Dear Scholar
Present Pi value 3.1415926...can not be obtained experimentally.
It means DIRECT EXPERIMENTATION is a futile exercise.
On the other hand the Real/True/Exact and an algebraic number can be obtained experimentally.
However we must realize that even this experiment gives the exact results by INDIRECT experimentation
I repeat by INDIRECT verification only.
Ok
non-transcendent basics can't be transformed using manipulations to transcendent or transcendental identities. It is a "salto qualitativo". For this reason is forbidden to divide with zero or to make a multiplication using the infinite concept, but these are the wrong procedures in CUSANUS' "coincidentia oppositorum". In the infinity a triangle and a circle are the same? Math nonsense, like the "Achilles" by Zenon, only 2000 years later Leibniz was able to make evidence for the nonsense inside the "Achilles"using Infinitesimal math.
Exact Pi-by experiment.mp4 -- What you demonstrate here in this video, is this how you originally found the mathematical expression for the "cosmic pi" value?
I don't understand why you not just used the value measured at first, 29.5 cm, which equals pi times d, and the measured d value, 9.4 cm, and take the ratio, which gives a value of 29.5 / 9.4 = 3.138... ≈ 3.14 for pi.
Dear Scholar
That approach is WRONG in computing the EXACT VALUE OF Pi.
You may look at this message
📷 Exact Pi-by experiment.mp4 My dear scholar
This experiment has 2 parts. In the 1st part we measure their dimensions with ruler. They are NOT accurate.As far as ruler values are concerned, though approximation ,but agree with each other. As they are right ,we go to the 2nd part. The answer is to VERIFY the EQUATION. When Equation is proved Right by the ruler values then we have to go to the equation and DERIVE the REAL Pi Value. So, Cosmic Pi is NOT NOT NOT .....derived from the experimental values . On the other hand, Pi is derived from the VERIFIED EQUATION . Hence it is the NATURAL Pi Value OK
I have watched already the complete video "Exact Pi-by experiment.mp4" and this is why I ask.
In this video you use the well-known relation that pi times diameter equals the circumference. Do you agree that this is the defining equation for pi -- in the sense that from this equation it becomes clear what the meaning of pi is?
Dear Scholar
My intention is to show the world how simple the experiment and how easy to derive the exact and real value of pi.
That is the greatness of NATURE.
Other things are insignificant for me.
How ever the attached experiment is very tedious
"My intention is to show the world how simple the experiment and how easy to derive the exact and real value of pi." -- You are completely wrong: The real value of pi is defined by the ratio between circumference and diameter. It is simple and easy to determine pi that way experimentally, and the world knows this already. Everything which is not compatible with this definition of pi is NOT pi, because the definition is unique.
"When Equation is proved Right by the ruler values ..." -- Well, your ruler values are of limited accuracy: The circumference has 3 valid digits, and the diameter has only 2. Therefore, your claim that you can rule out 3.141... in favor of 3.146... makes no sense, because you need at least four valid digits in all quantities to prove this.
Dear Scholar
Scientific criticism is NOT searching for what is wrong and how it can be called faulty . In the true sense ,criticism should SEE what has already been said and correctly represented or not.
Next: how best it can be refined without altering its basic truth.
Your arguments , I am sorry to tell you , are , like searching a piece of bone in brain or breast and saying negatively. It leads you no where and also discourages creative thinking in others.
Sorry, my dear Sarva Jagannadha Reddy, but it is up to you to come up with more "brain or breast" -- and it is the usual task of other scientists to "pick out the bones" (as I did, indeed). This is what happens when a manuscript is sent to the referees before publication in a journal, which is a quite well established procedure -- so don't be too surprised that now you receive such "referee comments".
You are right that too much criticism may lead to discourage. But we are doing science, so this aspect has a very low priority -- since the highest priority is to find the correct way of thinking and explaining; wrong ways of thinking and explaining have to be corrected, no matter what! And that's why we discuss here -- weren't you interested in such discussions, and isn't that the reason why you posted your works on ResearchGate?
"how best it can be refined without altering its basic truth" -- Very good point! So, what is the basic truth here? Of course it is "pi times diameter equals circumference", because it is true, and it is very basic -- isn't it?
"criticism should SEE what has already been said and correctly represented or not" -- Well, the same holds for the authors of new scientific works! So, are you sure you haven taken into account "what has already been said and correctly represented or not"?
What "truth" do you mean here, specifically? For me, "pi times diameter equals circumference" is the starting point. What do you start from?
Dear Scholar
I strongly believe Cosmic Pi is the truth
You strongly support 3.1415926.. of polygon is truth.
We are in the opposite poles .
Nearly 25 mathematicians of the world have accepted with the very FIRST Paper.
For you any number will not convince Cosmic Pi as the real one.
It is impossible to convince. This is my experience in the last 19 years.
Like you nearly 20 people went on arguing against Cosmic Pi without showing any error . They compare with polygon and argue.
"I strongly believe Cosmic Pi is the truth" -- Well, you already made a contradicting statement, remember? "Let it it be the Cosmic Pi is WRONG; I told you yesterday ' I do not care ' "
(https://www.researchgate.net/project/Discovery-of-the-TRUE-VALUE-of-Geometrical-Constant-COSMIC-Pi/update/5996b6d7b53d2ff30bda8c8e?replyToId=5a54b8824cde266d588154a8&_iepl%5BviewId%5D=RDFW2EdNTdp6f7B6tYLtjYZe&_iepl%5BsingleItemViewId%5D=kr2tgqgt4Q07dBicAX1Ix69C&_iepl%5BinteractionType%5D=projectUpdateView)
"Nearly 25 mathematicians of the world have accepted with the very FIRST Paper." -- That can't have been mathematicians, because Cosmic Pi is not a reasonable mathematical quantity.
"It is impossible to convince. This is my experience in the last 19 years." -- Right you are!! Why? Because mathematics is not about "convincing"; instead, it's about logic.
"Like you nearly 20 people went on arguing against Cosmic Pi without showing any error." -- This is funny, because I've shown you already several errors in your work, and also others here on Research Gate have done that!
It's just that you were reluctant to really understand their arguments and to draw the relevant conclusions; instead, you always sidestepped. Stop that!
"They compare with polygon and argue." -- Of course they do, because that's the gemoetrically easiest way to show that 3.146... cannot be pi. And they will continue to do so; it's just that you are not willing to really listen to them.
So, back on track, please, to clarify the most basic statement: "pi times diameter equals circumference" is the starting point. (Alternatively, we can start from "pi times radius squared equals area".) Do you agree or not? Just answer this question; no sidestepping!
Wait -- you've said so already (https://www.researchgate.net/post/Why_Does_Circle-Square_Composite_Construction_Rejects_Present_Pi_Number_31415926#view=5a535155ed99e1ebc9402152):
"14. What is the definition of pi = It is circumference of circle/Diameter of circle"
So, what are you waiting for? Just take your measured value for the circumference (as above: 29.5 cm), which equals pi times d, and the measured d value (as above: 9.4 cm), and take the ratio, which gives a value of 29.5 / 9.4 = 3.138... ≈ 3.14 for pi. And, you see, it is significantly smaller than 3.146 ≈ 3.15; therefore, "Cosmic Pi" does not hold for this measurement.
"Avoid wasting your valuable time please" -- I've just proven Cosmic Pi invalid for your own measurement, and that's all you have to say? You want me to keep silent? Sorry, not as long as you keep denying pi = 3.14159...
So, if you don't want to do it yourself, I take over your homework and calculate the circumference / diameter ratio belonging to your measurements (data taken from "EXPERIMENT BASED MATHEMATICAL.docx"):
Small wheel: 52.3 cm / 16.6 cm = 3.1506... ≈ 3.15, medium wheel: 139.8 cm / 44.4 cm = 3.1486... ≈ 3.15 (both rounded to last significant decimal place)
These two results do not allow to distinguish between the two numerical values under debate, 3.14159... and 3.14644... that differ by 0.00485..., because the measured lengths don't have enough significant decimal places.
Big wheel: 552.3 cm / 175.6 cm = 3.1452... ≈ 3.145 (rounded to last significant decimal place)
This result has four significant decimal places; the last significant decimal place is relevant for distinguishing between 3.14159... ≈ 3.142 and 3.14644... ≈ 3.146 (both rounded to the relevant decimal place). However, the experimental result lies between the two values under debate: 3.142 < 3.145 < 3.146.
So, there might be something wrong with the experiment, and before any conclusion can be drawn from it, this has to be checked. The following questions arise: Are there systematical errors involved? If so, can they be remedied?
I suggest the following: In the file "EXPERIMENT BASED MATHEMATICAL.docx" there is a photograph showing the measuring of the perimeter of the big wheel (Fig. 2). One can see that the measuring instrument was wrapped around the outside of the wheel, which possibly leads to a somewhat larger value of the circumference (due to the thickness of the measuring instrument).
One possibility to compensate this effect is to measure the circumference of the big wheel by putting the measuring instrument directly on top of the rim of the wheel, not around it. Eventually, this might result in a somewhat smaller value for the circumference, leading also to a smaller value of the calculated ratio.
On the other hand, taking into account also the data from the video (which give 29.5 / 9.4 = 3.138... ≈ 3.14 for pi), it becomes clear that so far the accuracy was not sufficient. Therefore it makes sense to perform further measurements, but with higher accuracy, both with respect to systematical errors and with respect to more significant decimal places -- at least one decimal place, because then there are no rounding errors in the relevant range.
Dear Scholar
you have every right to accept and SUPPORT 3.141....of polygon as pi of the circle.
Ok
And you must accept that a circumscribed polygon EXCLUDES 3.1464... as pi of the circle.
Dear Scholar
When the value of circumscribed polygon about a circle equal to 3.141....is WRONG , how can I SUPPORT it as RIGHT.
You can support it . But I will NOT.
And NEVER I insist any body to reject 3.141... of circumscribed polygon.
It has been followed for the last 2000 years. You may continue to follow this blunder for many more centuries.
But for me , after the discovery of Cosmic Pi I INSIST , this value 3.146 of Cosmic Pi is 100 % true.
Again, I CHALLENGE YOU AND THE WORLD OF MATHEMATICS to derive 3.141..... using RADIUS OF THE CIRCLE ALONE.
Radius is like Side of Square and Base & Altitude of Triangle.
It is NATURAL PROCEDURE and every one should RESPECT & FOLLOW.
WOULD YOU ACCEPT THIS CHALLENGE?
WOULD YOU DERIVE 3.141....FROM RADIUS ?
Look again at the data of the Big wheel: 552.3 cm / 175.6 cm = 3.1452... ≈ 3.145 (rounded to last significant decimal place). This is smaller than "Cosmic Pi" (≈ 3.146) and therefore REJECTS "Cosmic Pi" as pi of the circle.
Dear Scholar
We can not use left hand for all purposes as we perfectly use with RIGHT hand.
For every thing there is a method and it should oblige NATURE
"We can not use left hand for all purposes as we perfectly use with RIGHT hand. For every thing there is a method and it should oblige NATURE" -- Yes, of course -- and Nature also has set a ratio between circumference and diameter of a circle; this ratio is pi. Therefore, your Challenge "DERIVE 3.141....FROM RADIUS" is nonsense. Pi and the radius are independent quantities, because their product is the circumference.
"When the value of circumscribed polygon about a circle equal to 3.141....is WRONG, how can I SUPPORT it as RIGHT." -- Stop; I never said so! Of course, a polygon value is always just a polygon value, and not a true value of pi. However, the circumscribed polygon EXCLUDES 3.1464... as pi of the circle. That's all I say here; right now I don't say anything about the true value of pi.
Dear Jan-Martin Wagner,
But any ratio is part of the rational numbers set, right? In the case that we consider a ratio between circumference and diameter of a circle, we are considering also pi as a rational number, or we don't? And in this case, we know that this is an absurd, because pi never can be a rational number, because it is an irrational, right? Besides that, the irrational numbers, as pi, don't have a logic as any other number of rational, integer or natural numbers sets, right?
"But any ratio is part of the rational numbers set, right?" -- No, not at all! Only fractions of integer numbers are rational. However, pi is an irrational number, of course.
So, if pi is an irrational number, it can't be expressed as a ratio, right?
Dear Scholar P.P.Gattai
1.Yes, Pi is an irrational number.
2.The definition of Pi = circumference/ diameter.
3.Diameter is a rational entity and has a rational magnitude and has to be represented by a rational number
4.When a circle is inscribed in a square , the circle gets the properties of square and its diagonal.
5. When the side of the square is equal to 1, its diagonal is equal to square root of 2.
6.Side is a rational entity and diagonal is an irrational entity.
7. Therefore, diameter of circle = side of the superscribed square
8. And diagonal of the square = circumference of the inscribed circle IN ITS NATURE and however, QUANTUM is different between diagonal (root2)and the circumference of the inscribed circle of 1 diameter is exactly equal to (14-root2)/4.
9. And hence the magnitude of circumference SHOULD ALSO BE REPRESENTED BY SQUARE ROOT OF 2 ( similar to diagonal)
10. And that is the UNKNOWN truth till now with wrong number so called Pi number 3.1415926........ of polygon . This 3.1415926... has become an irrational number AND a transcendental number.
11. But the fact is the real Pi number should be an irrational number and an ALGEBRAIC number and definitely NOT a transcendental number.
12. What is the REAL Pi number then ?
13. The answer is (14-root2)/4
To conclude : Pi is an algebraic number having root2 as necessary part and parcel of circumference.
Dear Scholar
" An irrational number is a number that cannot be expressed as a fraction for any integers and .Irrational numbers have decimal expansions that neither terminate nor become periodic. ... Numbers of the form are irrational unless is the th power of an integer "
S. J. Reddy: "3. Diameter is a rational entity and has a rational magnitude and has to be represented by a rational number." -- No, not at all: The diameter can by any positive real number. As such, it can be rational or irrational, but that doesn't matter; in all cases, the circumference of the circle is pi times the diameter.
S. J. Reddy: "4. When a circle is inscribed in a square, the circle gets the properties of square and its diagonal." -- No, not at all: A circle stands for itself. Whether a square is there or not, doesn't mean anything for the circle. The diagonal of the square is just the diagonal of the square, and nothing more.
S. J. Reddy: "6. Side is a rational entity and diagonal is an irrational entity." -- No, not at all: The side can be any positive real number, just as the diameter. Therefore, if the side is an irrational number, the diagonal may be a rational one, or even an integer (e.g., diagonal = 2 and side = sqrt2).
S. J. Reddy: "8. And diagonal of the square = circumference of the inscribed circle IN ITS NATURE [...]" -- No, not at all: The diagonal is a straight line (for which the theorem of Pythagoras holds), whereas the circumference is a curved line (for which it just holds that circumference = pi times diameter); being curved means that it is of different geometrical nature.
(to be continued)
Dear Scholar
1. You are right. We can have a diameter equal to root2.
2. You are mistaken. The world had been under that WRONG impression till March 1998 the month of discovery of true Pi value.
The diagonal of square and the circumference of the INSCRIBED circle become similar in their NATURE. This is my work.
I mean diagonal and circumference do NOT become one but maintaining their individuality they acquire root2 for their quantum representation.
3.I mean that. when side is root2, the diagonal becomes 2.
4. Your doubt is acceptable.
My work says although diagonal is a straight line and circumference is a curve ,still, they ACQUIRE BASIC NATURE OF ROOT 2 while computing their quanta .
Secondly, I have been telling all these 20 years PYTHAGOREAN THEOREM is applied in inscribed and circumscribed polygons in and about a circle.
Polygon is a straight line entity and circle is a curve . How can we attribute 3.141... of straight lined polygon to curve type circle?
Think over my dear Scholar
5. Hence, I was forced to adopt a new approach to understand the CIRCLE in its right perspective and are not seen even in Euclid's classic ELEMENTS.
6. Therefore, I am unable to convince the world. Some gone to the low level of attacking me personally with abusive language.
One fragile man facing an army of mathematicians in the cause of a NEW TRUTH.
"The diagonal of square and the circumference of the INSCRIBED circle become similar in their NATURE." -- What do you mean by that; what similarity are you talking about? Well, they are both one-dimensional objects, but this holds for any circle and any square.
Maybe it's time for a philosophical interlude: Think about the fundamental question about the length of an arbitrarily curved line; how can it be measured? This is important since the diagonal is a straight line (for which it is clear what "length" means, namely the distance between the two endpoints), but the circumference is curved. How can we attribute a length value, defined for straight lines only, to a curved line?
S. J. Reddy: "8. [...] however, QUANTUM is different between diagonal (root2) and the circumference of the inscribed circle of 1 diameter is exactly equal to (14-root2)/4." -- No, not at all: (14-root2)/4 equals 3.1464..., which is larger than 22/7 = 3.1428... which, in turn, is larger than the circumference of the circle. Therefore, (14-root2)/4 is larger than the circumference of the circle, too.
However, this only finishes the subject with respect to the circle, because it leaves open what (14-root2)/4 really stands for.
Dear Scholar
You can believe any thing and say it is RIGHT
"You can believe any thing and say it is RIGHT" -- No: As a scientist I can't say anything I believe is right, because that would be against scientific ethics. Before I can say something is right, I need to check it and find the reason why it is right.
Remember what Peter Railton said: "Why is warrant important for knowledge? In part because true opinion might be reached by arbitrary, unreliable means."
And it's not my personal opinion that 3.1464... is larger than 3.1428...; don't you agree?
Dear Scholar
Any new truth first appears just like very blurred image. I mean this new concept or discovery gains perfection only with passing time by more and more supporting evidences contributed by the people who could see this "blurred image" and accept it as a truth to pursue further and make it a clear image.
Some Professors are Gernot Hoffmann, Constantine Karapappopulas and others.
Dear Sarva Jagannadha Reddy, what you just wrote here describes very nicely what I experience in my own research work: Any new truth first appears just like very blurred image. I mean this new concept or discovery gains perfection only with passing time by more and more supporting evidences contributed by the people who could see this "blurred image" and accept it as a truth to pursue further and make it a clear image.
However, the following questions remain: How do these contributions of more and more people work in detail? What about contradicting evidences? It would be nice if you could discuss these aspects in more detail.
Still, 3.1464... is larger than 3.1428...; don't you agree?
By the way, since you provided "Full page faxprint.pdf": There, Mr. Karapappopulas mentions a work of Ramanujan from the year 1914 (*), where pi was found "correct to 9 digits" (so Karapappopulas's hand-written remark) by a geometrical construction, resulting in the explicit expression (92 + 192/22)1/4 = 3.1415926525...
(*) Ramanujan, S. "Approximate geometrical constructions for Pi." Quarterly Journal of Mathematics 45 (1914): 350--374. So, probably you want to read this paper, my dear Sarva Jagannadha Reddy, because it contains what you've asked for, namely alternative geometrical methods for pi.
Dear Scholar
Squaring a circle was done up to 9 digits
It means the number 3.141....is WRONG
Cosmic Pi 3.146... does for ALL its digits
Conclusion is yours
Still, the following questions remain: How do these contributions of more and more people work in detail? What about contradicting evidences? It would be nice if you could discuss these aspects in more detail.
Still, 3.1464... is larger than 3.1428...; don't you agree?
"3.1428....is a WRONG pi value" -- Yes, of course! Remember, I never claimed 22/7 = 3.1428.... to be a correct pi value. So, why do you emphasize such an obvious fact?
Still, 3.1464... is larger than 3.1428...; don't you agree?
Dear Scholar
With your discussion I could see a new truth on Cosmic Pi
The title is : Jan-Martin Wagner Approach To Circle - Circumscribed Polygon Relation In Terms Of Square Root 2
I thank you very much my dear.
Here is the manuscript
Oh, thanks; I feel quite honoured -- but shouldn't it rather read "Jan-Martin-Wagner-inspired Approach"? Clearly, it's not my approach, but now it sounds so. Anyway, I've just printed the two pages to study the approach in detail; I'll comment on it later, here.
Dear Scholar
Your suggestion is apt.
I wrote the paper in the early morning at 3 AM.
Read the paper and let me have your opinion.
Oh; yes, I see -- you have written it down on the manuscript ("Tuesday, early morning, 3 AM").
Your drawing illustrates exactly what I meant: The smaller circle is perfectly inscribed with the octagon. The only thing that is a little different in my imagination is that here, we have two different circles, whereas I thought of just one -- which would be perfectly inscribend both with the square and with the octagon.
However, since everything scales with the radius, we can use your result for the smaller circle to calculate the segment length for an octagon that would truly circumscribe the bigger circle. The ratio of the two radius values is 0.5 / 0.46193976626 = 1.0823922, which gives for segment length s8, corresponding to the rescaled segment EF, a value of 1.0823922 * 0.38268343235 = 0.4142135624, which is exactly the value of tan(22.5°).
This means that here we come to the same result as I just discussed in the Comments section (https://www.researchgate.net/project/Discovery-of-the-TRUE-VALUE-of-Geometrical-Constant-COSMIC-Pi/update/5996b6d7b53d2ff30bda8c8e). So, if you have any objections there, we can use your present construction to double-check.
Side remark: I'm still working on the relevant answer I promised to give here, but meanwhile the discussion about the matter continues in the Comments related to the following: Research Proposal Prof. Jan-Martin Wagner's Inspired Approach In Support of Cosmic Pi
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