Pi

[C1ay]

Research shows that all the methods used, up to this present date, in finding the true value of Pi have falling short.

 

Your are required to support such claims so prove it.

[modest]

Very true C1ay. Also, these claims need supported:

 

The only reason why Pi is irrational and transcendental is because it has a false value of 3.14159265…

 

Please give a scientific source showing Pi's irrational and transcendental nature is false.

 

For about 4 thousand years the equation, c/d = Pi, has existed as the only method in finding the true value of Pi.

 

Please give a source showing that there is only one method of enumerating pi.

 

All of the above claims have been refuted by members in this thread and it is now your responsibility to support them as per the site rules.

 

~modest

[dkv]

Pi is a transcendental number. Pi is represented can be represented using a well defined function... therefore it is also a function.. pi=f(x,n) where n is the required accuracy.

[Guadalupe]

Very true C1ay. Also, these claims need supported:

 

 

 

Please give a scientific source showing Pi's irrational and transcendental nature is false.

 

~modest

 

 

Hi! modest :hyper:

 

I said, “The only reason why Pi is irrational and transcendental is because it has a false value of 3.14159265…”.

 

I did not say, Pi’s irrational and transcendental nature is false.

 

 

 

 

:)

[Guadalupe]

As numerous previous posts, and nearly any encyclopedia article or introductory math textbook explains, Guadalupe’s conclusion is simply wrong.

 

Guadalupe, my guess is that you are intuitively disturbed by the concept of irrational numbers – numbers that can’t be represented as terminating or repeating decimal numerals. This is a common reaction, that, in my experience, nearly all students experience at some time in their education.

 

However, many numbers, including Pi, have been rigorously proven to be irrational. Such proofs of the irrationality of Pi have been well known for over 200 years.

 

Your insistence that all of the many known mathematical expressions of Pi “fall short” and give a “false value” suggest to me that you need to learn some essential fundamental mathematical principles, not only about number systems, but the principle that rigorous, formal proof is more mathematically credible than intuitive feelings.

 

 

Hi! CraigD :hyper:

 

Yes, the proof of the irrationality of Pi has been well known for over 200 years but the false value of Pi has been irrational for about four thousand years.

 

2 + 2 = 4 True Value

 

2 + 2 = 3.5 False Value

 

 

:)

[C1ay]

I said, “The only reason why Pi is irrational and transcendental is because it has a false value of 3.14159265…”.

 

But that's not really a false value, it's simply an approximate value. There's no way to state an exact value for [math]\pi[/math] in base 10 so we use an approximate value, approximated by as many digits as the precision of the calculation requires. When you want to express it exactly then simply use [math]\pi[/math].

[Guadalupe]

Hi! :hyper:

 

This is based on my scientific research on the history and methods used in finding Pi.

 

History showed me that Archimedes, Liu Hui, and all the others, only used the method of geometry for measuring a perfect circle which gave us a false value of 3.14159265… as Pi.

 

I believe the equation, c/d = Pi, is about 4 thousand years old and was never used to find the true value for Pi.

 

By using this equation, “c/d = Pi” I drew, on poster boards and on a smooth plywood surface, several sizes of perfect circles and divided them by their diameter which gave me a true value of 3.15 as Pi.

 

The thickness of the pencil wasn’t important, when drawing a perfect circle; the important thing was to make sure that the outside end of the flat tip lead pencil matched the very end of both sides of its diameter.

 

I modified a measuring tool that allowed me to precisely measure, with small increments of fractions, around the circumference of a perfect circle. First with a 10 inch diameter, then a 20 inch, 25 inch, 30 inch, 35 inch, and a 37 inch diameter. All of them gave me a true value of 3.15 as Pi.

 

 

 

:)

[C1ay]

I modified a measuring tool that allowed me to precisely measure, with small increments of fractions, around the circumference of a perfect circle. First with a 10 inch diameter, then a 20 inch, 25 inch, 30 inch, 35 inch, and a 37 inch diameter.

 

What, EXACTLY, were the measurements of the circumferences of those circles?

[freeztar]

Hi! :hyper:

 

This is based on my scientific research on the history and methods used in finding Pi.

 

History showed me that Archimedes, Liu Hui, and all the others, only used the method of geometry for measuring a perfect circle which gave us a false value of 3.14159265… as Pi.

 

I believe the equation, c/d = Pi, is about 4 thousand years old and was never used to find the true value for Pi.

 

By using this equation, “c/d = Pi” I drew, on poster boards and on a smooth plywood surface, several sizes of perfect circles and divided them by their diameter which gave me a true value of 3.15 as Pi.

 

The thickness of the pencil wasn’t important, when drawing a perfect circle; the important thing was to make sure that the outside end of the flat tip lead pencil matched the very end of both sides of its diameter.

 

I modified a measuring tool that allowed me to precisely measure, with small increments of fractions, around the circumference of a perfect circle. First with a 10 inch diameter, then a 20 inch, 25 inch, 30 inch, 35 inch, and a 37 inch diameter. All of them gave me a true value of 3.15 as Pi.

 

 

 

:)

 

Guadalupe,

 

It's apparent that one of the following three scenarios is occurring:

 

• You do not understand the previous posts in this thread.
  
• You refuse to understand the previous posts in this thread.
  
• You understand what has been stated, but you continue on despite. (trolling)
  

In any case, I advise you to study the posts in this thread and consider your viewpoint on this subject.

 

I admire your enthusiasm for challenging convention and experimenting, but that needs to be tempered with basic understanding of what convention you are challenging and how your experimentation might be faulty/improved.

[Nootropic]

While we're at let's make the square root of 2 equal to 1.41 because I drew a perfect triangle and measured it perfectly in my perfect world. And then I decided we should make e = 2.71. As a matter of fact, let's abolish all irrational numbers because our geometric approximations are clearly the true and exact value.

 

Now isn't that just crazy?

[modest]

I just uesd Corel Draw to make a polygon of 500 segments (sides) with height and width 2.

 

I broke the polygon into its segments and distributed them in a level and flat line with ends touching. The length of segments measured 3.141 (Corel is limited to displaying thousands of a unit measured).

 

I don't mean to diminish the effort you put into your pencil and plywood method Guadalupe, but it took me less than a minute from the time I opened Corel until the time I started writing this post. Less than a minute from concept to results. A cheap computer can do more accurately the same thing a person would take hours doing less accurately.

 

We could also use the methods CraigD give in posts #9 and #20 to more accurately approximate pi in decimal form. That's what this really boils down to. Your method simply wasn't that accurate. Pi does not equal 3.15 and it is less accurate a representation than 3.14159.

 

~modest

[Guadalupe]

The method by which we are using to measure the circumference of a circle to find the true value of Pi was and is the use of polygons. Is the method futile?

 

We know and understand that a circle is not a polygon. This means that the use of finite or infinite amount of polygons/regular polygons cannot become, create, or make a circle.

 

This also means that this method of using polygons will never be accurate in measuring the circumference of a circle in finding the true value of Pi.

 

In conclusion, the four thousand year old method of using polygons to find the true value of Pi is futile.

 

 

 

:confused:

[Qfwfq]

In conclusion, the four thousand year old method of using polygons to find the true value of Pi is futile.

Have you studied the basics of topology? Do you know what it means to say that [imath]\mathbb{Q}[/imath] is dense in [imath]\mathbb{R}[/imath]?

 

If your metric space has Cauchy sequences that don't converge to any value in the same space, you can complete it. That is exactly how [imath]\mathbb{R}[/imath] is contructed from [imath]\mathbb{Q}[/imath]. Without this, with only rational values, the value of the ratio of circumference to diameter simply does not exist; neither do the solutions of many other problems including ones definable purely in terms of rational values.

 

Given that topology makes the construction by completion possible, if [imath]\mathbb{Q}[/imath] exists then so does [imath]\mathbb{R}[/imath] and approaching [imath]\pi[/imath] with a rational valued sequence is not futile at all.

[Guadalupe]

Hi! Qfwfq :)

 

For four thousand years we have overlooked the error of using this method of polygons in finding the true value of Pi.

 

We can make finite/infinite amounts of polygon/regular polygon that is as close to a circle as we want, the more sides we give it, the more it will look like a circle.

 

A polygon is composed of a finite/infinite set of straight line segments, and a circle is not.

 

A circle by definition is a smooth plane closed curve whose points are all on the same plane and at the same distance from a fixed point (the center).

 

A polygon is by definition a closed figure with straight line segments and a regular polygon is a polygon that has equal sides and congruent angles.

 

The equation c/d = Pi will always give us a true value of Pi but, the method of polygons will always give us an accurate approximation of a false value for Pi.

 

Thus, making this four thousand year old method of using a finite/infinite amount of polygons/regular polygons is indeed futile.

 

 

 

;)

[Zythryn]

The equation c/d = Pi will always give us a true value of Pi but, the method of polygons will always give us an accurate approximation of a false value for Pi.

 

Why then, does the method of polygons give us a very accurate approximation of the value of c/d?

 

Or, if you would rather, why don't you tell us what the true value of Pi is?

[C1ay]

The equation c/d = Pi will always give us a true value of Pi but, the method of polygons will always give us an accurate approximation of a false value for Pi.

 

Thus, making this four thousand year old method of using a finite/infinite amount of polygons/regular polygons is indeed futile.

 

Me thinks you have not been introduced to the concept of limits yet....

[Jimoin]

I think he's trolling and it's getting annoying!