Either area or circumference of a circle is a finite entity having a finite magnitude to be represented by a FINITE NUMBER. In other words Pi is a finite number and an algebraic number.
Our present pi value 3.1415926...in fact is that of a polygon.
Dragging limit concept here we have attributed to circle and thrust on circle as its pi value.
Real Pi is exact
In Euler's formula : e to the power i pi + 1 = 0 , pi here refers pi radians 180 degrees and NOT pi constant 3.14..
If constant is involved, Euler's formula itself becomes WRONG.
It means Euler's formula rejects outright, pi constant 3.14 in its fold.
As this is a fact then HOW could C.L.F. Lindemann (1882) say pi CONSTANT is a transcendental number based on Euler's formula?
Are we to accept that
Pi radians 180 degrees = Pi constant 3.14..?
email to : [email protected]
Dear Sarva,
We should not be running a political debate here.
You criticize the fact, that Pi is transcendental.
The beginning of a constructive and rigorous discussion on the topic would be to clarify the key concept TRANSCENDENTAL NUMBER to make sure, all of us are talking about the same thing.
That means, it is necessary, that you formally state, what you understand by TRANSCENDENTAL NUMBER.
Dear Sarva, in Euler formula pi is expressed by radians and it is the constant real number 3.1415....The fact that pi is a transcendental number is not a contradiction with the fact that pi is constant.
Why do you say that pi constant -> Euler formula wrong, what is your doubt?
Gianluca
Dear Scholar
Pi is not a transcendental number but an algebraic number
My submission is not for fun, please
You may read the attachment please
Dear Sarva,
I first thank you for your criticism, because we need it in Science.
Now about your critiscism, I have two fundamental remarks after fully reading your article and question:
1. You never formally defined the concept "TRANSCENDENTAL NUMBER"
2. We should avoid to mix (Science, Creator, Beauty, All celestial are sperical)
Thanks
Dear Scholar
what is wrong with the limit concept, have a look at it please
Dear Sarva,
We should not be running a political debate here.
You criticize the fact, that Pi is transcendental.
The beginning of a constructive and rigorous discussion on the topic would be to clarify the key concept TRANSCENDENTAL NUMBER to make sure, all of us are talking about the same thing.
That means, it is necessary, that you formally state, what you understand by TRANSCENDENTAL NUMBER.
Dear Scholar
For your right doubt refer page no 57 top corner (or page 86 at the bottom ) in the enclosed book
"Either area or circumference of a circle is a finite entity having a finite magnitude to be represented by a FINITE NUMBER. In other words Pi is a finite number and an algebraic number." -- What do you mean by "finite number"?
"Our present pi value 3.1415926...in fact is that of a polygon." No, it isn't; no polynom that you can draw has exactly that value as its circumference length. This is so because all polynoms, both inscribed and circumscribed ones, are just approximations for the true pi value.
Dear Scholar
"Finite " I mean specific and clear
Yes, 3.141... is an approximation. And it implies that there is another number and that is real , specific, limited, finite and exact and that is Cosmic Pi Number.
" 'Finite' I mean specific and clear" -- So, here is a test for you: Do you agree that 1/10 is such a specific and clear number? (There will be a follow-up question, but I want to make sure that we start from the same position.)
Yes: 1/10 (= 0.1 in the decimal system) is indeed a simple, specific and clear number. Having said this unambiguously, let's represent 1/10 not in the decimal sysem but in a different numbering scheme, namely in the binary system. I choose the binary system because it is used by computers. So, how does 1/10 look like "for the computer"?
First of all, we should better represent "10" in the binary system, of course, and then look for the reciprocal value -- like this: 1010 = 10102 (with the subsetted index giving the arithmetic system). So, the very same specific and clear number, 1/10 in the decimal system, is 1/1010 in the binary system. Do you know the result in the binary system?
Dear Scholar
Are you really interested in knowing a new truth OR interested in debate ?
I am sorry I am a wrong person for arguments and debate un-endingly.
The point here is that you are making a fuss about pi being "represented by a FINITE NUMBER", which is a concept that I don't understand. So, I asked these questions which I think could help me to understand it better. Please, let's just get it done quickly; have a look at 1/10 in the binary system and tell me how this fits into your concept of a "finite number".
"I don't know" -- Sorry: What exactly is it that you don't know?
Again: You said that, without doubt, "one tenth" is a finite number since it is specific and clear. In the decimal system, "one tenth" is written as "0.1", but in the binary system, "one tenth" is written (cf. Peter Breuer's remark) as "0.0001100110011001100110011001100110011001100110011001100110011001100..." Now, my question is: Do you still consider "one tenth" as a finite number? (Hint: This is a trick question; don't fall for it!)
"The word you are searching for is 'rational'. Not 'finite'." -- Well, I don't think so, because S. J. Reddy emphasizes sqrt2 being at the heart of his approach. So I think his point just is that he denies pi to be transcendental.
"An irrational dislike of irrationality?" -- Hmm: Isn't here one logical "not" too much?
Again: You said that, without doubt, "one tenth" is a finite number since it is specific and clear. In the decimal system, "one tenth" is written as "0.1", but in the binary system, "one tenth" is written as "0.0001100110011001100110011001100110011001100110011001100110011..." Now, my question is: Does this representation influence your judgement about "one tenth" being a finite number? Would you have considerd "one tenth" being a finite number if you had started from the binary representation?
Or, let's have a look at another number: What do you think of 9.99999999999999999999999999999999999999999...?
"In Euler's formula : e to the power i pi + 1 = 0 , pi here refers pi radians 180 degrees and NOT pi constant 3.14.." -- How do you know that?
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