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Originally posted by IblisLucifer
Pi (3.14159265...) can only be rational if you make 2 circles one inside the other put 2 on both sides of the inside one .[....] 9.1428571428571428571428571428571... much more rational
There are various other ways of finding the Lengths or Areas of particular Curve Lines, or Planes, which may very much facilitate the Practice; as for instance, in the Circle, the Diameter is to the Circumference as 1 to ... 3.14159, etc. = π
Originally posted by JackTheTripper
reply to post by jerryznv
Bah, your statement is begging the question (but it is good example of circular logic! )
Booze is a drink of the wise ones, so wise is the one who drinks booze..edit on 10-12-2011 by JackThBeTripper because: (no reason given)
Originally posted by 547000
Eh, what are you talking about? Be more clear please. It seems you are justifying your claims by using an inaccurate approximation of pi.
Originally posted by JackTheTripper
Originally posted by 547000
Eh, what are you talking about? Be more clear please. It seems you are justifying your claims by using an inaccurate approximation of pi.
WHAT? I am instead claiming that the current standard of pi is based by inacurate approximation of pi and I am uttering a closed form formula for pi, which can be proofed (using mathematics) to be correct and which gives the pi value 3.1446011... Please do download the pdf from the link on my signature below. Read it and and tell me why it is not correct.
Originally posted by Riffrafter
There are many "proofs" which once they were completed have proven to be paradoxical.
See Euclid for starters....
With that said, there is much more to Mr. Fibonacci than meets the eye. Many real mathematicians know this. It's just that they can't quite put their finger on exactly what "it" is.
Yet...
Supercomputers crunch away and hope springs eternal....
Originally posted by circlemaker
Dude... You can measure it with a stick and a string and it will still be 3.14159...
If the radius is 1, a half circle is pi. All numbers are relative to the distance between 0 and 1, including the length of a curve. It's pretty simple. I've measured it myself.
You can't just throw fibonacci and phi at something and magically transform it.
The best connection I've found between phi with pi is this: 1/phi*2 = 0.309. When you're sine value is 0.309, the radian value is 0.314 (pi/10).
From The infernal prime spiral -page
At the beginning (Graph 1), we can only see 2 rotating arms in the spiral. But gradually (Graph 2 and 3), we can see 2 big arms in which we have exactly 10 little arms.Why 10 ? I never used this number neither in the function nor in the program. Now, if we take x in degrees, we obtain a simple Archimede spiral less and less dense (due to the prime numbers rarefaction). So, would it be an hidden property of pi ?
- Isaac Keslassy (11 Apr 1999), who has found that it wasn't a property of pi but a property of a range including pi (3.141 to 3.144) : curious, no ?
[...]
- Erick Wong (03 Oct 1999), for his excellent explanations of all the phenomenas. Here are extracts from the mail:
The prime spiral on your web page is easily explained in terms of rational approximations to 2*Pi (this is why numbers close to Pi also work, since they have the same approximants).
The best rational approximations for 2*Pi, given by the continued fraction 6+1/(3+1/(1+1/(1+1/(7+1/(2+...))))) are 6/1, 19/3, 25/4, 44/7, 333/53, 710/113, ...
Now, imagine plotting the numbers (6n+1) in radians. We get the spiral instead of a straight line because 6 is not exactly 2*Pi.
The spirals are counterclockwise because 6 < 2*Pi radians.
I think that 19/3 and 25/4 are not close enough to 2*Pi to be recognized, and 44/7 is much better. Well, Phi(44)=20 and that's why there are 20 arms (the two large "gaps" correspond to the spirals 44n+[10,11,12] and 44n+[32,33,34], which are never prime. Now the spirals are clockwise because 44>2*Pi*7.
As we zoom out further, I expect to find spirals corresponding to the very good approximation 710/113. and ther should be exactly Phi(710)=280 arms.