Pi is circumference/ diameter. I tried with prime nos on radar graph and found a set of prime nos add upto 29. I took the differences of the adjacent nos and plotted the graph again. They add upto 22. I get 7 which is 29-22. Is there any relationship between prime numbers and the value of pi?
Hi,
The number Pi is the most famous mathematical constant. It is a "constant", because it corresponds to the constant ratio between the circumference of a circle and its diameter. Most people know its base — 3.14 — but then it gets tricky: and for good reason, it's an infinite number.
For more details please take a look at the links.
https://www.exploratorium.edu/pi/history-of-pi
https://byjus.com/maths/value-of-pi/
https://www.wondriumdaily.com/the-origins-of-pi/
https://cosmosmagazine.com/science/even-computers-cant-get-pi-exactly-right/
https://www.scienceabc.com/pure-sciences/do-we-have-any-mathematical-proof-that-pi-is-infinite.html
Best regards
3.1428571428571=π
If i find the difference of adjacent nos after the decimal, the series is repetitive
326326326326....
Question is why is it 22/7?
22 is 2²+18, 3²+13, 4²+6, 5²-3,
==> 2³+14, 3³-5,4³-42
==> 2⁴+6, 3⁴-59
7 is 2²+3, 3²-2, 4²-3²
==> 2³-1, 3³-20, 4³-57
==> 2⁴-3², 3⁴-73
If i consider a decimal number, 20/3= 6.6666...
20= 2²+ 2⁴, 3²+11, 4²+2², 5²-5, 6²- 4²
==> 2³+12, 3³-7,
==> 2⁴+4, 3⁴-61
3= 2²-1
==> 3²-6
No fraction as 4.44444...exists
But we have 3.33333=10/3
No fraction as 2.22222.. exists
We have 6.6666...= 20/3
No fraction as 5.55555... exists
No fraction as 7.7777 exists
Why ?
1,2,4,5,7,8,9==a series which excludes nos which appear as valid recurring decimals,(3,6)
Difference=1,2,1,2,1,1
If i break the nos 10 and 3 ,
10= 2²+6, 3²+1
==>2³+2, 3³-17
==>2⁴-6,
3= 2²-1
Powers of the numbers add up to 3.
20/3 is also same, 20= 2⁴+2², 3=2²-1⁴
Powers of the nos add up to 6
No _direct_ relationship but have a look at the Riemann Hypothesis or at the Basel problem.
I am scared of prime numbers. Every number is a unique formula. Is it true? Riemann found a way to get rid of my fears.
Lets consider the prime number 23.
2, 3, 1, 5, 6 , 0.6666...
I get 5×6- (2×3+1). Used up almost the real nos.
Lets consider 13.
1,3,2,4,3,0.3333...
I get ( 1+3+2+4+3). Used up all real nos.
Last number is 19. 19 is 91 as well which is not prime.
1,9,8,10,9
(1+8+10) excluding both 9 .
So, every nos is unique but Riemann still challenges us to find it.
Ok, lets try 79 or 97
7,9,2,16,2
( 7×9+16) exclude the 2s as difference is 2 of the digits.
Mr. Riemann was right . Its not so unique.
Lets do 79 again.
7,9,2,63,16,0. 7777
( 63 +16)
97 is 9,7,2,16,63, 1.2857142..
Exclude the 7, 63+16+9×2
Tricky and beautiful.
When a number is added to another number, we get an new increased number.
When a number is reduced from another number, we get the original number.
Well i am thinking whether numbers can multiply in terms of reproduction. A number when multiplies , exhibits property of the biological plants , like grass. Sort of incorrect assessment.
pi is a transcedental number very useful when worked with on a complex plane
I'm not sure that the relationship that you mention generalises (remember 22/7 is only an approximation to pi). However, there certainly are interesting connections between divisibility and pi. For example, if you take two random integers, the probability that they are coprime (or relatively prime) is given by 6/pi^2. If we take the product of (1-(1/p^2)) over all the primes the answer converges to 6/pi^2. And pi crops up in approximations to sums of Euler's phi function, etc.
https://mathoverflow.net/questions/16991/what-are-the-connections-between-pi-and-prime-numbers
If a prime number is x and the next prime number is (x+2) then a pattern is observed in the radar graph for the palindromic series. 3,4,3,1,x,1,3,4,3
Compare to 3,4,3,1,x+2,1,3,4,3
Eg: 71, 73 is x
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