I studied ancient history and mathematics and learned that many of the Greeks findings were taken from the Babylonians who acquired much of their knowledge from the Sumerians of Iraq. They had the best estimate for PI in the ancient world and they knew the Pathogrium Theorem more 1000 years earlier than the Greeks!

Thank you my dear Scholar

Pythagorean Theorem got full life with the introduction of square root of 2 for diagonal. Hence this credit has gone to Pythagoras of Samos.

In my view that my work in seeing the EXACT Pi called Cosmic Pi in March 1998 is ALSO because of INTRODUCTION OF ROOT 2 for diagonal.

Therefore, I strongly say the finding of COSMIC PI equal to (14-root2)/4 = 3.1464466...and the CREDIT GOES TO HIPPASUS OF METAPONTUM the student of Pythagorean School who introduced root 2 in Geometry in 500 BC.

Your definitions are not clear. Do you claim that the area of a unit circle is approximately 3.1464466 or do you claim the area is approximately 3.1415926 ? If only one of these values represents the area, what does the other value represent?

Dear Scholar

The TRUE Pi value is EXACT. It is (14-root2)/4

Present Pi number is POLYGON BASED. It is 3.1415926.......

It is thrust on circle as its Pi and we have been following for the last 2000 years.

There is error in its derivation. Here is the document of Prof. Vitthal Jadhav

Putting a word in capital letters nowadays means shouting that shouting is not a valid scientific argument. I asked you a simple question about which area the unit circle has: Please answer that instead of refering to exact and polygon based pi values, because I am not sure what the difference is.

In the text you refer to it is claimed that when n tends to infinity then delta tends to zero, but n*delta does not tend to zero. This last claim is not explained and it is wrong. To see that it is wrong one just upper bound n*delta by the difference between an inscribed polygon and an circumscribed polygon.

Actually the original calculating of Archimedes demonstrates that the circumference of a circumscribed regular polygon with 96 edges is less than 3+1/7 times the diameter. This old calculation does not need any limiting process. As a consequence the area of regular polygon with 96 edges circumscribed a unit circle is less than 3+1/7. If you agree that the area of the circle is less than the area of a circumscribed polygon we get that the area of a unit circle is less than 3+1/7. Since the value (14-root2)/4 is greater than 3+1/7 it cannot be the area of a unit circle.

Dear Scholar

In the enclosed attachment of Archimedes' method ,let us take 48-gon and do this exercise

Perimeter of polygon / diameter of circle = 3.139350157/1=3.139350157

--------------------------------------------------------------------------------------------------

How can we take diameter of the circle in denominator ?-

--------------------------------------------------------------------------------------------------------

We have to take TWICE the value of " u" in the Table in the denominator.

Then

u=0.498929461 * 2 = 0.997858922

let us do this now

3.139350157 / 0.997858922 = 3.14608617289

---------------------------------------------------------------------------------------

So pi value 3.146.............is the correct one.

-------------------------------------------------------------------------------------

So, AT EVERY DOUBLING OF EDGES OF POLYGON THE NUMERATOR MUST BY REDUCED " DIAMETER " i.e., less than 1

Yes, the area of the circumscribed regular 48-edged polygon is approximately 3.14608617289 . This gives an upper bound on the area of the unit circle, but (14-root2)/4 = 3.146446609407 implying that (14-root2)/4 has a value that is greater than the area of a circle.

If you want other people to understand why you think the value of (14-root2)/4 is important, please, tell us what you think the area of a unit circle is. Reference to pi just obscures the communication. Please, stop shouting at us (this is the modern meaning of using kapital letter).

I am sorry if I have hurt you

"The following are FACTS:" -- No, they aren't! And here is why:

"1. Polygon based 3.1415926... has been thrust on circle as its Pi." -- There are many ways to obtain the decimal representation of pi, not only the polygon method; therefore, 3.1415926... is not polygon based. Here are two examples for other ways to obtain pi: 1.) Euler's infinite sum of the inverses of the squares of all natural numbers: pi^2 / 6 = 1/1^2 + 1/2^2 + 1/3^2 + 1/4^2 + ... = 1/1 + 1/4 + 1/9 + 1/16 + ... (cf. https://www.youtube.com/watch?v=d-o3eB9sfls); 2.) Leibniz's infinite sum for arctan(1): pi / 4 = 1 - 1/3 + 1/5 - 1/7 - 1/9 + ... (cf. https://proofwiki.org/wiki/Leibniz%27s_Formula_for_Pi).

"2. Pi has been called a transcendental number since 1882." -- In his publication "Ueber die Zahl pi", F. Lindemann has shown why pi is a transcendental number. The essence is that Euler's number e ist transcendental, and that e raised to an algebraic power is also transcendental. However, since e^(i pi) equals -1 (cf. https://www.youtube.com/watch?v=F_0yfvm0UoU and https://www.youtube.com/watch?v=mvmuCPvRoWQ or https://www.youtube.com/watch?v=Yi3bT-82O5s and https://www.youtube.com/watch?v=-dhHrg-KbJ0) and since -1 is not transcendental, pi cannot be algebraic (cf. https://www.youtube.com/watch?v=seUU2bZtfgM).

"3. From 1882 we have been told that Squaring a Circle is an UNSOLVED GEOMETRICAL PROBLEM." -- Since thanks to Lindemann we know why pi is transcendental, we immediately know also that it is impossible to square a circle. Therefore, this geometrical problem isn't an unsolved problem anymore, because it's not a problem anymore: We know the solution -- namely, that there is no solution.

"4. Hippocrates' work has been ignored, although squaring of circle was done. It is a Historical Blunder." -- Since thanks to mathematical logic we know that squaring the circle is impossible, we need not care about anybody's efforts to square the circle. All such claims are illusions; at best, they are more or less close approximations.

This settles the matter from the mathematical point of view. It just remains to test the various mathematical predictions by real-world investigations, determining pi experimentally.

Dear Scholar

Very good. In my view if you want to live in darkness/ illusion of Lindemann's WRONG world continue it. YES continue it...

I am doubly happy that I came out of 3.141.. as pi and

2. pi is a transcendental number ( TN)

-------------------------------------------------

You are the loser and be blind to the TRUTH.

---------------------------

1. I STRONGLY believe that pi is (14-root2)/4

2. Pi is an algebraic number

3. Squaring a Circle is MAN CREATED it as UNSOLVED problem

-----------------------------

Wrong number 3.141... made people BLIND to the truth about circle

You may call me BLIND or a FOOL yes a FOOL I repeat million times, and still I prefer these abusing words to ,rather than believing 3.141... as pi and ,transcendental number etc.

OK

"1. I STRONGLY believe that pi is (14-root2)/4" -- This cannot be pi, because it's too large, which is proven by using circumscribing polygons.

Circumscribing polygons are a perfect geometrical construction, having the circle inscribed with them as a square does. Therefore, they are on the same level as most of your constructions, starting from the circle inscribed with a square.

So, circumscribing polygons fulfill all of your requirements for a valid geometrical construction. Why should you be afraid of them?

But if you just don't like circumscribing polygons and prefer a different geometrical construction -- since you are interested in finding new ways to find pi anyway -- better have a look at https://www.youtube.com/watch?v=d-o3eB9sfls because it's about a very nice geometrical construction, I'm quite sure you'll like it!

"2. Pi is an algebraic number" -- Do you have any idea about the ratio between the amount of algebraic numbers compared to amount of the transcendental numbers among the whole set of real numbers?

"You may call me BLIND or a FOOL yes a FOOL I repeat million times, and still I prefer these abusing words" -- No, I never did, and I never will; why should I?

You made all these nice constructions showing the presence of (14 – sqrt2)/4, so how could you be blind or a fool? Just a small test is missing to see the real meaning of this number.

Dear Scholar

Did you or any body see circumscribed polygon of large number of sides about a circle? It is just an imagination. We do not know that polygon having so many sides remains outside circle

I do not mean you. I was abused so : idiot ,arrogant, etc.

If I look at the youtube I would be losing ORIGINALITY of the method.

"Did you or any body see circumscribed polygon of large number of sides about a circle? It is just an imagination. We do not know that polygon having so many sides remains outside circle" -- We do know very well, I told you already several times how to construct it!

So, oncemore for you: Take your circle inscribed with a square as you use it frequently yourself. In these constructions of yours, does the square remain outside the circle (except for the midpoints of its sides where it coincides with the circle)?

"I do not mean you. I was abused so : idiot ,arrogant, etc." -- Oh; well, you seem to be somewhat stoic, but everybody has the right to.

However, previously you wrote: "You are the loser and be blind to the TRUTH." Why did you write it, and whom did you mean by that?

"If I look at the youtube I would be losing ORIGINALITY of the method." -- Of which method, please? It is not fully clear to me what you mean here.