1/2)=2/sqrt(3)=1.154700538379
Then looking at the sum itself, we end up with 1.154700538379 at n=20.
You can try it with any other number and it works, some just take more time to converge.
So clearly the series is not the problem.
Hardly pi experiments gives measurement that close to 3.14 coz it's a bit shorter than it should be.
As you have already effectively admitted, measurements are prone to error.
Regardless, if they are getting a value lower than the known value of pi, why are you suggesting a value which is higher?
Now either point out exactly what step you object to, with an explanation of why; or admit pi is correct and phew is nonsense; or remain silent and never bring it up again.
Poll