Irrational Pi Defrocked

[Robust]

Clearly shown? Where ?

 

Shown here,tom....in that all known pi vaues (but one) are irrational. The highly touted "irrational" pi is neither unique nor sacrosanct.

[C1ay]

Shown here,tom....in that all known pi vaues (but one) are irrational. The highly touted "irrational" pi is neither unique nor sacrosanct.

What you fail to realize is that there is only one value of pi, all of the other values are simply approximations rounded of to the required number of digits for the accuracy required. Values like those taught in high school, 3.14, 22/7, etc. are not pi, they are approximations. For a machinist cutting a press fit these are not even good approximations. The machinist must use a figure accurate to the third or fourth decimal place or better.

 

Then there is that value you use, 256/81, that isn't even a good approximation by today's standards. It is only accurate to the first place after the decimal. A value fitting for the ages of old where they counted the days catch using sticks and pebbles.

[Qfwfq]

We're not on the same page here - root 2 rules in my book and is an irrational number,

That's a relief, at least you don't claim root 2 being rational, but you fail to notice that this means my example of a close continuum in the Cartesian plane has an irrational area. I posted in a hurry yesterday and, with Murphy's law, I gave it a wrong factor, it's 1 over thrice root 2 or, if you prefer, root 2 over 6. Work it out.

 

as are all numbers not whole or with ending decimal

This is also a wrong thing you say. Before arguing upon whether or not pi is rational you should at least know what rational means. Is 1/3 rational or irrational? By definition it's rational, in terms of decimals it is:

 

1/3 = 0.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333.......

[Rincewind]

The highly touted "irrational" pi is neither unique nor sacrosanct.

Quite so, Robust; it's merely correct.

[maddog]

Before arguing upon whether or not pi is rational you should at least know what rational means. Is 1/3 rational or irrational? By definition it's rational, in terms of decimals it is: ...

Robust,

 

I would say the definition of rational is that a ratio can be formed. So 1/3 can be the ratio of 1 over 3.

This does NOT mean that the number of decimals repeat. So the opposite is true. An irrational value

has no ratio it is EQUAL to. I Emphasize '=' because you seem to think 'close is good enough' ! This

is where your math is weak. By definition one ratio cannot equal another (unless both numerator &

denominator are Both factors of the other). This is in particular WHY there can be NO PI based on

RATIOS. This IN NO WAY CAN (PI) BE RATIONAL !!! :) Another way to think of an irrational

number is a number where in decimal form the value (number of decimals is never ending) and does

NOT repeat. For any rational number in decimal form may have a never-ending sequence yet there

exists some sequence that repeats. What makes PI so unique is that PI can not be made to be any

polonomial expansion of Finite order. For any such expansion is ONLY an APROXIMATION to PI.

The series must be of inifinit order to get to pi :) :) :)

 

maddog

[Robust]

maddog, you say that the series must be infinite to get to pi. What about the finite pi of 3.1640625? Given the aforementioned area to the circle of 16 units the radius 2.2487 ad infinitun; r^2 *pi = 16 area. Accordingly, by the irrational pi: radius = 2.2567 ad infinitum and r^2 *pi = 16 area. Pi is arbitrary - it is Root 2 that rules!

[Rincewind]

What about the finite pi of 3.1640625?

This is a nonsense statement. 3.1640625 is quite simply not pi, because it is not the ratio between the diameter and circumference of a circle; it is not what you get when you divide the circumference of a circle by that same circle's diameter.

[tarak]

I am not a maths person ,but I do understand that Pi is a constant and is the ratio between the circumference of the circle and it's diametre.This means any circular figure has a to have constant proportionate dimensions irrespective of their sizes.Similarly closed figures with equal dimensions like square or cube must have a constant ratio like diagonal length and triangles with right angles work on pythogoras theorem.Are there any other basic constants in mathematics as strong as Pi which seems to me as one of the most important number which has been there for ages.

[Qfwfq]

Robust,

 

I would say the definition of rational is that a ratio can be formed. So 1/3 can be the ratio of 1 over 3.

1/3 is the ratio of one over three. And hence it is rational.

 

I hope you didn't take me for Robust... :)

 

What makes PI so unique is that PI can not be made to be any

polonomial expansion of Finite order.

:) That doesn't make pi quite unique.

[Robust]

1/3 is the ratio of one over three. And hence it is rational.

 

I hope you didn't take me for Robust... ;)

 

;) That doesn't make pi quite unique.

 

What difference does it make if is pi rational or irrational? I have shown clearly an irrational pi that IS finite and yet arriving at the same results as any of the known rational pi values. The entire gist of this thread being merely to show that the irrational pi of Lindemann/Euler & Company is not the sacrosanct piece it is claimed to be. Nice algorithm but nothing more.

[Buffy]

What difference does it make if is pi rational or irrational?

All I can say is that I wish my math profs were as easy going as you are on these kinds of issues...I would have gotten all straight A's!

 

Close Enuf 4 Country Music,

Buffy

[tom]

irrational pi that IS finite

An irrational nummber can't be finite.

[Rincewind]

An irrational nummber can't be finite.

I think we need to define what is meant by the term "finite," and what we are trying to communicate here.

 

Pi is a finite positive number -- its value is between 3 and 4.

Pi is, however, an irrational number -- it has an infinite expansion with no discernable pattern or repetition of number series.

 

I think this is where we are getting confusion regarding the use of the words finite and infinite.

[tom]

Sorry for the confusion.

[C1ay]

I have shown clearly an irrational pi that IS finite...

No you haven't. You have shown some poor approximation of pi that is outdated by 1000s of years.

[wrong]

maddog, you say that the series must be infinite to get to pi. What about the finite pi of 3.1640625? Given the aforementioned area to the circle of 16 units the radius 2.2487 ad infinitun; r^2 *pi = 16 area. Accordingly, by the irrational pi: radius = 2.2567 ad infinitum and r^2 *pi = 16 area. Pi is arbitrary - it is Root 2 that rules!

 

 

Well if a super scribed regular polygon with 90 sides outside a circle of a radius of 1 unit has a perimeter of 3.142869254....(ie 2° tan x 180 ) then your value of 3.1640625 is simply wrong as it is a greater value and kindergarten logic demands that a straight line is a shorter route than a curved line

[Robust]

No you haven't. You have shown some poor approximation of pi that is outdated by 1000s of years.

 

Yes, I have, Clay. And where do you get the notion that the finite pi iis 1000's of years old? It was arrived at only this last year. Let's cut to the chase here ....prove for us that the irratrional pi value of 3.14159....is more accurate than that of, say,3.16409...ad infinitum.