Reconsidering Pi: Examining the Controversy Surrounding its Accuracy

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In summary: I think you're going to need to explain what you even mean. I mean, Pi exists, there are algebraic methods for computing it out to n decimal places, so it's well defined. Do you mean that you don't think that Pi is the right constant to use in the equation Pi*radius^2 = area of the geometric object called a circle?In what way is Pi wrong? There must be some specific context or definition of Pi that you are referring to?I came up with this "Inside a regular inscribed hexagon, the radius of the circle is equal to the sides of the hexagon". It was my beginning. I believe Pi is not needed and that it is not accurate.
  • #1
crocque
28
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I'm not sure it's safe to post real theorems here.

Is it?
 
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  • #2
I'm new and not sure how to even ask. I feel like I'm on to something, but... there's that uncertainty.
 
  • #3
Dear god I hope your theorem is "pi = 4" or "pi is rational".
 
  • #4
Certainly not, but this is why I'm hesitant to post. I'm in a beginning stage. I don't have the answer yet. I just see it.
 
  • #5
What are you asking exactly? Post your theorems if you have any!
 
  • #6
Is it wrong because Tau is right?

I think you're going to need to explain what you even mean. I mean, Pi exists, there are algebraic methods for computing it out to n decimal places, so it's well defined. Do you mean that you don't think that Pi is the right constant to use in the equation Pi*radius^2 = area of the geometric object called a circle?
 
  • #7
In what way is Pi wrong? There must be some specific context or definition of Pi that you are referring to?
 
  • #8
I came up with this "Inside a regular inscribed hexagon, the radius of the circle is equal to the sides of the hexagon".

It was my beginning. I believe Pi is not needed and that it is not accurate. The area of a circle, or even better a sphere, can be done with no numbers, just variables. It's a work in progress. I feel I need a partner with good object and spatial orientation to understand where I am headed, less everyone will think I'm crazy, lol.

If I could just find one person that understands this part. I might convice you of the rest. I saw the theorem, but it took others besides me to prove it for me, with much persistence on my part. Now that I'm working on a new one, I feel it's ground breaking and it scares me.

I'm not asking anyone to care, but if you think there's any value in studying what I'm saying, by all means, talk to me.
 
  • #9
that sounds very interesting
 
  • #10
crocque said:
I came up with this "Inside a regular inscribed hexagon, the radius of the circle is equal to the sides of the hexagon".

It was my beginning. I believe Pi is not needed and that it is not accurate.

If you are talking about a regular hexagon in which a circle is inscribed that just grazes the sides of the hexagon (at their centres) then the radius of the circle is [SQRT(3)]/2 (~0.866) times the length of the sides of the hexagon.

If you are talking about a regular hexagon in which a circle is inscribed that passes through the apexes of the hexagon, then the radius of the circle is clearly the same length as the sides of the hexagon, because the line from the centre to an apex is one side of two of the equilateral triangles that form a set of 6 nested equilateral triangles forming the hexagon, and it is also a radius of the circle, so radius and all sides are identical.

This used to be the classic way of drawing a hexagon, with ruler and compasses, before there was an excess amount of computer power to make your brain go soft.

What's your point?
 
  • #11
It is simply not true that a circle inscribed in a regular hexagon has a radius equal to the sides of the hexagon.
 
  • #12
It simply is true. I proved it in the 10th grade. Check it out, disprove it, if you wish.
 
  • #13
crocque said:
I came up with this "Inside a regular inscribed hexagon, the radius of the circle is equal to the sides of the hexagon".

It was my beginning. I believe Pi is not needed and that it is not accurate. The area of a circle, or even better a sphere, can be done with no numbers, just variables. It's a work in progress. I feel I need a partner with good object and spatial orientation to understand where I am headed, less everyone will think I'm crazy, lol.

If I could just find one person that understands this part. I might convice you of the rest. I saw the theorem, but it took others besides me to prove it for me, with much persistence on my part. Now that I'm working on a new one, I feel it's ground breaking and it scares me.

I'm not asking anyone to care, but if you think there's any value in studying what I'm saying, by all means, talk to me.

I'm just curious as to what you mean.

Do you believe Pi is not the correct number to describe the area of a circle of radius 1? That the ratio of the circumference to the diameter is not constant? What does the hexagon's perimeter imply about the area of the circle? Have you found anything "wrong" with current proofs?
 
  • #14
See this is why I get scared, if someone does realize what I'm sayng they will run with it. Then again, it's my theorem. No one wanted to believe me then or now, still true.
 
  • #15
daveyp225 said:
I'm just curious as to what you mean.

Do you believe Pi is not the correct number to describe the area of a circle of radius 1? That the ratio of the circumference to the diameter is not constant? What does the hexagon's perimeter imply about the area of the circle? Have you found anything "wrong" with current proofs?
No Pi isn't the right number, in my mind. I'm looking outside the cricle. No circle is perfect. That's why gemotery is the only way. Yeah we can use algebra to form curvatures, doen't make it correct. Think 3 dimensional.

I don't want to say everything because I feel only a certain type of person can see this.
 
  • #16
crocque said:
It simply is true. I proved it in the 10th grade. Check it out, disprove it, if you wish.

Please post your proof
 
  • #17
crocque said:
It simply is true. I proved it in the 10th grade. Check it out, disprove it, if you wish.

No, it's not. You probably proved it when the circle is circumscribed by the hexagon, not inscribed.
 
  • #18
I didn't come to these forums to show off, more to meet people that are thinkers like myself. I don't have the background to discuss this with education on my side, it's something I see.

I really need to get into college again, but I'm 40, still I love learning.
 
  • #19
disregardthat said:
No, it's not. You probably proved it when the circle is circumscribed by the hexagon, not inscribed.
I asked you nicely if you do not believe me that disprove it. Please do not tell me what I already know.

I promise you they are equal. No need to get defensive.
 
  • #20
Where's a professor when you need one?
 
  • #21
crocque said:
No Pi isn't the right number, in my mind. I'm looking outside the cricle. No circle is perfect. That's why gemotery is the only way. Yeah we can use algebra to form curvatures, doen't make it correct. Think 3 dimensional.

I don't want to say everything because I feel only a certain type of person can see this.

What do you mean by "no circle is perfect"? Pi has many different definitions, so it looks like you've narrowed your disagreement down to: C/D is not a constant number. If you don't accept the calculus proofs, why not? I understand you don't want to reveal your "theorem" but you seem to be unintentionally trolling the forum. If I made a thread saying that I can clearly "see" that gravity actually did not exist but didn't want to communicate my idea, what would you think?
 
  • #22
cmb said:
If you are talking about a regular hexagon in which a circle is inscribed that just grazes the sides of the hexagon (at their centres) then the radius of the circle is [SQRT(3)]/2 (~0.866) times the length of the sides of the hexagon.

If you are talking about a regular hexagon in which a circle is inscribed that passes through the apexes of the hexagon, then the radius of the circle is clearly the same length as the sides of the hexagon, because the line from the centre to an apex is one side of two of the equilateral triangles that form a set of 6 nested equilateral triangles forming the hexagon, and it is also a radius of the circle, so radius and all sides are identical.

This used to be the classic way of drawing a hexagon, with ruler and compasses, before there was an excess amount of computer power to make your brain go soft.

What's your point?
You're getting close. Just think a bit more outside the circle.
 
  • #23
daveyp225 said:
What do you mean by "no circle is perfect"? Pi has many different definitions, so it looks like you've narrowed your disagreement down to: C/D is not a constant number. If you don't accept the calculus proofs, why not? I understand you don't want to reveal your "theorem" but you seem to be unintentionally trolling the forum. If I made a thread saying that I can clearly "see" that gravity actually did not exist but didn't want to communicate my idea, what would you think?

troll, really?, I just joined the forums. I joined to ask about this math problem that has been in my head forever. Thought maybe I should actually ask some knowledgeable people. Forgive me, I'm just saying I think this can be done geometrically. This is not my first time debating this in life. I'm not trying to argue with anyone. I'm looking for help.

Really I wish this was a trool and I was crazy, it's not a troll but I might be crazy. I usually talk on the xbox forums, I came here to get real ideas.

But ok, see, if you have the triangular base of a sphere and know the radius. There is a way to use that radius and find out what the missing area is whether it is a circle or a sphere. I am working on it. Need more specifics? I've thought about it for 20 years.

It's not Pi. no 22/7
 
  • #24
Circle seems to be different, not like a square, but it is. It follows the same rules. Just another geometrical object. This is what I am trying to achieve.
 
  • #25
Crocque, could you please clearly state what you're thinking about??

And I would love to see the proof with that hexagon, do you mind giving it??
 
  • #26
The proof to my theorem is simple. 1 line down, 1 line across, another line down to form one side of a hexagon. One radius up, one sideways, another one down. They both equal 3.

I'm not going to write out a proof, you end up with 6 equilateral triangles. I just saw it, I didn't need a proof, my teacher's helped me prove it. To be honest, I don't even remember the proof, but, like I said, prove me wrong. I think we did something with the angles and proved it. Was 20 years ago.

Chad's Theorem "Inside a regular inscribed hexagon, the radius of the circle is equal to the sides of the hexagon."
 
  • #27
crocque said:
It simply is true. I proved it in the 10th grade. Check it out, disprove it, if you wish.
No, it's not. The radius of the inscribed circle is the distance from the center of the hexagon to the center of one side. The length of one side of the regular hexagon is equal to the distance from the center of the hexagon to a vertex of the hexagon. If we take "x" as the length of a side of the hexagon, then drawing the line segment from the center of the hexagon to the center of a side gives a right triangle with one leg of length x/2 and hypotenuse of length x. The length of the other leg is [itex]\sqrt{x^2- x^2/4}= x\sqrt{3}/2[/itex].

That is, the radius of a circle inscribed in a hexagon of side length x is
[tex]\frac{x\sqrt{3}}{2}[/tex]

NOT equal to the side length. It is the radius on the circle circumscribed about a hexagon that is equal to a side of the hexagon.
 
  • #28
HallsofIvy said:
No, it's not. The radius of the inscribed circle is the distance from the center of the hexagon to the center of one side. The length of one side of the regular hexagon is equal to the distance from the center of the hexagon to a vertex of the hexagon. If we take "x" as the length of a side of the hexagon, then drawing the line segment from the center of the hexagon to the center of a side gives a right triangle with one leg of length x/2 and hypotenuse of length x. The length of the other leg is [itex]\sqrt{x^2- x^2/4}= x\sqrt{3}/2[/itex].

That is, the radius of a circle inscribed in a hexagon of side length x is
[tex]\frac{x\sqrt{3}}{2}[/tex]

NOT equal to the side length. It is the radius on the circle circumscribed about a hexagon that is equal to a side of the hexagon.
Draw it out measure it, whatever you need to do. You're saying the same things I've heard before. It's is not almost equal, nearly equal, it is equal. Debate it all you want. you're overlooking the fact that when the hexagon is inscribed, the radius is right there, already equal, just as a hexagon is. The radius of the circle is just that, just because it happens to be one side of a triangle, it's still the radius, you know the point from the center of a circle to the perimeter? what are you saying? Ty for your time.

Will anyone take me seriously please? If not disprove me. But you can't, there's the problem. I know I'm right. I just want help going further. This theorem is old news.
 
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  • #29
I'm trying to remember but I think I proved it by angles. If this angle and that angle are such a degree, you have an equitateral triangle. Hard to remember. This talk of circumscribed is nonsense, sides would be larger than the radius.
 
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  • #30
crocque said:
Draw it out measure it, whatever you need to do. You're saying the same things I've heard before. It's is not almost equal, nearly equal, it is equal. Debate it all you want. you're overlooking the fact that when the hexagon is inscribed, the radius is right there, already equal, just as a hexagon is. Ty for your time.

Will anyone take me seriously please? If not disprove me. But you can't, there's the problem. I know I'm right. I just want help going further. This theorem is old news.

You claim it's true, so you prove it. That's how it works. The two things are not equal.

And no, as long as you don't prove this, nobody will take you serious.

Perhaps download http://www.geogebra.org/cms/ and draw it out. If it comes out to be equal, then you're likely right. But it won't come out equal.
 
  • #31
crocque said:
I'm trying to remember but I think I proved it by angles. If this angle and that angle are such a degree, you have an equitateral triangle. Hard to remember.

You say you've been working on this for 20 years already?? Hard to believe...
 
  • #32
When a hexagon is inscribed inside the circle, it is true. Not the other way around.
 
  • #34
Visual aid to the discussion. Radius = 1. Therefore side of triangle = 1. Sum of hexagon sides = 6x1=6. Circumference of circle = 2*pi*r = 6.2832...
 

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  • #35
crocque said:
You're getting close. Just think a bit more outside the circle.

If you tell us in what way I am 'close', then maybe we can guess what the hecky you're talking about!

As I said, and others repeated even with a diagram, yes a hexgaon that inscribes a circle has sides of the same length as the circle's radius. This is known. You've no right to try to ensnare folks in your weird guessing game. You've got our attention [more than you deserve] so now dish up or clam up.
 
<h2>What is the controversy surrounding the accuracy of pi?</h2><p>The controversy surrounding the accuracy of pi revolves around the fact that it is an irrational number, meaning it cannot be expressed as a finite decimal. This has led to debates about whether the commonly accepted value of 3.14159 is truly accurate or if it should be calculated to more decimal places.</p><h2>Why is it important to reconsider the accuracy of pi?</h2><p>Reconsidering the accuracy of pi is important because it is a fundamental constant in mathematics and has widespread applications in various fields such as engineering, physics, and astronomy. A small error in its value can have significant consequences in these areas.</p><h2>What methods have been used to calculate the value of pi?</h2><p>There have been several methods used to calculate the value of pi, including geometric methods (such as inscribing polygons within a circle), infinite series (such as the Leibniz formula), and iterative algorithms (such as the Gauss-Legendre algorithm). Each method has its own advantages and limitations.</p><h2>Is there a definitive answer to the accuracy of pi?</h2><p>No, there is no definitive answer to the accuracy of pi. As an irrational number, it has an infinite number of decimal places and can never be fully calculated. However, through advanced computing and mathematical techniques, we can calculate its value to a high degree of accuracy.</p><h2>What are the implications of a more accurate value of pi?</h2><p>A more accurate value of pi could have significant implications in fields such as engineering and physics, where precise calculations are crucial. It could also lead to a better understanding of the nature of irrational numbers and their role in mathematics.</p>

What is the controversy surrounding the accuracy of pi?

The controversy surrounding the accuracy of pi revolves around the fact that it is an irrational number, meaning it cannot be expressed as a finite decimal. This has led to debates about whether the commonly accepted value of 3.14159 is truly accurate or if it should be calculated to more decimal places.

Why is it important to reconsider the accuracy of pi?

Reconsidering the accuracy of pi is important because it is a fundamental constant in mathematics and has widespread applications in various fields such as engineering, physics, and astronomy. A small error in its value can have significant consequences in these areas.

What methods have been used to calculate the value of pi?

There have been several methods used to calculate the value of pi, including geometric methods (such as inscribing polygons within a circle), infinite series (such as the Leibniz formula), and iterative algorithms (such as the Gauss-Legendre algorithm). Each method has its own advantages and limitations.

Is there a definitive answer to the accuracy of pi?

No, there is no definitive answer to the accuracy of pi. As an irrational number, it has an infinite number of decimal places and can never be fully calculated. However, through advanced computing and mathematical techniques, we can calculate its value to a high degree of accuracy.

What are the implications of a more accurate value of pi?

A more accurate value of pi could have significant implications in fields such as engineering and physics, where precise calculations are crucial. It could also lead to a better understanding of the nature of irrational numbers and their role in mathematics.

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