Irrational Pi Defrocked

[Robust]

Clay, you are correct in that I am not a maths person persay, but mistaken on all other counts. As regards the rasius of a circle, it is whatever the circumference dictates, pi being nothing more than the ratio of line to arc, radius describes the line and radian the arc it subtends. Pi is but the ratio of one to the other, not the determinasnt.

 

History records a number of authenticated oi values. There has been another since the irrational pi - a finite pi value of 3.1640625. All that notwithstanding, the formula given here proves that one pi value is no more outstanding than another as to describing area of the circle.

 

I do understand the reticence, but events are moving on, friends, and I suggest we move with them.

[C1ay]

sqrt area/sqrt pi = radius;

r^2*pi = area.

Clay, you are correct in that I am not a maths person persay, but mistaken on all other counts. As regards the rasius of a circle, it is whatever the circumference dictates, pi being nothing more than the ratio of line to arc, radius describes the line and radian the arc it subtends. Pi is but the ratio of one to the other, not the determinasnt.

 

History records a number of authenticated oi values. There has been another since the irrational pi - a finite pi value of 3.1640625. All that notwithstanding, the formula given here proves that one pi value is no more outstanding than another as to describing area of the circle.

 

So then, based on your formula (sqrt area/sqrt pi = radius) you are stating that:

 

sqrt area/sqrt (3.1640625) = radius and

sqrt area/sqrt (3.14159) = radius

 

will both give the same radius for the same area? Prove it.

[Qfwfq]

No he isn't stating that they will both give the same radius for the same area, he states that the two distinct radius values will give back the same area, when multiplied by the respective divisor.

 

This is quite c1ear, C1ay, and the proof is elementary. His only trouble is that this doesn't mean that the different pi-r pairs are all good, just because ab/a is independent of a.

[Qfwfq]

As regards the rasius of a circle, it is whatever the circumference dictates, pi being nothing more than the ratio of line to arc, radius describes the line and radian the arc it subtends. Pi is but the ratio of one to the other, not the determinasnt.

Pi is the ratio of what to what?

 

It is the ratio of circumference to diameter, or half the ratio of circumference to radius. On a flat manifold, with euclidean metric, it has one fixed value that has been proven irrational and transcendental.

 

On a smooth manifold the ratio can depend on r, but the limit for r approaching zero will be the same value it has on the flat manifold.

 

If the manifold isn't smooth the limit may be different. Take a conical surface and consider all circles centred on the cone's vertex, the radii being measured along any generator. The ratio will be independent of r and less than 2pi, it is diminished according to the sine of the angle between the generator and the cone's axis. You can have a rational value of the ratio, if you like. It can be anywhere between zero and 2pi. For circles with a different centre, the ratio will be different. Work it out.

[C1ay]

No he isn't stating that they will both give the same radius for the same area...

Yes he is, here's a quote of the post that started this whole thread, emphasis mine:

 

Introduced on an Australian science forum is a formula showing Euler's highly touted irrational pi to have no greater authority than any of the other numerous pi values of historical reference. The new formula was given as solving a mechanical engineering problem requiring a given radius for the turning of a circular disc of any specified area - given as follows:

 

FORMULA: sqrt area/ sqrt pi ^ = radius; thus, radius * pi = area.

 

Please note change in formula from that originally given.

The formula gives the radius to any circle of a prescribed area - regardless of any and all known pi values as might be applied. What do you think?

 

 

"All things number and harmony." - Pythagoras

 

For me his claim is obvious, what do you think?

[Qfwfq]

For me his claim is obvious, what do you think?

Call it poor wording. He doesn't mean the same value of radius, regardless of the value of pi, he simply takes the fact that you can recover the same area as being a good CRC or something.

[Qfwfq]

Now we're really past any limit, aren't we? Arguing about what he meant and what he didn't mean... :D ;) ;) !!!

 

:D

[C1ay]

He doesn't mean the same value of radius, regardless of the value of pi....

 

Which was my only point. I was always taught that any given circle only has one radius, the one that's equal to half of the diameter.

[maddog]

Clay, the value 3.1622 you cite is not a pi value - it's the sqrt of 16 - the given area.

Huh ??!!?? I am not sure I understood what you just said. Now let me get this straight (I will repeat):

You are saying that

 

Sqrt(16) = 3.1622 ??? <== Is this Exact ???

 

Is not 4 * 4 = 16 ? If so, I can write the following.

 

4*4 = 4^2 = 16. Take Sqrt of both sides and I get

 

4 = Sqrt(16). So how do you get 3.1622 ??? Totally beyond me.

 

Does this mean that Sqrt(4) = 1.2844 ??? If so, all the building, bridges and tunnels are built all wrong!!!!

 

Maddog

[C1ay]

Huh ??!!?? I am not sure I understood what you just said. Now let me get this straight (I will repeat):

You are saying that

 

Sqrt(16) = 3.1622 ??? <== Is this Exact ???

 

Is not 4 * 4 = 16 ? If so, I can write the following.

 

4*4 = 4^2 = 16. Take Sqrt of both sides and I get

 

4 = Sqrt(16). So how do you get 3.1622 ??? Totally beyond me.

 

Does this mean that Sqrt(4) = 1.2844 ??? If so, all the building, bridges and tunnels are built all wrong!!!!

 

Maddog

 

 

He's referring to this post.

[Qfwfq]

...the one that's equal to half of the diameter.

If the same circle did have more than one diameter, there'd be just as many HalfTheDiameters, wouldn't there be?

 

Maddog, I supposed he meant root of 10, we can grant him at lest that I think.

[wrong]

The Australian Science forum Robust refers to is SSSF at http://www2b.abc.net.au/science/k2/stn/

he found no supporters there for his rational pi,his non-transcendinal pi, his rational sq root of 2,his idea that all circles have 2 different diameters and many other wonderous maths tricks including papers to maths journals ,patents etc all non existant.

[Robust]

The Australian Science forum Robust refers to is SSSF at http://www2b.abc.net.au/science/k2/stn/

he found no supporters there for his rational pi,his non-transcendinal pi, his rational sq root of 2,his idea that all circles have 2 different diameters and many other wonderous maths tricks including papers to maths journals ,patents etc all non existant.

And it is your sort of ad hominen behaviourn WRONG that makes it the place tha t it is. Do you have anything to contrbute to this topic or able to show where it is in error? This appears to be a constructively directed forum. Please don't drag your TPS garbage in here.

 

That being said, do you have any constructive criticism that might be helpful to this topic?

[MortenS]

Robust, you have still not answered how you can come from a given area, to a given radius using different values of pi. If the value of pi does not matter, clearly this should be possible.

 

Circle 1, using the irrational, transcendent pi (3.14592654....

Area = 16

radius = sqrt(16)/sqrt(3.141592654....) = 2.256758334...

 

Circle 2: Using your finite value of pi...= 3.1640625

 

Area = 16

radius = sqrt(16)/sqrt(3.1640625) = 2.248730781...

 

Now, 2.2567... is obviously not the same as 2.2487...

 

Why are not the two radii in a circle with the same area equal using your method?

[C1ay]

Robust,

Why are not the two radii in a circle with the same area equal using your method?

 

Don't hold your breath MortenS. That reply would require a constructive contribution.

[Robust]

Robust, you have still not answered how you can come from a given area, to a given radius using different values of pi. If the value of pi does not matter, clearly this should be possible.

 

Circle 1, using the irrational, transcendent pi (3.14592654....

Area = 16

radius = sqrt(16)/sqrt(3.141592654....) = 2.256758334...

 

Circle 2: Using your finite value of pi...= 3.1640625

 

Area = 16

radius = sqrt(16)/sqrt(3.1640625) = 2.248730781...

 

Now, 2.2567... is obviously not the same as 2.2487...

 

Why are not the two radii in a circle with the same area equal using your method?

 

MotonS, they are not equal because of using different pi values to arrive at them (pi is arbitrary), yet both giving the same area - that's one of the essential points I'm trying to make.I'm having connection problems with my computer - so let me get back to you with more on this.

[MortenS]

I do understand that if you start from a given area with a given pi value, you come to a given radius. If you use that given radius, with the given pi value, you get back to the given area. That is just the nature of equations.

Problem is, both area and radius are connected in a circle. It is impossible to get two circles with the same area, yet different radii. This implies that pi is a constant, and not an arbitrary value.