I will write on some mathematics ideas. Basel Problem. I have found out solution angles to it.
I shall write about it.
The Basel problem was; what is
1+1/2²+1/3²+1/4²+ . . . . . equal to.
1/2² is 1²/2² , 1²/3² and so on. These are nothing but angles in a semicircle. Have you understood this point. i.e tan²theta.
So, therefore, pi squared term is really there. Because pi is circumference by diameter. Circle is a truth.
Now, I wrote about doubling and 1/4th stuff earlier.
1+1/4*2²+1/3²+1/4*4²+1/5²+ . . . . . . equals pi by √6 (not correct! Maybe rounding off! Maybe not!! Maybe desktop of 50 crores! Maybe not!) in the above equation.
This equation when squared(yes !!) is the Basel problem equation.
This means,
1+1/2²+1/3²+1/4²+ . . . . . equal to pi squared by 6.
(No 50 crores desktop needed. Recursive functions should be sufficient., I guess. I am a one line C program writer.)
Yoo !! Hoo !! I have understood why these things happen. Whether correct or not correct. It seems correct to some extent. But not fully. I need money to explain this. Rs.10 crores and I am yours and my explanations too.
Reason is 4/5 -3/4 is the Riemann Zeta function. And . . . . . . . . . . 4/5 and 3/4 are so close. Did you get it ?
If I keep the (n³+1)th term as negative then the result of above is indeed pi by √6. i.e 9th term, 28th term etc.
Similarly, in the series,
1+1/2+1/3+1/4+1/5+ . . . . . . dividing by 2 and subtracting at (n²+1)th place gives √6.
This finishes the topic.
I shall write about it.
The Basel problem was; what is
1+1/2²+1/3²+1/4²+ . . . . . equal to.
1/2² is 1²/2² , 1²/3² and so on. These are nothing but angles in a semicircle. Have you understood this point. i.e tan²theta.
So, therefore, pi squared term is really there. Because pi is circumference by diameter. Circle is a truth.
Now, I wrote about doubling and 1/4th stuff earlier.
1+1/4*2²+1/3²+1/4*4²+1/5²+ . . . . . . equals pi by √6 (not correct! Maybe rounding off! Maybe not!! Maybe desktop of 50 crores! Maybe not!) in the above equation.
This equation when squared(yes !!) is the Basel problem equation.
This means,
1+1/2²+1/3²+1/4²+ . . . . . equal to pi squared by 6.
(No 50 crores desktop needed. Recursive functions should be sufficient., I guess. I am a one line C program writer.)
Yoo !! Hoo !! I have understood why these things happen. Whether correct or not correct. It seems correct to some extent. But not fully. I need money to explain this. Rs.10 crores and I am yours and my explanations too.
Reason is 4/5 -3/4 is the Riemann Zeta function. And . . . . . . . . . . 4/5 and 3/4 are so close. Did you get it ?
If I keep the (n³+1)th term as negative then the result of above is indeed pi by √6. i.e 9th term, 28th term etc.
Similarly, in the series,
1+1/2+1/3+1/4+1/5+ . . . . . . dividing by 2 and subtracting at (n²+1)th place gives √6.
This finishes the topic.
The explanations are as per string theory. And string theory is a valid method and a subject in itself.
ReplyDeleteMy favourite mathematicians are:
ReplyDelete1.Euler
2.Laplace
3.Fourier
I learnt the theta and tan equation of Madhava of Sangamagrama. I learnt a few concepts.
ReplyDeleteThen I bought one book on works of Ramanujan. It cost 7000 rupees. $100.
Ramanujan possibly pioneered mock theta functions.
I plan to do Riemann hypothesis.
I plan to do Fermat's last theorem.
Pietro Mengoli posed the Basel problem in 1644. It was first solved by Leonhard Euler in 1734.
ReplyDelete#PythaShastri had vision of 3,2 to 4,5 and 1,2,3,4,5,9,10. This is nothing but Basel problem.
There are proofs by Fourier and Cauchy on Basel problem too. Modern mathematics.
This finishes #PythaShastri posers.
"A rigorous proof using Fourier series" is close to my level of understanding.
ReplyDeleteThis finishes the topic of discussion.