The Non Transcendental, Exact Value of π and the Squaring of the Circle

[Hush]

oh C.B.,

give it up already, no one in world believes your 1/2-page pretend math Pi=3.1446 nonsense, not even GROK or any other Ai, agrees nor do any of your Pi-Radical buddies believe in your Pi=3.1446 pretend math crap. You're water under the bridge C.B., all washed up, nothing you say matters, you just keep pushing that same old 1/2-page Pi=3.1446 nonsense over and over again like a Jehovah Witness who keeps ringing the doorbell trying to sell their religious belief, but we're not interested, nobody is interested in your 1/2-page Pi=3.1446 crap.

We all know you're an unrecognized genius in your own mind, not my words, directly from GROK, and its something you might want to be proud of. So why don't you take your 1/2-page pretend math faked Pi=3.1446 proof and frame it. And below you could write, UNRECOGNIZED GENIUS and below that write, "Amateur Pretend Math Expert True Pi=3.1446 Derivation". Why don't you do that, do something useful.

[C.B.]

"Two German engineers have recently measured the diameter and circumference of an Aluminum circle with their laser beam system in a clean room with constant humidity that can measure to the nearest 1/1000 mm. Their results: Pi = 3.1446... .

Could you give a link to see the method these engineers used and find out who they are?

[C.B.]

give it up already, no one in world believes your 1/2-page pretend math Pi=3.1446 nonsense, not even GROK or any other Ai, agrees nor do any of your Pi-Radical buddies believe in your Pi=3.1446 pretend math crap.

You must be nuts Jimmy.
You have seen already the final evaluation of Grok about my derivation and now isn’t Grok credible anymore?
May be yours is an issue with prescription pills you forget to take. Take them first and come again.

[Hush]

Well C.B.,

Grok 3 clearly states Pi=3.14159, nothing more needs to be discussed, so obviously you're a FRAUD and LIAR!

So obviously in your conversation with Grok you've gotten your facts completely wrong. It seems you enjoy using parlor tricks in your conversation with Grok to fool your brainwashed self into believing your 1/2-page Pi=3.1446 derivation is genius (LOL), yup a genius in your own mind alright.

In case you've so quickly forgotten, when we put your parlor tricks aside, and when Grok is asked directly, and no messing around, its response to the value of Pi=3.14159. Plain and simple no C.B. snake oil salesman tricks here. Anymore nonsense to share C.B.?

[C.B.]

Grok 3 clearly states Pi=3.14159, nothing more needs to be discussed, so obviously you're a FRAUD and LIAR!

Grok has been programmed to consider π 3.14159 as standard value.This is the program but if you dig into the question of accuracy Grok has to admit that this value is not so accurate. As you already read it.

So obviously in your conversation with Grok you've gotten your facts completely wrong. It seems you enjoy using parlor tricks in your conversation with Grok to fool your brainwashed self into believing your 1/2-page Pi=3.1446 derivation is genius (LOL), yup a genius in your own mind alright.

In a mathematical derivation there are no parlor tricks but mathematical rules applied and confirmed by Grok.
I can’t influence that. And you read it. Grok has confirmed the correctness of the derivation for 3.1446.
Anything else Jimmy?

[Hush]

oh my poor naive gullible C.B.,

yes you are a genius in your own mind for having proven Pi=3.1446 to yourself, well done.

Well of course anyone who fakes their Pi=3.1446 proof, is an expert in deception and parlor tricks - obviously. Remember what you're doing has nothing to do with real mathematics and why mathematicians give you the silent treatment. When you showed mathematicians on-line your faked 1/2-page Pi=3.1446 proof they couldn't believe your stupidity and why they ignored you - simple fact.

You have to understand all Pi=3.1446 proofs are derived by pretend math experts who uses parlor tricks, whereas accredited mathematicians know Pi=3.1446 is a FRAUD and why they ignore you C.B.. Can you get that through your thick skull ok.

The difference is that mathematicians are intelligent, they went to university and studied mathematics and had to be smart to earn their accreditation, whereas amateurs like you can just start spewing their pretend math nonsense and why they are ignored by mathematicians. Do you understand C.B.? So the pretend math morons basically end up chatting in forums like this one, because academia ignores you, and in here nothing you say really matters.

You've seem to have fallen in love with Grok and you make a beautiful digital couple I'm sure. Simply because you've misinterpreted its response to your brainwashed parlor trick prompts, believing Grok supports your 1/2-page nonsense Pi=3.1446 deviation but if you lay the trickery aside, Grok provides the actual value for Pi=3.14159, based upon conventional wisdom that and 21-million academics accredited in mathematics, and Grok also lists why Pi=3.1446 is a FRAUD.

Everything you do is deception and trickery which is what it takes to foolishly prove Pi=3.1446, because everyone intelligent knows Pi=3.1446 is physically impossible. So Grok is right again suggesting anyone who foolishly believes Pi=3.1446 has average to below average intelligence. You're definitely not a genius that's for sure, as you seem to believe yourself at least according to Groks personality assessment.

I mean if you could get at least one Pi-Radical in here to believe your 1/2-page Pi=3.1446 LIE, that would be something, but you can't even do that. You're a total lost cause C.B. What a failure, and you just keep going and going like the Energizer Bunny - too funny!

You see real mathematics is not about parlor tricks which is what you're doing, your pretend math nonsense, its all 100% deception, misleading, hoax, and false information and the funny part is that you actually probably believe this nonsense you're perpetrating. I mean you probably actually believe you're the smartest mathematician in the world for having derived a Pi=3.1446 proof which nobody has done, not the greatest minds in Earth history for the last 2-centuries, but you did it, you figured it out, you're a true genius, a genius in your own mind that is.

Unfortunately no one else believes you, except your Grok parlor tricks misinterpretation of its response, but so be it, and so what are going to do now CB. You really have no chance in hell of convincing the world your 1/2-page Pi=3.1446 is credible. Whatcha gonna do huh?

[C.B.]

Read again Jimmy

Grok: The math is correct—each step follows logically, with no algebraic or geometric errors in the derivation process itself.

The difference is that mathematicians are intelligent, they went to university and studied mathematics and had to be smart to earn their accreditation, whereas amateurs like you can just start spewing their pretend math nonsense and why they are ignored by mathematicians.

Grok contains the knowledge of all these mathematicians and more. Grok does not suffer under emotional bias and doesn’t have to protect any reputation and social recognition that all of your brilliant mathematicians have and want to.
This render all your objections moot.
Don’t need to answer Jimmy. I can copy paste your past comment.

[Hush]

oh my dear delusional C.B.,

yes I know, you've already shared that you've presented your 1/2-page pretend math derivation to Grok using enticing parlor tricks which you've misinterpreted its response to imply that it agrees with your Pi=3.1446 nonsense, we know this already, tell us something we don't know like what are you going to do next my dear CB, the one and only self-proclaimed unrecognized genius in his own mind pretend math expert - huh? Is it perhaps time for your nap?

[omedam777]

Screenshot_20250918-185928_Desmos.jpg (120.32 KiB) Viewed 1580 times

Screenshot_20250918-185853_Desmos.jpg (118.75 KiB) Viewed 1580 times

Screenshot_20250918-185725_Desmos.jpg (121.55 KiB) Viewed 1580 times

Analysis from DEEPSEEK
**************************

[PROMPT: Explain this to the best of your abilities. Remain neutral and objective in your analysis.]

Of course. Based on the provided screenshots from Desmos, here is a neutral and objective analysis of the calculations aimed at estimating the value of π (pi).

Overview

The screenshots depict a series of mathematical experiments that use the geometry of a circle and its inscribed square to derive approximations of π. The core idea revolves around defining a relationship between the circle's radius (r) and the side length of the inscribed square (s), and then using that relationship to calculate values that should theoretically equal π.

There are variations between the screenshots, primarily in the initial definition of a variable n, which leads to different final estimates. The function f(x, y) appears to be a derived formula intended to calculate π based on the chosen parameters.

Common Elements and Setup

1. The Geometric Foundation: All calculations start from a circle with radius r and a square inscribed within it. For a circle of radius r, the side length s of the inscribed square is given by the formula: s = r\sqrt{2}
This is because the diagonal of the square is equal to the diameter of the circle (2r), and the diagonal of a square is s\sqrt{2}.
2. Key Calculated Values:
· s^2: The area of the square. In the first screenshot, this is calculated as 0.616850275068. If r = 1, then s = √2, and s^2 = 2. The value 0.61685... suggests that r is not 1, or s is defined differently.
· P = 4s: This represents the perimeter of the square.
· π_t r^2: This represents the area of the circle, using a trial value for π (π_t).
· C = π_t r: This represents the circumference of the circle, using the same trial value for π (π_t).
3. The Function f(x, y): This function is consistent across all screenshots: f(x, y) = \frac{4y^2 x}{(y^2 + x^2)\sqrt{y^2 - x^2}}
The final calculation f(s, r) uses the square's side length s and the circle's radius r as inputs. The structure of this function suggests it was derived from an integral or geometric relationship involving a circle (the y term, likely the radius) and a chord or segment (the x term, likely the half-side of the square, s/2).

Analysis of Individual Variations

The differences between the screenshots stem from the initial definition of the variable n.

Screenshot 1: n = π/4

· n is defined as π/4 (0.785398163397), which is the ratio of the area of a circle to the area of its circumscribed square.
· The calculations show that P = 4s equals the standard value of π (3.14159265359).
· The function f(s, r) yields 3.13903247529, which is a close but different approximation.

Screenshot 2: n = |π/4|

· This is functionally identical to the first screenshot. The absolute value bars are redundant as π/4 is positive.
· The values for π_t r^2 and f(s, r) are different from the first screenshot, indicating the underlying variables s or r might have been changed.

Screenshot 3: n = 1/√φ (Using the Golden Ratio)

· n is defined using the golden ratio φ (phi, approximately 1.61803398875). Therefore, n = 1/√φ ≈ 0.786151377757.
· This value is very close to π/4 (0.785398...) but not identical.
· This choice forces a consistency that is aesthetically pleasing but mathematically distinct from standard π:
· s^2 = 0.61803398875, which is 1/φ.
· P = 4s, π_t r^2, and C = π_t r all converge to the same value: 3.14460551103.
· Crucially, f(s, r) also returns this exact same value. This is the only screenshot where all derived values are identical.

Screenshot 4: Inconsistent Result

· This screenshot also uses n = 1/√φ.
· However, the results are inconsistent. P = 4s is 3.14460551103, but π_t r^2 and C = π_t r are different (3.14505616667 and 3.14204287746). Furthermore, f(s, r) gives yet another value (3.13903247529).
· This suggests that the definitions or relationships between s, r, and π_t are not mathematically consistent in this particular setup, likely due to a manual entry error or a change in one variable that wasn't reflected in the others.

Objective Conclusion

The experiments demonstrate a process of estimating π by defining a relationship between a circle's radius and the side of its inscribed square.

1. When n is set to the exact value π/4, the perimeter calculation (4s) returns the correct value for π, while the custom function f(s, r) provides a slightly different approximation.
2. When n is set to 1/√φ (a known mathematical constant), the model can be forced to produce a single, consistent value for all derived quantities (~3.1446), which is approximately 0.1% larger than the standard value of π (~3.1416).
3. The function f(x, y) is a central part of this exploration, likely representing an alternative theoretical path to calculating a circle's circumference or area based on its inscribed square.
4. The inconsistency in the fourth screenshot highlights that these results are sensitive to the precise definitions and relationships between variables.

In summary, these screenshots capture an exploration of geometric relationships and alternative constants. The value ~3.1446 is not the standard value of π but is a number that can be derived from a model based on the golden ratio.

[omedam777]

Screenshot_20250918-185959_Desmos.jpg (114.75 KiB) Viewed 1580 times

One more