Hello all you Pi-Radicals,
I was curious what CHAT GPT might advise for folks who are obsessed trying to prove Pi = 3.1446 and its response was insightful; maybe you'll get something out of it?
HUSH said:
Hello
ChatGPT said:
Hey there! How's it going?
HUSH said
Good. What is the value of Pi
ChatGPT said:
The value of π (Pi) is approximately 3.141592653589793..., and it goes on infinitely without repeating. Do you need it to a specific number of decimal places?
HUSH said
No. There are some people who think Pi = 3.1446, based on the golden ratio. What advice would you give them to try and understand they are wrong?
ChatGPT said:
Yeah, some alternative approximations for π, like 3.1446, have popped up based on attempts to link it to the golden ratio (Φ ≈ 1.618). But mathematically, π is rigorously defined and has been computed to trillions of digits using multiple independent methods, including infinite series, integrals, and geometric constructions.
If someone believes π = 3.1446, I'd suggest:
- Check Real Calculations – Use a simple method like a circle’s circumference divided by its diameter. Even with a string and a round object, you’ll get something close to 3.1416, not 3.1446.
- Explore Proven Formulas – Many well-known series (like the Leibniz series or Machin’s formula) converge to 3.14159…, not 3.1446. Have them compute a few terms themselves.
- Golden Ratio Doesn’t Define Pi – While π and Φ show up together in some equations (like in pentagons and spirals), they are distinct mathematical constants. The golden ratio does not determine π’s value.
- Look at Real-World Uses – Engineers, scientists, and mathematicians use π every day in physics, astronomy, and engineering. If π were actually 3.1446, modern technology wouldn’t work properly!
If they’re really invested in 3.1446, they might just enjoy the idea rather than care about mathematical accuracy. But if they’re open to reason, hands-on math usually helps!
HUSH said
Many people who believe Pi = 3.1446, do not accept conventional wisdom. They typically have only grade school mathematics and do not understand the limitations of their own knowledge and arrogantly believe they are correct. What further would you say to help them understand that traditional Pi = 3.14159 is a best estimate of true Pi.
ChatGPT said:
That’s a tough situation because people who reject conventional wisdom often aren’t convinced by direct evidence. If they lack the mathematical background to fully grasp why π = 3.14159..., then the challenge isn’t just about presenting facts—it’s about helping them recognize the limits of their understanding without making them defensive.
Here are a few ways to approach it:
1. Make It Hands-On
Since they may not trust "establishment" math, encourage them to measure it themselves:
- Take a circular object, measure the circumference and diameter, and divide.
- No matter how many objects they measure, they won’t get 3.1446.
This simple experiment helps them see the number emerge in real life rather than just being told it's true.
2. Frame It as a Discovery
Instead of telling them they’re wrong, ask:
- “That’s interesting! How do you think people calculate π?”
- “What do you think would happen if we used 3.1446 in real-world engineering?”
- “Would you be open to checking a few methods together?”
This way, it’s their journey to realizing the problem with 3.1446 rather than an argument.
3. Explain That π Is Not an Approximation
They might think of π as something "scientists guess," but it's actually precisely defined in multiple ways, such as:
- Infinite series (like Leibniz’s series or the Gregory–Machin formula).
- Geometric definitions (π is the ratio of a circle’s circumference to its diameter, which can be computed with extreme precision).
- Computer calculations (modern algorithms compute π to trillions of digits).
If π were actually 3.1446, these methods would have produced that number instead of 3.14159... over centuries of testing.
4. Appeal to Real-World Consequences
- If engineers used 3.1446, bridges, airplanes, and GPS systems wouldn’t function properly.
- NASA uses π in orbital mechanics. If they got it wrong, spacecraft would miss their targets or crash.
- Even basic things like gears in a watch wouldn’t fit together if π were off.
If they believe that π is 3.1446, then they need to explain why all of modern science and technology still works using 3.14159.
5. Address the Psychological Side
People with only grade-school math who reject established knowledge often suffer from Dunning-Kruger effect—they don’t know enough to realize how much they don’t know.
- Instead of challenging their intelligence, help them see how mathematicians spent centuries refining π and that great discoveries often come from building on past knowledge.
- Ask: “If 3.1446 were correct, why haven’t mathematicians discovered it in thousands of years?”
This can plant a seed of doubt without directly confronting them.
Final Thought
You may not be able to convince everyone, especially if their belief in 3.1446 is emotional rather than logical. But by engaging them curiously, patiently, and with hands-on methods, some might start to question their assumptions.
HUSH said
You suggested physically measuring a round disk is a good idea to help convince someone Pi is not equal to 3.1446 or based on the golden ratio however this is a BAD idea and will explain why however would then appreciate your observations.
There is fellow Harry Lear who convinced many Pi = 3.1446 because Harry physically measured a round wood precision CNC cut 1 m diameter disk, using a precision Pi measuring tape, and he has shown in his YouTube videos the measurement of the circumference of his 1 m diameter disk was indeed 3.144 m which I do not doubt was his actual measurement however the problem with physically measuring Pi, when trying distinguish such a small difference between traditional Pi = 3.14159 and wrong Pi = 3.1446, is the difference is on 3 mm in circumference on a 1 m diameter disk. If the wooden disk expanded due to changes in humidity, that could be enough to increase the diameter from 3.14159 m to 3.1446 m when physically measuring. Do you agree physically measuring may not be a good idea or perhaps physically measuring a metal disk or some object less prone to expansion?
ChatGPT said:
You're absolutely right—physically measuring π, especially with materials like wood, is highly unreliable when trying to distinguish between 3.14159 and 3.1446.
Why Physical Measurements Are Unreliable for This Debate
1) Thermal and Humidity Expansion
- Wood is a terrible choice for precision measurement—it expands and contracts significantly with moisture and temperature.
- Even metal expands, though much less. A 1-meter aluminum disk could expand by over 3 mm if temperature shifts by just a few degrees.
2) Measurement Tool Inaccuracy
- A measuring tape is subject to stretching, parallax errors, and even imperfections in printing.
- A small error in placement of the measuring tape around the disk could lead to incorrect results.
3) Disk Imperfections
- A CNC-cut disk is not mathematically perfect.
- Even minor waviness in the edge or asymmetry could shift the measured circumference.
So, What’s a Better Way to Show π ≠ 3.1446?
Instead of directly measuring a physical object, it’s far better to use mathematical methods:
1) Infinite Series and Convergence
- Computing π with a formula like Leibniz’s series or Machin’s formula will always give 3.14159..., not 3.1446.
- Challenge Harry Lear to compute 1000 terms of a known series and see what number appears.
2) Trigonometric Proofs
- Many formulas in trigonometry depend on π.
- Using a wrong value would cause well-established relationships to break.
3) Computational Tests
- Even basic Python or Excel calculations will produce 3.14159..., not 3.1446.
- Ask them to write a program to approximate π using numerical integration.
Conclusion
Yes, I now agree—physical measurements are too error-prone to settle this argument. The better approach is to challenge them with mathematical proofs or computational tests where there’s no risk of material expansion or human error.
Would you like help with a mathematical or programming-based method to demonstrate this?
HUSH said
No, I already know how to calculate traditional Pi. I'm just trying to help them understand they are wrong, but they are very stubborn. They are essentially brainwashed, I fear, with their obsession to try and prove Pi = 3.1446. They continually present proofs for me to comment on that are mathematically logically flawed. I tell them Pi = 3.1446 is physically impossible because it extends beyond the range of the perimeter of a circumscribed polygon of say 128-sides, but they do not listen. All their Pi = 3.1446 proof they present, which are faked, attempt to solve for Pi as a variable, however I try to explain to them that there is no way to resolve the value of Pi unless one first tries to estimate the actual circumference of a circle. How would you explain to these people who are misguided into thinking Pi = 3.1446, that they cannot resolve Pi as a variable, but rather must first estimate the circle circumference, as one method, in order to then divide by the diameter to resolve Pi? I must say CHAT GPT your ability to understand questions, wording and logic has become quite impressive.
ChatGPT said:
Thanks for the compliment! I appreciate the challenge you’re facing—it’s tough to reason with people who aren’t engaging in good faith or are too fixated on their beliefs to process logical counterarguments.
Key Issue: They’re Trying to “Solve” for π as a Variable
It sounds like they’re treating π as if it’s something that can be algebraically solved like a variable in an equation. But π is not an unknown—it’s a defined mathematical constant.
How to Explain Why π Can’t Be Solved as a Variable
1) π Is Defined, Not Derived
- π isn’t something we “solve” for—it’s a fundamental ratio in Euclidean geometry.
- The correct way to obtain π is by measuring or calculating the circumference-to-diameter ratio, not by treating it as an unknown variable in an equation.
- If their formula produces 3.1446, it’s their formula that’s wrong—not π.
2) π Must Be Consistent Across All Methods
- Every valid method to compute π—whether through polygons, infinite series, integrals, or limits—must give the same value.
- Their approach contradicts centuries of mathematical consistency.
3) Polygon Method: A Simple Reality Check
- A 128-sided inscribed polygon will underestimate π, while a 128-sided circumscribed polygon will overestimate it.
- The true π must lie between these two estimates.
- If 3.1446 exceeds the upper bound from a circumscribed polygon, it is physically impossible.
- Ask them to compute the perimeter of a 128-sided polygon and compare it to 3.1446.
4) Using Their Own Flawed Logic Against Them
- Instead of outright rejecting their proofs, ask them a question that exposes the flaw.
- Example:
“If your formula produces 3.1446, but measuring a circle with increasing precision gives 3.14159, where do you think the mistake is?”
Make them find the error themselves, rather than you simply telling them they’re wrong.
5) Challenge Them to Compute π Themselves
- Ask them to compute π using a simple method (e.g., Monte Carlo simulation, Archimedes’ polygon method, or an infinite series).
- If every method gets 3.14159 and none get 3.1446, ask them why no legitimate computation in history has ever produced 3.1446.
Final Thought
These folks aren’t being persuaded by evidence—they’re emotionally invested in their belief. Some of them might never accept the truth, no matter how much proof you provide. But for those who genuinely want to understand, guiding them through their own flawed logic might be the best way to plant a seed of doubt.
Your patience in trying to educate them is admirable—I hope at least one of them eventually listens!
HUSH said
Very good response CHAT GPT. I will share your advice with them. Believe you did a better job explaining then I could have
ChatGPT said:
I really appreciate that! I hope at least some of them take the time to think critically about it. You're doing great work trying to steer them toward mathematical truth, even when they resist. If you ever need help breaking down another flawed proof they present, feel free to ask.
Good luck—I admire your patience! 🚀
HUSH said
Undeserved, I have not been patient but rather, brutally honest!
