Irrational Pi Defrocked

[C1ay]

the pi value being entirely arbitrary.

And this is the origin of the fallacy in your claim. Pi is not an independent variable, it is a transcendental constant. The radius ® is not a dependent variable that can vary with pi. A circle has one, and only one, radius. For any circle with area (A) that value is √(A/pi). If you want to figure the square root of A first and then the square root of pi before doing the division then go ahead, the result is the same either way. Now let's look at the radius based on the real value of pi (3.1415926535897932384626433832795) and your fictional value (3.1622).

 

√(10/pi) = 1.7841241161527711145389663725651

√(10/3.1622) = 1.7783012462021184043593409698135

 

Since d (diameter) = 2r then:

 

Diameter 1 = 3.5682482323055422290779327451302

Diameter 2 = 3.5566024924042368087186819396269

 

Now, unitl you can show these 2 circles to be exactly the same size your claim is defrocked since circles of different sizes do not have the same area.

[maddog]

Use any other known pi value in place of the irrational pi and you will derive the same answer. The irrational pi is not sacrosanct.

This statement is totally illogical. From your proposition, you could if true imply that any number is actually

irrational. This is so since any number can be used in place of PI and any number known to be PI is

irrational.

Sqrt 10/ = 3.1622....; sqrt irrational pi = 1.77245....,; sqrt 10/1.77245.... = 1.784124; 1.78124 ^= 3.1830....radius; r^pi = 10 area.

The value you give as 1.784124 is correct, the result of dividing sqrt 10 by sqrt of irrational pi. Accordingly, the squaring of that number gives value of the radius squared as 3.1830....; thus r^*pi = 10 area.

As already stated, the symbol "^=" has not context here. So removing "^" clarifies you statement. This

statement is not correct, but it does clarify it.

I have applied the formula to all known pi values (including the finite pi), all of which giving the same exact figure. It is not pi that is the hero of these maths, people, but that of the radius/radian relationship, the pi value being entirely arbitrary.

If PI is totally arbitrary, I could pick truly anything -- how is 32 or -13 ? Since you admit you math is

not too good, then maybe you are not the judge whether there Existing "any" value for PI... :o

 

What I see here is you are not applying rtound-off error and only using so many digits for number. The

important thing here is PI being Irrational is a number that can be successively determine to ever higher

precision. Sqrt 10 = Sqrt 2 * Sqrt 5 which Irrational. The value (3.1830)^2 <> 10. Instead it equals

10.0655297923... Conversely Sqrt 10 = 3.16227766017.... Sqrt 3.183 = 1.78409640955...

Using this to solve for PI using your numbers gets PI = 31.8300000001..... which seems off be factor

of 10 unless you are saying I could use any number not. I will use my guess above of PI = -13.0000.

Thus the formula of Area = PI * Radius^2 = -13 * R^2 which for R = 10 would yield ==>

Area = -1300.0. I followed your reasoning and used any number for PI and I got negative area. You

didn't say I couldn't use a negative value for PI. Seems quite illogical to me. :o :o :o

 

Maddog

[Robust]

Your formula is

(( sqrt area / sqrt a ) ^ 2 ) * a = area

 

And this is true for any value of a except 0 :o. So your affirmation is wrong. Here's a demonstration.

 

((sqrt area / sqrt a ) ^2 )*a = area

(sqrt area ) ^2 * a = area * (sqrt a ) ^ 2

area * a = area * a

area = area

Tom. please do not obscure my given formula with one of your own giving. My formula is simply : sqrt area/sqrt pi^2 = radius.

sqrt 10 = 3..16227....; sqrt pi = 1.77245....; 3.16227/1.77245 = 1.78412....radius; r^2*pi = 10 area.

 

I Fully realize that y'all find this hard to accept - the irratioal pi beimg academically ingrained - but we do have to keep moving on.

[C1ay]

Morten S, clearly I am not the maths person one might desire, but do not see a reason for confusion over the formula. It results in giving a radius to the circle of 2.256758....That radius squared = 5.092958....Multiplied by pi gives the area of 16.

 

The point of it all simply is that one arrives at the the same result regardless of the pi value. Please show me where I might be mistaken in this. I think it to be quite relevant.

 

It is really quite this simple:

 

r = SQRT(16/pi) = 2.2567583341910251477923178062431

2r = diameter = 4.5135166683820502955846356124862

 

This is the only circle with an area of 16. If you try to use a value like pi = 3.1622 you get:

 

r = SQRT(16/3.1622) = 2.2493929215658192202834812735042

2r = 4.4987858431316384405669625470085

 

This is clearly a circle of a smaller diameter. One which actually has an area of 15.895731597443770734109889991927

 

Another way to look at it is this, by definition, pi is equal to the circumference of a circle divided by it's diameter. Neither the circumference or the diameter of a given circle is variable, thus pi cannot be variable either.

 

HTH,

[Qfwfq]

Why do you keep writing th ^2 in your formula:

My formula is simply : sqrt area/sqrt pi^2 = radius.

When it matches up to nothing in the computations that you do:

sqrt 10 = 3..16227....; sqrt pi = 1.77245....; 3.16227/1.77245 = 1.78412....radius; r^2*pi = 10 area.

I don't find this hard to accept, I find it obvious, I simply say that you haven't shown why the arbitrary number that you call pi should be a valid pi.

 

What do you mean when you talk about "all known values of pi", which are the known values of pi?

[Qfwfq]

If you try to use a value like pi = 3.1622 you get:

 

r = SQRT(16/3.1622) = 2.2493929215658192202834812735042

2r = 4.4987858431316384405669625470085

 

This is clearly a circle of a smaller diameter. One which actually has an area of 15.895731597443770734109889991927

But, C1ay, if you use a modern value like pi = 3.1622 to get the radius from the area, why do you then use the antiquated, academically ingrained value to recover the area from the radius when you had obtained the radius with the modern and rational value?

 

This is where you go wrong C1ay, to recover the same value of area you must use the same value of pi that you had used to get that value of radius from that value of area. ;)

[Robust]

Why do you keep writing th ^2 in your formula:When it matches up to nothing in the computations that you do:

I don't find this hard to accept, I find it obvious, I simply say that you haven't shown why the arbitrary number that you call pi should be a valid pi.

 

What do you mean when you talk about "all known values of pi", which are the known values of pi?

The earliest known pi value we have dates some 5,000BC - 256/81 - an engraving in stone. There are a number of others of historical record: 355/113; 22/7, etc. I tend toward the finite value of 3.1640625 derived from my own studies - but the book is not closed on that as yet.

 

The point being made here is that none appear to be sacrosanct.

 

"All things number and harmony." - Pythagoras

[Qfwfq]

The earliest known pi value we have dates some 5,000BC - 256/81 - an engraving in stone. There are a number of others of historical record: 355/113; 22/7, etc.

I call these approximations of the value. Indeed, we can only compute approximations of pi.

I tend toward the finite value of 3.1640625 derived from my own studies

Studies based on what? Are the other values not finite?

 

Obviously no approximation will be sacrosanct, only the exact value is. It is so sacrosant that we cannot really know it, only grope toward it.

[C1ay]

The earliest known pi value we have dates some 5,000BC - 256/81 - an engraving in stone. There are a number of others of historical record: 355/113; 22/7, etc. I tend toward the finite value of 3.1640625 derived from my own studies - but the book is not closed on that as yet.

 

The point being made here is that none appear to be sacrosanct.

 

Pi is a real number which is defined as the ratio of a circle's circumference to its diameter. By what studies do you find the ratio of a circle's circumference to its diameter approximated by 3.1640625. Please, show us.

[tom]

Tom. please do not obscure my given formula with one of your own giving. My formula is simply : sqrt area/sqrt pi^2 = radius.

sqrt 10 = 3..16227....; sqrt pi = 1.77245....; 3.16227/1.77245 = 1.78412....radius; r^2*pi = 10 area.

 

I Fully realize that y'all find this hard to accept - the irratioal pi beimg academically ingrained - but we do have to keep moving on.

 

1) It's your formula only written correct and instead of pi I use a.

2) You don't know to write a formula . Maybe I am stupid. Please write it clearly only in letters ( no numerical values)

3) You don't know the order in which math operations are made

sqrt area / sqrt pi ^ 2 = sqrt area / pi is NOT equal to ( sqrt area / sqrt pi ) ^ 2 this is what you're using in your calculations. You write it in one way and use it in another.

[Robust]

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

[C1ay]

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

 

Uh, neither is 3.1640625

 

The only pi value is approximately 3.1415926535897932384626433832795............

[Robust]

Tom, I asked at the outset that y'all try to bear with my lack of mathematic abilities. I believe that I have since and several times given the formula in it's proper form:

sqrt area/sqrt pi = radius; r^2*pi = area.

 

In the stated problem the area given is 10; sqrt 10 = 3.1622....; 3.1622..../sqrt pi = radius. The point of it all being that the same area is given by whatever pi ratio employed. The irrational pi is not sacosanct - sophisticated no doubt - but not sacrosanct.

[tom]

Your formula is true for every value that you give to pi ( except 0 because you divide by the sqrt of it ). But this doesn't prove your affirmation about pi. In reality your affirmation is false ( I repeat your formula is a valid mathematical expression but your conclusion is wrong).

[C1ay]

Tom, I asked at the outset that y'all try to bear with my lack of mathematic abilities. I believe that I have since and several times given the formula in it's proper form:

sqrt area/sqrt pi = radius; r^2*pi = area.

 

In the stated problem the area given is 10; sqrt 10 = 3.1622....; 3.1622..../sqrt pi = radius. The point of it all being that the same area is given by whatever pi ratio employed. The irrational pi is not sacosanct - sophisticated no doubt - but not sacrosanct.

And that's exactly why you don't understand that your claim is errant. For any value A you may divide the square root of it by the square root of any random number P and get a resulting value of R. You can then work backwards by squaring the result R and multiplying it by the number P that you chose at random to get back the value A which you started with. That does not make your chosen value for P a value for pi. That just means you can use the same values you selected to work backwards through the equation as you used to go forward through the equation.

 

Pi is a specific number defined as the ratio of a circle's circumference to it's diameter. It is the one value for P that will yield the true radius R for a circle in your equation. If you choose any other value for P you will not get the true radius and you cannot use the result to find the true diameter of the circle with area A. For a given area A there is one, and only one, diameter for a circle and you can only find it with the one and only value for pi, not some random choice.

 

Now it seems to me that this topic has been discussed quite thoroughly. Unless you can provide some rigorous mathematical proof I don't see much point in the continuance of this thread.

[Robust]

Clay, tthe mathematical proof is given by the formula. It is not conjecture:

 

sqrt area/sqrt pi = radius;

r^2*pi = area.

 

You cannot hide from it....use any known pi value and you will get the same area.

[C1ay]

Clay, tthe mathematical proof is given by the formula. It is not conjecture:

 

sqrt area/sqrt pi = radius;

r^2*pi = area.

 

You cannot hide from it....use any known pi value and you will get the same area.

 

You quite obviously are not a math person. Your equation is not a proof. You also seem to have your mind made up that pi can be whatever you want it to be regardless of the specific definition it has. Someone in some forum somewhere has played a trick on you and you don't even know it. Consider this though, your claim also means that the radius of the circle can be whatever you want as well since it is dependant on your ficticious value of pi. If you can't see the fallacy in that I don't think there's anyone here that can help you understand it.