Most of the formulas for pi are based on mathematical functions. But a few of them are not. These are driven by intuitions and are based on numbers, prime numbers or square roots.
Here are some of them :-
Two of them from Euler. And one from Viete.
Yesterday evening I was thinking hard on root 2, root 3, root 4 . . . . . . etc.
Then I found that
The 12th term was 0.25908. The 13th term was 0.52634. Their average is 0.39271. And 0.39271 is about pi/8.
The results in Wolfram from root(2) to root(5000) and root(5001) are:-
Here are some of them :-
Yesterday evening I was thinking hard on root 2, root 3, root 4 . . . . . . etc.
Then I found that
The results in Wolfram from root(2) to root(5000) and root(5001) are:-
The average sway is (0.40217207+0.38803135)/2 = 0.3951017. It is pi/7.95135.
So the sway remains at about pi by 8.
Indeed the Gauss Error Function observed here.
Can any mathematicians say why this discrepancy?
ReplyDeleteIt should be either pi by 8. If you believe in pi.
Or it should be roughly pi by 8. If you believe in irrational numbers.
In my opinion either pi is correct or irrational numbers like root(2), root(3) are correct.
If my argument is wrong; what is the correct answer then?
What we can do is instead of dividing by 2 (average sway) we can divide by 1.99/2.01 in every term. Maybe next time 1.98/2.02 and so on. So that pi by 8 is always obtained.
ReplyDeleteMaybe there is a pattern. Maybe this is the Gauss error function !!
One needs to dream and also deliver. This is how mathematicians should be working.
I think it is indeed Gauss error function.
ReplyDelete