Pi or Phew??? The Circle Line Ain't Consist of Strainght Lines!!!

In micro scale, you treat outer limit and inner limit as the SAME value, that's why you conclude the circle line is the SAME as both outer limit and inner limit whose value would validate Pi.

This is a FALLACY of thinking! Cause when you enlarge the micro scale to be 90°, the circle line will equal BETWEEN 1.4142 AND 2. And it's NOT necessarily 1.5701 AKA pi/2. Either in micro scale and 90° scale, the circle line value equals BETWEEN outer limit and inner limit. Why you treat micro value to be IDENTICAL with 90° scale???
The exact reality is, such circle line ain't straight line, and it must be beyond the inner limit but not beyond outer limit. Straight line approach would be correct only if the circle line was a bunch of micro straight lines which is not the case.

By real experiment, Phew still has the chance to beat Pi. ^_^

The correct value of circle line is between pi and outer limit.

After much thought, Danang has made the revolutionary discovery that a circle has, indeed, no straight lines. The world holds its breath for the next breakthrough.

Thank you, Kami.
Anyway most, if not all of my posts are nonmainstream. It takes time to come to firm conclusion whether it's true or false.
But something for sure: I've been doing research with data and logic. Not following textbooks blindly as done by so many people as well as 'academic society'.

To research independently is among the most pleasurable activities on earth even though hardly people would hear discoveries I have found through such research.

C'est la vie 😀

For 1° angle, scale 1000 meters of radius, both chords (tan & sin) equals +/- 17.453 meters each, the space between both chords equals 0.038 meters, or 3.8 centimeters.
when the arc gets straighten, it will become 17.453 meters plus 0.166 meters AKA 16.6 centimeters that emerges outside the scords to be 8.3 centimeters + 8.3 centimeters at both edges of the chords.

Or ii we take the scale 100 meters of radius, there will be:
2 x 1.7453 meters of chords with the space 0.38 centimeters or 3.8 milimeters. the straighten arc will be 1.7453 meters and 2 x 0.83 centimeters, or 8.3 milimeters each.

Does it make sense? You tell me.

One thing for sure: IT'S BEYOND 1.7453 meters, as THE PI TERRITORY.

So... Pi is INCORRECT, a bit shorter than it should be.

This is why it's hard to meet Pi in REAL EXPERIMENT

Suppose the angle = one millionth degrees, then there will be one million tiny segments that are MISSING from pi based calculation.

Circle Area equals MORE than Pi. so is circumference which is actually MORE than 2 x Pi. Why? Because the smaller angle, sin & tan chords will be relatively in the same length, for human sight only reach to +/- milimeter scale while there always SPACE between tan & sin chords. The curved lines also never be handled by pi based calculation which is stuck on Straight Lines.

Bruh, π is literally defined as circumference/diameter. You just can't have a rational value for π

Bruh, π is literally defined as circumference/diameter. You just can't have a rational value for π

Firsly we should diagnose the circle reality under logic way instead, i.e. in a tiny angle, chords - either for sin and tan - both lengths are are relatively the same, and less than the arc length. That's why pi size is not align with the actual C/D.

I used to think phew is right only for 1D, while for 2D pi is right. Please skip my old post about it.

Either for 1D and 2D phew 3.17157 applies well, at least in real experiment.

Challenge for Pi based calculation:
Can you do the same as Phew?



The ingredients are available on the actual circle:
0.2928932
0.7071067 etc.
and some algebra & phytagoras

You've wrapped your brain up on your own axle.

Show where the circumference of a circle deviates from 2piR in euclidean geometry.

Challenge for Pi based calculation:
Can you do the same as Phew?



The ingredients are available on the actual circle:
0.2928932
0.7071067 etc.
and some algebra & phytagoras

What even do you want to achieve here? All you showed is area calculation with Pythagoras theorem. And correct me if I'm wrong, but the area in purple is ≈ 0.2929 and not 0.1465, is it? What even is your STATEMENT? You must have one, right?

You've wrapped your brain up on your own axle.

Show where the circumference of a circle deviates from 2piR in euclidean geometry.

Logic first. You cannot measure an arc by staight line.
Under 1000 meters of radius and 1° of angle, two chords: as long as 17 meters and 45 centimeters and 3 milimeters each, with a space of 3.8 centimeters in which an arc stays, the consequence is, the arc becomes longer than both cords.

Quote from: Danang on April 22, 2024, 01:36:42 PM

Challenge for Pi based calculation:
Can you do the same as Phew?



The ingredients are available on the actual circle:
0.2928932
0.7071067 etc.
and some algebra & phytagoras

What even do you want to achieve here? All you showed is area calculation with Pythagoras theorem. And correct me if I'm wrong, but the area in purple is ≈ 0.2929 and not 0.1465, is it? What even is your STATEMENT? You must have one, right?

The area size of phew is correct. It's (0.2928932x1):2.

The killer point is:
ALL AREAS ON THAT DIAGRAM, EITHER RECTANGLE AND CURVED, MAKE PERFECTLY 2X2=4. AND THERE ARE SIMILARITY OF SIZE BETWEEN CERTAIN AREAS IN THE CIRCLE AND AREAS OUTSIDE THE CIRCLE.

Can pi based measurement do the same? Feel free to show it.

>> Rectangle, triangle, curved areas

The killer point is:
ALL AREAS ON THAT DIAGRAM, EITHER RECTANGLE AND CURVED, MAKE PERFECTLY 2X2=4. AND THERE ARE SIMILARITY OF SIZE BETWEEN CERTAIN AREAS IN THE CIRCLE AND AREAS OUTSIDE THE CIRCLE.

Can pi based measurement do the same? Feel free to show it.

Before you make your killer point, go pick up a grammar textbook.

By all areas, what exactly do you mean? Are you telling me that the area I've marked in black is equal to the area I've marked in red?

Logic first. You cannot measure an arc by staight line.
Under 1000 meters of radius and 1° of angle, two chords: as long as 17 meters and 45 centimeters and 3 milimeters each, with a space of 3.8 centimeters in which an arc stays, the consequence is, the arc becomes longer than both cords.

What are you on and where can I get some?
Jokes aside, since middle school, we've all been taught about π. We were even given an experiment. "Take a thread and wrap it around the circumference of a circle and cut it when you go one full circle. Now take the thread and wrap it around the diameter of the same circle. The thread will cover the diameter a little more than three times." And if you're precise and use a large circle, you'll come close to 3.14. That's it. There's no need for angles and tan and cos and sin chords and whatever mess you have in mind.

In micro scale, you treat outer limit and inner limit as the SAME value, that's why you conclude the circle line is the SAME as both outer limit and inner limit whose value would validate Pi.

No, the way it works is you make something which is an upper bound, and something which is a lower bound. Then the real value lies somewhere between.
e.g. with your demonstration of a 4 sided shape, you have a lower bound of 2*sqrt(2), i.e. 2.8284, and an upper bound of 4.
This upper and lower bound does not tell you it is the actual value of pi, it just provides an upper and lower limit.
You then need to go to a smaller angle, and as you do you get a better upper and lower limit, as they converge to the value of pi.

In effect, what you are trying to do is find an n sided shape, in one case, the distance from the centre to the corner is 1 unit, so it fits inside the circle and the perimeter of this shape is a lower limit on the value of 2*pi; in the other case the distance from the centre to the centre of a side is 1 unit, so the circle fits inside it and the perimeter of this shape is an upper limit on the value of 2*pi.

One thing for sure: IT'S BEYOND 1.7453 meters, as THE PI TERRITORY.

Or you can do the math properly.

But before you even try doing that, your calculator is internally using pi.

But doing this, you want to use an angle of 1 degree, this means you are going for a 360 sided polygon. But you take half the angle to calculate the value of tan (the upper bound) and sin (the lower bound), and multiply that by 360 to get the bounds for pi.

Doing this we get 3.1416724047 as an upper bound and 3.1415527794 as a lower bound.
The value of pi, 3.1415926536, fits nicely between these.

So still no problem there.

In your case, you are adding in steps which are ultimately unnecessary
First you are scaling up the size of the circle, which means you then need to divide by it to get back to pi.
And you are using both sides of the sector/chord/tangent, which means the perimeter will bound 2*pi, so you then need to divide by 2.
And in doing so, you show extreme dishonesty by failing to round correctly and stating them to the point they are equal.
The value you provided for tan was 17.453735581...
Notice how the digit after you rounded is a 7?
The standard rules of rounding, as 7 is greater than or equal to 5, YOU ROUND UP! not down.

And what makes it even more damning is that the standards don't apply when you are finding an upper and lower bound. When doing that, it doesn't matter what the value is you always round down for the lower bound and up for the upper bound.
So doing that honestly, you still get 17.454 for the upper bound and 17.543 for the lower bound.

You have dishonestly rounded to get your upper bound as less than the actual lower bound.
No wonder you have entirely failed.

You then proceed to add in extra BS about "the space between chords" that is entirely irrelevant and does not affect the calculation at all.

Then you basically just complain that it doesn't match your BS number which doesn't work at all.

Where was this difference in chords in your prior BS about 90 degrees? No where, because it is pure BS.

We see that the sine version is a straight line. The tangent version produces an apex further away, and the arc is cutting that corner, meaning it is shorter, but still longer than the straight line.

Suppose the angle = one millionth degrees, then there will be one million tiny segments that are MISSING from pi based calculation.

No, they will be missing from your calculation, because you don't do the math properly.

Circle Area equals MORE than Pi

It equals pi*r^2.
For a unit circle, it is pi. Not more. No matter how much BS you invent, it will not be more.

Because the smaller angle, sin & tan chords will be relatively in the same length, for human sight only reach to +/- milimeter scale while there always SPACE between tan & sin chords.

Which just further shows the 2 values converge.
But no, just like the length of sin and tan converge, the space between them shrinks to nothing.

And do you know why there is the disparity?
Because the circumference is proportional to radius.
So that extra bit gets split up among every chord.

e.g. in the previous example, you had a difference of 0.000665.
If you multiply that by 360, you get 0.239, which is more than you 0.038.
So no problem there.

The curved lines also never be handled by pi based calculation which is stuck on Straight Lines.

Yes it is, by having 1 value which overestimates, and 1 value which underestimates.
That means the curve lies between.

You accept that with your example at 90 degrees. Why pretend it doesn't work now?

in a tiny angle, chords - either for sin and tan - both lengths are are relatively the same, and less than the arc length.

No. For tiny angles, all three lengths are basically the same. But tan is slightly longer than the arc which is slightly longer than the arc.
It doesn't matter how small you go, the tangent will always be longer than the arc length which will always be longer than the sin.
We can see this by doubling up.
The tangent is a long path with a single corner.
The arc is a curved and more direct path which is shorter, it cuts the corner.
And sine is a straight path being the shortest.

Anyone who says otherwise either has no idea what they are talking about, or they are lying.

Challenge for Pi based calculation:
Can you do the same as Phew?

Considering phew is wrong, why would we want to?

Under 1000 meters of radius and 1° of angle, two chords: as long as 17 meters and 45 centimeters and 3 milimeters each, with a space of 3.8 centimeters in which an arc stays, the consequence is, the arc becomes longer than both cords.

Why don't you try this in practice, filming the entire thing without any cuts, and show what you get?
And no, one is 17 m, 45 cm and 3 mm; the other is 17 m, 45 cm and 4 mm. The arc is in between.

AND THERE ARE SIMILARITY OF SIZE BETWEEN CERTAIN AREAS IN THE CIRCLE AND AREAS OUTSIDE THE CIRCLE.

Is there? or are you just lying like you do so often?

e.g. I assume you are claiming the yellow square is the same area as either one or both of the yellow portions inside the circle you have highlighted. But can you prove it?
No. You can just assert it must be true.

e.g. going for the yellow, the yellow square outside is easy.
You have a unit circle. So the length from the centre along the diagonal to the yellow square is 1. So the horizontal distance is 1/sqrt(2)=sqrt(2)/2. So the width of the yellow square is (1-sqrt(2)/2). So the area of the yellow square is (1-sqrt(2)/2)^2 = 1+2/4-2*sqrt(2)/2 = 1+1/2-sqrt(2)=1.5-sqrt(2), which is roughly 0.08578643763.
Inside the circle is more complex. We have the quarter circle (with an area of pi/4), from which we then subtract the square and 2 triangles.
The square is sqrt(2)/2 wide. The rectangles have 1 length of sqrt(2)/2, and one length of (1-sqrt(2)/2).
This gives us a total area we need to subtract of (sqrt(2)/2)^2 + 2*(1/2)*(sqrt(2)/2)*(1-sqrt(2)/2) = (sqrt(2)/2)*((sqrt(2)/2) + 1-sqrt(2)/2)=sqrt(2)/2
So the area in yellow is pi/4-sqrt(2)/2, or roughly 0.0782913822109.

So no, the area is not the same. You falsely claim it is to pretend pi must be 3.171573

If danang is a transtemporal being, if a 3D vector were introduced to the 2D sine, what would it be to get his result?

Next up on the news, Indiana Phew Bill

Should we wander to various discourses while the basic is being neglegted?

Calculator force you to use imaginery constant called "Pi" along with inacurate trigonometry.

Try 5° angle, with radius 100 m, or anything you wish... and you'll dump Pi right away.

Feel free to post it 👌

If danang is a transtemporal being, if a 3D vector were introduced to the 2D sine, what would it be to get his result?

3-1 = 2 

Quote from: Danang on April 23, 2024, 01:52:49 AM

Logic first. You cannot measure an arc by staight line.
Under 1000 meters of radius and 1° of angle, two chords: as long as 17 meters and 45 centimeters and 3 milimeters each, with a space of 3.8 centimeters in which an arc stays, the consequence is, the arc becomes longer than both cords.

What are you on and where can I get some?
Jokes aside, since middle school, we've all been taught about π. We were even given an experiment. "Take a thread and wrap it around the circumference of a circle and cut it when you go one full circle. Now take the thread and wrap it around the diameter of the same circle. The thread will cover the diameter a little more than three times." And if you're precise and use a large circle, you'll come close to 3.14. That's it. There's no need for angles and tan and cos and sin chords and whatever mess you have in mind.

Use tape, homade one is okay. Thread is risky to inacurate.
Phew will manifest.

You can calculate everthing by suitable chord length. What you need is just imagination for 1 to 10 meters of chord. Pick angle = 10° or less. Radius 100 to 1000 m.
If you wanna do experiment with tools, that's even better.

In short, if the chord is relatively IDENTICAL with arc at, say, 5 ° angle, it means pi is useless. One of joke of the century 

Can pi geometry do the same as phew geometry?

Jackblack refused to show it.

Okay, I knew you don't dare to present something inapplicable.

Should we wander to various discourses while the basic is being neglegted?

You mean the basics of understanding upper and lower limits and how the constrain the value, showing your nonsense is wrong?
The basics of trying to justify claims instead of just baselessly asserting things must be true?

Calculator force you to use imaginery constant called "Pi" along with inacurate trigonometry.

That is your claim which you cannot justify.

In short, if the chord is relatively IDENTICAL with arc at, say, 5 ° angle, it means pi is useless.

No, it means nothing like that.
The point of the process is that the upper bound and lower bound converge.
i.e. they become very close, and that places it close to the true value?

One of joke of the century 

In order for you to be a joke, you would need to be funny.
You aren't funny. You are pathetic.

Can pi geometry do the same as phew geometry?

Again, why would anyone care to replicate BS which just leads to BS?

Can you justify your BS? NO! You just assert it must be true.
Why should the yellow regions be equal?

😃 and again, you refuse to respond the challenge of 5° calculation. Should I show it? ~

And I don't think pi proponents would show 5° capculation, in which the chord length and the arc length are relatively IDENTICAL. 🤔

Here you are 👇

Before I can prove you wrong, let me get this straight: you believe that the ration of circumference to diameter is equal to 3.1715?

Before I can prove you wrong, let me get this straight: you believe that the ration of circumference to diameter is equal to 3.1715?

It is!

Quote from: EarthIsRotund on April 24, 2024, 09:20:26 PM

Before I can prove you wrong, let me get this straight: you believe that the ration of circumference to diameter is equal to 3.1715?

It is!

Now that that is clarified, what is the value of 90° in radians?