6 hours ago, mike.appleby said:

since no one wants to read the paper and some are just intent on attacking me, let me clarify something

Let me clarify a few things:

“Reading the paper” can’t be a requirement, per our rules. As I pointed out before, material for discussion must be posted here. Not conveyed via links or uploads

Attacking what you post is not attacking you. They are quite distinct. Challenging your claims is what happens in science.

I started this paper to prove Pi has dimensions, During my journey, i realised that pi does not govern curvature in the vacuum (oh how i can hear the teeth grinding now) .

Why do you expect grinding? Is there a mainstream claim that pi “governs” curvature? Please share it.

In GR, energy-momentum is the primary thing thst governs curvature

Rather i found that Z₀ does. this is realised due to the fact that nature does not provide perfect circles. (again teeth grinding).

Again, who claims this?

You’re arguing against a strawman

just read the paper and at least look at the logic/non logic that i used, then you can attack my idea and not me.

Post the idea.

Everything up until deriving Gravity and explaining what it is, is on me, after that is when ai used my theory to answer other questions and solve issues (again based on my theory, weather right or wrong) such as the de broglie wave (later called particle duality) and the 2 slit experiment.

But don’t post the AI stuff

On 7/24/2025 at 7:53 AM, joigus said:

Transcendental numbers would be something like the beyond of the beyond. That's the realm of pi, e, and phi (the golden ratio).

The golden ratio is not transcendental:

[math]\varphi =\dfrac{1+\sqrt{5}}{2}[/math]

Or putting it another way, it is a solution of the quadratic equation:

[math]\varphi^{2} - \varphi - 1 = 0[/math]

[If the above LaTex doesn't render, please refresh browser]

The golden ratio has an interesting property: it is representative of a family of numbers that are the least rational of all the numbers. By contrast, the Liouville numbers are numbers that are more closely approximated by rational numbers than all other numbers, and they are transcendental.

48 minutes ago, KJW said:

The golden ratio is not transcendental:

φ=1+5–√2

Or putting it another way, it is a solution of the quadratic equation:

φ2−φ−1=0

[If the above LaTex doesn't render, please refresh browser]

The golden ratio has an interesting property: it is representative of a family of numbers that are the least rational of all the numbers. By contrast, the Liouville numbers are numbers that are more closely approximated by rational numbers than all other numbers, and they are transcendental.

You're right. It's not. It's the most irrational number according to iterated fraction decomposition (or whatever it's called). That's what threw me off and I (incorrectly) included it in the list.

Thank you.

Continued fractions. That's the name. It's more irrational than any other irrational number, but not transcendental.

"More irrational" meaning the next continued fraction approximation is about as bad as the previous one.

Meaning,

\[ \varphi=\frac{1}{1+\frac{1}{1+\frac{1}{\cdots}}} \]

because there's always a 1 coefficient in the next iterative step.

Really appreciated +1.

Edited July 25Jul 25 by joigus
correction

1 hour ago, joigus said:

You're right. It's not. It's the most irrational number according to iterated fraction decomposition (or whatever it's called). That's what threw me off and I (incorrectly) included it in the list.

Thank you.

Continued fractions. That's the name. It's more irrational than any other irrational number, but not transcendental.

"More irrational" meaning the next continued fraction approximation is about as bad as the previous one.

Meaning,

φ=11+11+1⋯

because there's always a 1 coefficient in the next iterative step.

Really appreciated +1.

I think it is interesting that there are two distinct, even somewhat contrary, notions of degrees of irrationality. For example, one can consider the following sequence as a sequence of increasing irrationality:

rational numbers

solutions of quadratic equations with integer coefficients

solutions of cubic equations with integer coefficients

solutions of quartic equations with integer coefficients

...

solutions of polynomial equations of finite degree n with integer coefficients

...

transcendental numbers

Or alternatively, one can consider how well a given number can be approximated by a rational number relative to the size of the denominator of the rational number, as indicated by the irrationality exponent [math]\mu(x)[/math] in the expression:

[math]\left|x - \dfrac{p}{q}\right| < \dfrac{1}{q^{\mu}}[/math]

Quite remarkably, the Liouville numbers, which are transcendental numbers, have infinite irrationality exponent and are most closely approximated by rational numbers, whereas the golden ratio, a solution of a quadratic equation, with irrationality exponent 2, is poorly approximated by rational numbers, being an extreme case of the Hurwitz inequality:

[math]\left|x - \dfrac{p}{q}\right| < \dfrac{1}{\sqrt{5}q^2}[/math]

Even worse than the golden ratio are other rational numbers (approximated by rational numbers that are not equal to the number), which have irrationality exponent 1.

3 hours ago, swansont said:

Let me clarify a few things:

“Reading the paper” can’t be a requirement, per our rules. As I pointed out before, material for discussion must be posted here. Not conveyed via links or uploads

Attacking what you post is not attacking you. They are quite distinct. Challenging your claims is what happens in science.

Why do you expect grinding? Is there a mainstream claim that pi “governs” curvature? Please share it.

In GR, energy-momentum is the primary thing thst governs curvature

Again, who claims this?

You’re arguing against a strawman

Post the idea.

But don’t post the AI stuff

Ok understood. I am now going to take the advice given

3 hours ago, swansont said:

Let me clarify a few things:

“Reading the paper” can’t be a requirement, per our rules. As I pointed out before, material for discussion must be posted here. Not conveyed via links or uploads

Attacking what you post is not attacking you. They are quite distinct. Challenging your claims is what happens in science.

Why do you expect grinding? Is there a mainstream claim that pi “governs” curvature? Please share it.

In GR, energy-momentum is the primary thing thst governs curvature

Again, who claims this?

You’re arguing against a strawman

Post the idea.

But don’t post the AI stuff

Understood, sorry. I am going to take exchemists advice (which i think is brilliant and insightful) and re assess the theory from a new angle. That was exactly what I was looking for in the criticism and challenges to it. I will return when I have adjusted it.. until then thank you all

No problem, I do apologise if I came across as a tad rude, I have had this kind of ridicule my whole life and I can get a little defensive about it.. as I tried to say the whole time, I do respect and appreciate all the criticism and advice from everyone

Thank you

On 7/23/2025 at 6:48 PM, mike.appleby said:

After 2 years of work

You spent 2 years on this?
Thats alot of hardwork

I think the idea that π emerges not just mathematically but as a resonant feature of space is intriguing. It reminds me of how natural frequencies in string theory or cavity QED systems define discrete allowed states — your analogy to “π-locked curvature shells” kind of follows that logic.

But I was wondering: have you tried expressing this through a formal action or Lagrangian? It might help clarify whether π is a true physical scaling factor or just a geometric coincidence

Hi, i am currently adjusting it to show that pi does not need to be dimensional, but the whole thing will remain as is just there will be something added to clarify.. apparently they don't like it if you mess with pi, and now I see the error. I will keep you updated.. thank you for your comment.

7 minutes ago, mike.appleby said:

Hi, i am currently adjusting it to show that pi does not need to be dimensional, but the whole thing will remain as is just there will be something added to clarify.. apparently they don't like it if you mess with pi, and now I see the error. I will keep you updated.. thank you for your comment.

It has some flaws and you are working on the most critical one but,I personally find it very interesting.
I was also thinking about Pi before i found your post.

Can you tell whether are you aiming for quantum theory or classical?


Best Of Luck.

The idea of π as a deeper physical signal of resonance is intriguing, but treating it like a dimension or a field constant misrepresents what π actually is — a dimensionless geometric ratio, not a physical axis.
I’ve been thinking more about your idea that π plays a deeper role in the structure of space — and I agree that it's very interesting. The fact that π keeps showing up in physics — from spherical geometry to black hole entropy and quantum resonances — suggests it's not just a mathematical artifact.

But I think there’s a more physically accurate way to express your insight, without treating π as a dimension-:

1. Instead of viewing π as a physical dimension, you could describe it as a resonant scaling factor that naturally appears due to the geometry of space.
   For example:

   In circular and spherical systems, standing waves form only when the wave fits the boundary:

   [math]λn=2πrn\lambda_n = \frac{2\pi r}{n}λn=n2πr[/math]

   π shows up in the quantization conditions, not because it’s a dimension, but because of the geometry.

This same logic applies in:

• Spherical harmonics,

• Vacuum field oscillations (if the vacuum resonates),

• Black hole entropy [math]S∝A∝4πr2S \propto A \propto 4\pi r^2S∝A∝4πr2[/math],

• And the energy levels of confined systems (atoms, quantum wells).

So rather than saying “π is a dimension”, you might say something like:

“We propose that π emerges as a resonance quantizer in spherical vacuum curvature modes. These π-locked shells represent standing geometric waveforms of curvature, not a new spacetime axis.”

I respect the unique path you’re exploring — and I hope this helps refine it further.

I was thinking to start exploring Pi and make a theory but you have started first,so now its your task.
You should fulfill the task,as you started it. Because ideas belong to the universe, not to individuals. And if you’re the one who can finish the journey — with clarity, honesty, and rigor — then that’s your gift and your responsibility.

Just now, KJW said:

transcendental numbers

Or alternatively, one can consider how well a given number can be approximated by a rational number relative to the size of the denominator of the rational number, as indicated by the irrationality exponent μ(x) in the expression:

∣∣∣x−pq∣∣∣<1qμ

Quite remarkably, the Liouville numbers, which are transcendental numbers, have infinite irrationality exponent and are most closely approximated by rational numbers, whereas the golden ratio, a solution of a quadratic equation, with irrationality exponent 2, is poorly approximated by rational numbers, being an extreme case of the Hurwitz inequality:

∣∣∣x−pq∣∣∣<15–√q2

Even worse than the golden ratio are other rational numbers (approximated by rational numbers that are not equal to the number), which have irrationality exponent 1.

Thank you for exploring this further. +1

This question is far from fully worked out so 20th century studies have revealed that the 19th cent pat heirarchy of integers, rationals, reals, complex, etc.

Yes louiville's theorem is important but the new stuff was ushered in by Hensel and his p-adics., leading to the notion of other number fields that are different from the reals

@mike.appleby It might be worth exploring the mathematical question of what is a number a bit further and selecting a suitable understanding for your purposes.

Understanding that sequence ( integers, rationals, reals, complex, etc.) is enough for your purposes.

Suffice it to say the 'Pi ' is a real number, nothing special at all.
As such it appears in many ways in mathematics, in geometry, calculus, trigonometry etc, just like any other number.

But note I mentioned coefficients before.

Coefficients are more general than numbers in that are modifiers, but they can refer to other things than quantity.

Numbers are the usual ( but not exclusive) quantifiers.

Numbers are quantifiers of properties that can carry units or dimensions.

Young's modulus for example carries units.

But other properties such as refractive index do not.
Nevertheless they still need quantifying.

But there are also different types of number.

And these different types obey different rules of arithmetic.

For example adding first and fifteenth make no sense at all.

Such numbers are called Ordinal Numbers nad carry no meaning of quantity.

Numbers that convey quantity are called Cardinal Numbers.

Remember also that, for instance π is a symbol or representation of the number itself: It is not the nember.

I called it poetically ironic because Buckinghams π theorem is named after the mathematicians use of the capital Pi to represent multiplication in the same way capital sigma is used to represent addition.

So as (nearly) always it is more complicated than we might like.

Hi all, after taking the advice posted, I took another deep look at the theory. I realised to my amazement that the suggestion to couple pi with something else normalised to 1 actually already exists within the theory. The twist factor already does it.. if you apply the twist factor to the equation over 3 dimensional space xyz, then normalise xy to =1(at 360 degrees) then z (which represents the tangential twist is shown between 0 and 1 0-360degrees). This provides the same outcome as my initial theory without the need for pi to have units..rather I give the twist factor the units... i will post the updated work once it is done..thank you all.

1 hour ago, Dhillon1724X said:

It has some flaws and you are working on the most critical one but,I personally find it very interesting.
I was also thinking about Pi before i found your post.

Can you tell whether are you aiming for quantum theory or classical?


Best Of Luck.

The idea of π as a deeper physical signal of resonance is intriguing, but treating it like a dimension or a field constant misrepresents what π actually is — a dimensionless geometric ratio, not a physical axis.
I’ve been thinking more about your idea that π plays a deeper role in the structure of space — and I agree that it's very interesting. The fact that π keeps showing up in physics — from spherical geometry to black hole entropy and quantum resonances — suggests it's not just a mathematical artifact.

But I think there’s a more physically accurate way to express your insight, without treating π as a dimension-:

1. Instead of viewing π as a physical dimension, you could describe it as a resonant scaling factor that naturally appears due to the geometry of space.
   For example:

   In circular and spherical systems, standing waves form only when the wave fits the boundary:

   λn=2πrnλn=2πrnλn=n2πr

   π shows up in the quantization conditions, not because it’s a dimension, but because of the geometry.

This same logic applies in:

• Spherical harmonics,

• Vacuum field oscillations (if the vacuum resonates),

• Black hole entropy S∝A∝4πr2S∝A∝4πr2S∝A∝4πr2,

• And the energy levels of confined systems (atoms, quantum wells).

So rather than saying “π is a dimension”, you might say something like:

“We propose that π emerges as a resonance quantizer in spherical vacuum curvature modes. These π-locked shells represent standing geometric waveforms of curvature, not a new spacetime axis.”

I respect the unique path you’re exploring — and I hope this helps refine it further.

I was thinking to start exploring Pi and make a theory but you have started first,so now its your task.
You should fulfill the task,as you started it. Because ideas belong to the universe, not to individuals. And if you’re the one who can finish the journey — with clarity, honesty, and rigor — then that’s your gift and your responsibility.

Hi maybe we could collaborate once I nail down the most important error. As I said earlier, I am putting this out open source so that we can advance science not to claim credit (if it's worth it) so I don't mind if we work together.. that goes for everyone....

39 minutes ago, mike.appleby said:

Hi maybe we could collaborate once I nail down the most important error.

I will help wherever i can without even collaborating.

Thanks for giving me opportunity.I will look forward to it.

Can you clarify,
What your aim is?
What your work aims to do?

10 hours ago, KJW said:

I think it is interesting that there are two distinct, even somewhat contrary, notions of degrees of irrationality.

Agreed. There's perhaps no simple definition of a "degree of irrationality".

For lack of a better term, I would call the one based on continued fractions a criterion based on how non-algorithmic the approximation is, the one based on Liouville's numbers a metric definition, and the one based on polynomial equations an analytic one.

Which one is more relevant as concerns natural laws? One can only wonder at this point.

4 hours ago, mike.appleby said:

ealised to my amazement that the suggestion to couple pi with something else normalised to 1

I have dipped in an out of this thread so please forgive me if I am repeating other contributions from good posters.

Pi is not physical, neither is a circle, square or triangle. They are idealised geometric objects and numbers that can be derived from them.

Platonic.

You will absolutely never find a circle in the universe

Physics is empirical, things we can observe, measure and detect.

It turns out that the mathematics of those objects can be used effectively in physical theories.

Pi is not physical.

22 minutes ago, pinball1970 said:

I have dipped in an out of this thread so please forgive me if I am repeating other contributions from good posters.

Pi is not physical, neither is a circle, square or triangle. They are idealised geometric objects and numbers that can be derived from them.

Platonic.

You will absolutely never find a circle in the universe

Physics is empirical, things we can observe, measure and detect.

It turns out that the mathematics of those objects can be used effectively in physical theories.

Pi is not physical.

yes i now agree, as i have explained. i found the flaw in my thinking and am correcting it now, thank you for your imput, i will be updating soon (no units for Pi) so i hope you will keep popping in and contributing..

Just to add my two cents ...

Mike should realize that we use mathematical models to describe the workings of physical reality.
These models have to be mathematically self consistent, otherwise they are useless.
Pi, along with other mathematical constants, and the whole of mathematic theory, are the building blocks and tools used to build the models.
The tools and building blocks are not a result of the physical reality.

4 hours ago, Dhillon1724X said:

I will help wherever i can without even collaborating.

Oh great ...
Add more AI content to get further down the rabbit hole.

I think it is worth saying that every situation in which π appears is in some way connected to a circle. To see that this is true, for any given expression in which π appears, consider why it is π that appears in the expression. This means tracing the number back to its definition, which was originally based on the circle. For example, consider the gamma function of a half-integer:

[math]\displaystyle \Gamma(\dfrac{3}{2}) = \int_{0}^{\infty} \sqrt{t}\ \exp(-t)\ dt[/math]

[math]\displaystyle \text{Let } t = x^2\ \ \ \ ;\ \ \ \ dt = 2x\ dx[/math]

[math]\displaystyle \Gamma(\dfrac{3}{2}) = \int_{0}^{\infty} 2x^2\ \exp(-x^2)\ dx[/math]

[math]\displaystyle = \int_{0}^{\infty} \exp(-x^2)\ dx\ \ \ \ \ \text{(integration by parts:}\ u=x,dv=2x\exp(-x^2)\ \text{)}[/math]

[math]\displaystyle \int_{0}^{\infty}\int_{0}^{\pi/2} r\ \exp(-r^2)\ d\theta\ dr = \dfrac{\pi}{4} \int_{0}^{\infty} 2r\ \exp(-r^2)\ dr[/math]

[math]\displaystyle = \dfrac{\pi}{4} \int_{0}^{\infty} \exp(-t)\ dt = \dfrac{\pi}{4}[/math]

[math]\displaystyle \int_{0}^{\infty}\int_{0}^{\pi/2} r\ \exp(-r^2)\ d\theta\ dr = \int_{0}^{\infty}\int_{0}^{\infty} \exp(-x^2-y^2)\ dx\ dy[/math]

[math]\displaystyle = \int_{0}^{\infty} \exp(-x^2)\ dx\ \cdot \int_{0}^{\infty} \exp(-y^2)\ dy = \dfrac{\pi}{4}[/math]

[math]\displaystyle \text{Therefore }\ \ \Gamma(\dfrac{3}{2}) = \int_{0}^{\infty} \exp(-x^2)\ dx = \dfrac{\sqrt{\pi}}{2}[/math]

[If the above LaTex doesn't render, please refresh browser]

In this case, the connection to a circle is the use of polar coordinates to evaluate the definite integral of the Gaussian function.

Edited July 25Jul 25 by KJW

37 minutes ago, KJW said:

I think it is worth saying that every situation in which π appears is in some way connected to a circle. To see that this is true, for any given expression in which π appears, consider why it is π that appears in the expression. This means tracing the number back to its definition, which was originally based on the circle. For example, consider the gamma function of a half-integer:

[math]\displaystyle \Gamma(\dfrac{3}{2}) = \int_{0}^{\infty} \sqrt{t}\ \exp(-t)\ dt[/math]

[math]\displaystyle \text{Let } t = x^2\ \ \ \ ;\ \ \ \ dt = 2x\ dx[/math]

[math]\displaystyle \Gamma(\dfrac{3}{2}) = \int_{0}^{\infty} 2x^2\ \exp(-x^2)\ dx[/math]

[math]\displaystyle = \int_{0}^{\infty} \exp(-x^2)\ dx\ \ \ \ \ \text{(integration by parts:}\ u=x,dv=2x\exp(-x^2)\ \text{)}[/math]

[math]\displaystyle \int_{0}^{\infty}\int_{0}^{\pi/2} r\ \exp(-r^2)\ d\theta\ dr = \dfrac{\pi}{4} \int_{0}^{\infty} 2r\ \exp(-r^2)\ dr[/math]

[math]\displaystyle = \dfrac{\pi}{4} \int_{0}^{\infty} \exp(-t)\ dt = \dfrac{\pi}{4}[/math]

[math]\displaystyle \int_{0}^{\infty}\int_{0}^{\pi/2} r\ \exp(-r^2)\ d\theta\ dr = \int_{0}^{\infty}\int_{0}^{\infty} \exp(-x^2-y^2)\ dx\ dy[/math]

[math]\displaystyle = \int_{0}^{\infty} \exp(-x^2)\ dx\ \cdot \int_{0}^{\infty} \exp(-y^2)\ dy = \dfrac{\pi}{4}[/math]

[math]\displaystyle \text{Therefore }\ \ \Gamma(\dfrac{3}{2}) = \int_{0}^{\infty} \exp(-x^2)\ dx = \dfrac{\sqrt{\pi}}{2}[/math]

[If the above LaTex doesn't render, please refresh browser]

In this case, the connection to a circle is the use of polar coordinates to evaluate the definite integral of the Gaussian function.

i agree somewhat, my new definition uses co-ordinates to enable the dimensions for pi. ie pi is dimensionless but in physical applications is accompanied by a magnetic torsion field twist factor in 3 dimensional space. when we look at a circle, we are looking at a flat plain ie x,y co-ordinates. this adds up to 360 degrees, by setting this to a value of 1 (1 loop of 360 degrees) we can then dictate that the z axis portrays the Longitudinal twist of a helix. thus giving rise to the ability to couple it with pi and assign units to the pair (carried by the twist). this then allows me to use pi in the way i did without declaring it to be anything other than it is.. more is coming from this

50 minutes ago, KJW said:

I think it is worth saying that every situation in which π appears is in some way connected to a circle. To see that this is true, for any given expression in which π appears, consider why it is π that appears in the expression. This means tracing the number back to its definition, which was originally based on the circle. For example, consider the gamma function of a half-integer:

Γ(32)=∫∞0t√ exp(−t) dt

Let t=x2    ;    dt=2x dx

Γ(32)=∫∞02x2 exp(−x2) dx

=∫∞0exp(−x2) dx     (integration by parts: u=x,dv=2xexp(−x2) )

∫∞0∫π/20r exp(−r2) dθ dr=π4∫∞02r exp(−r2) dr

=π4∫∞0exp(−t) dt=π4

∫∞0∫π/20r exp(−r2) dθ dr=∫∞0∫∞0exp(−x2−y2) dx dy

=∫∞0exp(−x2) dx ⋅∫∞0exp(−y2) dy=π4

Therefore   Γ(32)=∫∞0exp(−x2) dx=π−−√2

[If the above LaTex doesn't render, please refresh browser]

In this case, the connection to a circle is the use of polar coordinates to evaluate the definite integral of the Gaussian function.

how do you insert all these equations? or do you type them?

i have decided to start a new conversation with my new and improved theory called - VRT - a Pi based twist reality, this was done to clear the air and start fresh.. hope you guys dont mind, hopefully ill see you there

Edited July 25Jul 25 by mike.appleby

24 minutes ago, mike.appleby said:

Sure, there are theories that tackle the mathematical issue and give us somewhat explanations, but none of them explain what the underlying reason is that all curvature (no matter where observed) is governed, or at least connected through this dimensionless constant

Can you give some specific examples of this? As KJW has noted, circles and cyclic phenomena are often involved, and there’s nothing that needs to be justified about that.

28 minutes ago, mike.appleby said:

if we don’t believe that (π) is random, then what within the vacuum ensures that it is always the result of proportionality of a circles radius to its circumference (without exception)?

The ratio of circumference to diameter must have a value. Since the difference between circles is only a matter of linear scaling, that ratio is the same for all circles. Nothing mystical about this at all. That’s how math works.

2 minutes ago, swansont said:

Can you give some specific examples of this? As KJW has noted, circles and cyclic phenomena are often involved, and there’s nothing that needs to be justified about that.

i cant give examples if i dont know of any, what he just said was posted just today and i did not read it before writing this theory. i could change that line but i already posted the theory in a new topic thread

Just now, mike.appleby said:

i cant give examples if i dont know of any, what he just said was posted just today and i did not read it before writing this theory. i could change that line but i already posted the theory in a new topic thread

How can you state it as a premise without having some examples of it?

Just now, mike.appleby said:

how do you insert all these equations? or do you type them?

There are several ways.

The forum editor allows you to to do some very simple but very useful things like superscript and subscript directly, and is the only tech forum I Know that does this.
Click on the three dots at the right hand end of the top bar.

You can enhance that by using the extended character set to select other simple maths symbols, greek letters and the like.

Just open (by typinginto the search bar) the Windows tool 'Charmap.exe'
Then select the symbols you want and copy/paste them inot the text.
It can be more efficient to have two or three selected and delete the ones you don't want from the pasting.

All this only gives in line maths.

So if you want fractions or more complicated expressions, As KJW is showing., we use LaTex or MathML.

There are a couple of free online editors.

Just assemble the expressions, then copy and paste from the editor to SF.

I use a commercial version called MathType.

https://www.sciweavers.org/free-online-latex-equation-editor

https://editor.codecogs.com/

Just now, pinball1970 said:

Pi is not physical.

Just now, KJW said:

I think it is worth saying that every situation in which π appears is in some way connected to a circle.

Actually you can construct Pi geometrically, without a circle.

Draw a line about 5 units long.

You have constructed all the number between ~0 and ~5

This must include Pi as it is such a number.

But it is impossible to draw a line of exactly Pi units length with standard construction techniques.

2 minutes ago, swansont said:

13 minutes ago, studiot said:

Actually you can construct Pi geometrically, without a circle.

Draw a line about 5 units long.

You have constructed all the number between ~0 and ~5

This must include Pi as it is such a number.

But it is impossible to draw a line of exactly Pi units length with standard construction techniques.

haha, i love this.. non negotiable, best argument ive seen in a while...

7 hours ago, MigL said:

Oh great ...
Add more AI content to get further down the rabbit hole.

I just suggested him something.Whether he reach a dead end or build something,it’s on him.

Giving critiques or just help someone to improve is AI too?

I know he is doing something very different and it is flawed.But if I I can help in anything then I will help.

I already told him that it’s flawed.

Edited July 26Jul 26 by Dhillon1724X

On 7/26/2025 at 5:20 AM, studiot said:

Actually you can construct Pi geometrically, without a circle.

Draw a line about 5 units long.

You have constructed all the number between ~0 and ~5

This must include Pi as it is such a number.

This assumes that you know, at least approximately, the value of π.

Just now, KJW said:

This assumes that you know, at least approximately, the value of π.

Yes it does.

So what ?