A Simple Experiment Proves π = 4

[LongtimeAirman]

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Zyxzevn.
The only thing that you have is the experiment.
An simple experiment with is very inaccurate.
Everything depends on that the balls have exactly the same speed.

Airman. We now have an experiment that proves that motion along a curve is 4/pi longer than previously thought.

It’s incredibly simple and easy to do, first demonstrated with wooden sections of a child’s train set. Steven’s transparent pvc tubing setup cost less than $100. One can use glue, cardboard and marbles instead.

Two tracks, circular and straight, with “linear” distances of 3.14 and 4 both become distance 4 when balls move in those tracks. That reveals more than a 20% error in distance and velocity calculations in curves.

Zyxzevn. Now, if we look at the experiment, I can clearly see that something is wrong.
I listed some of the things that should clearly be considered.
I also explained how these things will cause the balls to have different speeds.
It is clear that you do not understand it well, but
just denying these issues does not remove them.

You now have no good theory and no good experiment.

Airman. You keep denying the fact that there is no evidence of cumulative friction. You haven’t explained, you’ve merely suggested, that there is a friction, or cheating that only affects the circular track.

It's a fine experiment. You just don’t have a good answer to it.
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[Zyxzevn]

It's a fine experiment. You just don’t have a good answer to it.
.

It is a bad experiment, due to a bad setup.

For the experiment to work:
1) The speed of the ball just before entering the circular path
must be the same as the speed as it comes out of the circular path.
This speeds must be exactly match the ball that follows the straight path.
2) The paths must be exactly the same.
3) The height of the paths must be exactly the same.
4) The table must be exactly horizontal.
5) The measurements must be accurate.
6) The tubes must be perfectly smooth.

From the video it is clear that all these requirements are NOT met.

1) The ball is a lot slower when it leaves the curved path.
Just measure the amount of pixels that the ball goes in the curved path.
In the end the ball is very slow. So there is clearly a difference in resistance between both tubes.

2) Due to the tube, the ball follows the outside of the circular path. The bending of the
tube shall stretch the plastic tube and shall also affect the length of the path.

3) The height of the paths are not the same. The ball will follow the outside of the tube
in the curved path. So the ball will gain potential energy, while slowing down.
See:
\ / or \ O/ Sorry, my ascii does not have any circular characters.
\___O___/ \______/
Just like when you throw a ball into the air. It slows down and falls back.

4) Not visible in the video. Even a slight tilt of the table can affect the final speed of the balls a lot.

5) The measurements are totally inaccurate. It is not even clear that these tubes might be the same length
at all. I just have to trust the maker that it is somewhere near to it.

6) There is no way the tubes were industry level quality in smoothness. It is normal for bend tubes to
form dents.

From these simple observations, one can easily tell that the experimenter does NOT
know shit about physics. And that he does not know how to setup the experiment properly.
His experiment is a total failure. See the 6 point above.

But if he would know anything about physics, he would not be doing this experiment anyway,
because he would know that Pi does not change when movement is involved.
That is because Pi is always independent of movement.
A rope around a bottle does not get longer when I turn the bottle instead of my hand around the bottle.
It is even a very very silly idea.
But Miles does not understand it, that is because Miles does not know shit about maths.
He did not do the calculation as I did. Instead he invents all kinds of complex
physics to push his own false ideas. If you are good with physics and maths you can do these
complex calculations by using Pi=3.1415.. I am sorry to tell you, but Miles is not so good,
so invents his own maths and physics instead.

Pi is a mathematical constant, that does not change, WHATEVER you do with it.

And because PI=3.1415... , all stuff works exactly as we see it.

[Zyxzevn]

I see this Pi=4 thing as the result of the really bad education in the USA.

[Grey Cloud]

I'm rubbish at maths and fully admit that I may be missing something very simple here, but...
What relevance has the speed of an object moving around a circle to the area of the circle? That is, whether the object travels at 10 mph or 100 mph, the area of the circle does not change... at least here in Britain as far as I know.

[LongtimeAirman]

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Zyxzevn.
It is a bad experiment, due to a bad setup.

For the experiment to work:
1) The speed of the ball just before entering the circular path
must be the same as the speed as it comes out of the circular path.
This speeds must be exactly match the ball that follows the straight path.
2) The paths must be exactly the same.
3) The height of the paths must be exactly the same.
4) The table must be exactly horizontal.
5) The measurements must be accurate.
6) The tubes must be perfectly smooth.

From the video it is clear that all these requirements are NOT met.

1) The ball is a lot slower when it leaves the curved path.
Just measure the amount of pixels that the ball goes in the curved path.
In the end the ball is very slow. So there is clearly a difference in resistance between both tubes.

Airman. False. The experiment stops at the end of the loop since the loop cannot cross itself and stay on the flat surface. There is no final straight section to calculate final velocity.

I would consider adding a third s-curve and new final straight sections to allow the calculation. Releasing balls simultaneously then becomes a problem. Any solution has its pro’s and con’s.

Zyxzevn. 2) Due to the tube, the ball follows the outside of the circular path. The bending of the
tube shall stretch the plastic tube and shall also affect the length of the path.

Airman. False. We’ve covered this point before. Look at the two circumferences you’re trying to compare.

StevenOPiEq4finalTwo.gif (8.27 KiB) Viewed 8619 times

No overt bending or stretching is observed in the video. Any lesser yet significant bending or stretching amounts to friction. None is observed, we may assume there is no track deformation.

Zyxzevn. 3) The height of the paths are not the same. The ball will follow the outside of the tube
in the curved path. So the ball will gain potential energy, while slowing down.
See:
\ / or \ O/ Sorry, my ascii does not have any circular characters.
\___O___/ \______/
Just like when you throw a ball into the air. It slows down and falls back.

Airman. I disagree, all marks are hit simultaneously, and there is no observed slowing. I agree, the pvc tubing does allow the ball to bank slightly, but the difference is negligible and does not affect the experiment’s outcome.

Zyxzevn. 4) Not visible in the video. Even a slight tilt of the table can affect the final speed of the balls a lot.

Airman. False. Also not visible is any substantiation of a claim that amounts to fraud. There is no such evidence. Please do not make accusatory statements without any support whatsoever.

Zyxzevn. 5) The measurements are totally inaccurate. It is not even clear that these tubes might be the same length at all. I just have to trust the maker that it is somewhere near to it.

Airman. False. In what way are the "measurements" totally inaccurate? The experiment is described and documented. All marks are clear and are used in the video. Again, please do not make accusatory statements without any support.

Zyxzevn. 6) There is no way the tubes were industry level quality in smoothness. It is normal for bend tubes to form dents.

Airman. False. There is absolutely no evidence of any friction or erratic ball path behavior indicated. It’s clear you’ve never worked with pvc tubing. It’s very smooth and cooperative when bent gently and not folded.

Zyxzevn. From these simple observations, one can easily tell that the experimenter does NOT
know shit about physics. And that he does not know how to setup the experiment properly.
His experiment is a total failure. See the 6 point above.

Airman. I’ve answered your criticisms.

You’ve mainly demonstrated complete bias against the experiment. You’ve absolutely no proof of the majority of your claims but that doesn’t stop you from making and repeating those claims. You have absolutely no right to cast aspersions at Steven but that doesn’t stop you either.

Of course the experiment stands on its own. How does one discredit simple demonstrations of physics? Proof, you might say, of a good experiment.

......................................

Grey Cloud. What relevance has the speed of an object moving around a circle to the area of the circle? That is, whether the object travels at 10 mph or 100 mph, the area of the circle does not change... at least here in Britain as far as I know.

Airman. During motion, the physical distance of the curve may be longer but I don’t see any change of area. I suppose the ellipse rule where equal areas are described by equal times is not affected. As velocity is increased curvature is increased and so your question might better apply to the relationship between radius and angular velocity (see post above Re: A Simple Experiment Proves π = 4 http://www.thunderbolts.info/forum/phpB ... 115342mple Experiment Proves π = 4 ). Zyxzevn brought up area as another example of approximating pi somehow showing Miles wrong. That’s all that comes to my mind.
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[kell1990]

Pi is 3.14157 on out to a billion or so places. Get over it. It is not 4 and will never be 4, no matter how many posts are made trying to declare it as something else.

BTW, some of us have made a very good living existing in the Cartesian world, day in and day out. Whether it was in constructing refineries or chemical plants or wharves or high-rise buildings or some other kind of civil engineering project, we were always able to think in Cartesian day in and day out. X, y and z all the time. I really resent the snide remarks of some that some of us can "only think in two dimensions." (Some of us can actually think in 4 or more dimensions....who knew?)

Some of the newer members ought to think about this before they seek to dress some of us down.

[5boxen]

Can somebody just clarify what exactly is meant by "kinematic pi"?

I think that everyone would agree that usual pi is defined to be ratio of circumferences/diameter

It would clarify matters quite a bit imho to have a straightforward definition of "kinematic pi" as some ratio of easily understood quantities.

e.g if I have a circle (of radius R if it matters) and something traveling along it at constant speed s then what exactly is "kinematic pi" as a ratio?

[JouniJokela]

Can somebody just clarify what exactly is meant by "kinematic pi"?

I think I should be able, as it come's from my comment. -Though I must admit, that I haven't never thought before, that there actually is this kind of ratio.
Most of the usable calculation in this "area" is done with unit "m^2/s^2".
(Btw, Einstein's E=mc^2 is also basically "just" c^2)

This means its either "velocity squared", or "acceleration x lenght".
The Froude-law practically says that; "velocity squared" = "acceleration x lenght".
https://en.wikipedia.org/wiki/Froude_number
So this must be the correct unit when this ratio is calculated.
So basically as, for a straight line; x=v*t=4
then for the curved path it must be v^2/a and then forward with the eguations of angular acceleration etc,

https://en.wikipedia.org/wiki/Angular_acceleration

With these principles also Leonhard Euler generat his universal pump&turbine equations;
https://en.wikipedia.org/wiki/Euler%27s ... e_equation
"Y" is the "specific supply" which is a mass less unit and similarily valid for every turbomachine, water, gas or whatever it uses.

This forum doesn't support Math-jax equations. So to get some readable equations, I have to do it through figures.
I will do it some time in future.
This thema is very interesting; As I just calculated the Planck's constant through the speed of light, and for this calculation I need to find the "ultimate" diameter of a molecule; which I did through "kinetic gas theories", and now as I have this diameter, It's really easy to calculate the "nominal angular momentum of the speed of light".

Hell, my language must be some terrible Gibberish, but I have an idea here. THANKS.
I actually was expecting that I can get the elementary charge calculated directly when I have solved the Planck's constant. But I went out if Ideas. Now I have one again. If some is interested what I am talking here, see this;
https://www.researchgate.net/publicatio ... H_07102016
and here's more material, if some one get's fanatic;
https://www.researchgate.net/project/QE ... everything

... And just for clarity; in my world "Pi" is approx 3.1415, but this "4" ratio is very interesting observation.

[LongtimeAirman]

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5boxen, Welcome to the New Insights and Mad Ideas board.

Pi is still defined as the ratio of a circles’ circumference and diameter. In geometry, pi = 3.14.

The experiment shows us a new curved-motion metric. Objects in circular motion must travel 4/pi longer to complete a circumference than geometry currently assumes. For objects in curved motion, let’s call it kinematic motion, pi = 4.

The metric doesn't apply to linear and static dimensions. The metric only applies to distances and velocities along curves.

kell1990, while everyone makes errors, engineers make it work. Thank you Sir.
.

[5boxen]

Pi is still defined as the ratio of a circles’ circumference and diameter. In geometry, pi = 3.14.

The experiment shows us a new curved-motion metric. Objects in circular motion must travel 4/pi longer to complete a circumference than geometry currently assumes. For objects in curved motion, let’s call it kinematic motion, pi = 4.

The metric doesn't apply to linear and static dimensions. The metric only applies to distances and velocities along curves.
.

Thanks for the helpful reply.

I'm trying to think of a way to reproduce the youtube video's results, but in a simpler way where I don't have to build a bunch of tubes and such.

So, in my living room I have an old vinyl/LP turntable.
i.e. a circle of diameter 12in and, when turned on, rotations of 33 1/3 revolutions per minute.

Let's say I rest a penny near the outside of a record and turn it on.
If I did the math right, it takes about 1.8 seconds to complete exactly one revolution.

Statically, people would say that the penny travelled a distance equal to the (static) circumference of the circle, so distance = (static pi)*(diameter) = (3.14159...)*(12in) = about 37.7 in.

I'm trying to get a picture in my head of where the extra 4/pi longer time factor comes in.

I think I get a sense of where mathis is going with the cycloid story, but there my circle is rolling also in a linear direction. Do I need to do this as well? i.e. pick up my turntable and walk with it while it's turned on? But in the youtube video that doesn't seem to be required to get the phenomenon to happen...?

Interesting stuff!

[Zyxzevn]

[quote=Airman.] I’ve answered your criticisms. [/quote]

No you didn't.
Each of the problems are not addressed.
You just denied all the problems.

PI is not gonna change whatever experiment you do.
That is because PI is the circumference of a circle.
It is a mathematical CONSTANT that does not change in whatever universe or system.

But in your replies is clear that you are not doing physics.
Physics is about investigating each problem, and measure the problem.
You do not do that. You just deny the problems.

Let me show this with problem 1:

[quote=Airman.]False....[/quote]

What?
Did you NOT measure the speed?

Well I did not expect you did. Or even understand how you can do it.

So let me explain:

If an object moves in a movie, you can use the framerate to measure the speed of the object.
You have to take some things in account, because the camera may move as well.

But if you use each frame after then the next frame, you can draw a line between the first position of the
object, and then the next position. Correct these positions with the movement of the camera. It would be easier
if the camera would be completely still. After correction, the length of this line can be expressed in pixels.
If the camera is not moving towards the object, this line is DIRECTLY related to the speed of the object.
So if the object would go the same speed, we would see a similar length of the line.
If the object slows down, the length of the line will be smaller.
If you have a good measurement, you can even translate the pixels to meter/seconds.

Do that for the shown experiment for each frame in the curved path, and in the straight path.
Then make a graph, where you put the length of each line versus the time.

This will show you how the speed changes in the complete setup.

Is what you need to do yourself. It is how you do real physics.

If you do it, you will see that the graph of the ball in the curved path goes down a bit.

Do you know what that means?

[LongtimeAirman]

.

5boxen. I'm trying to think of a way to reproduce the youtube video's results, but in a simpler way where I don't have to build a bunch of tubes and such.

So, in my living room I have an old vinyl/LP turntable.
i.e. a circle of diameter 12in and, when turned on, rotations of 33 1/3 revolutions per minute.

Let's say I rest a penny near the outside of a record and turn it on.
If I did the math right, it takes about 1.8 seconds to complete exactly one revolution.

Statically, people would say that the penny travelled a distance equal to the (static) circumference of the circle, so distance = (static pi)*(diameter) = (3.14159...)*(12in) = about 37.7 in.

Airman. Your math is correct (pi=3.14).

Only one problem. A penny on a turntable is an example of rotational and not kinematic motion. The penny is part of the rotating, static dimensions of the turntable. The new curved motion metric doesn’t apply to axial or angular rotations.

Steven’s experiment applies to orbits, running or driving around curves.

Still, the turntable seems provocative – a spinning surface, the possibilities...

Steven’s experiment has two tracks, circular and straight, 55.3cm and 70.4cm long, side-by-side. Two balls enter the ramps, are accelerated by gravity, then enter the tracks at equal velocity and hit all marks simultaneously.

One might mount various pvc tracks on old vinyl records, unfortunately, the table’s spin would provide a constant acceleration outwards, with no way to shut the acceleration off (easily done with the end of Steven’s gravity assist ramp). Steven’s equal velocities are replaced with constant acceleration. I don’t see a way to demonstrate the curve metric using a turntable. Feel free to show me wrong.

5boxen. I'm trying to get a picture in my head of where the extra 4/pi longer time factor comes in.

I think I get a sense of where mathis is going with the cycloid story, but there my circle is rolling also in a linear direction. Do I need to do this as well? i.e. pick up my turntable and walk with it while it's turned on? But in the youtube video that doesn't seem to be required to get the phenomenon to happen...?

Interesting stuff!

Airman. Please review Miles’ pi papers. Essentially, orbits are accelerations. The term orbital velocity is a misnomer since it can be described by two orthogonal velocities. Those two velocities and time (3 variables) are necessary for a full analysis. The cycloid computation is an example containing all the necessary considerations.

Please don’t wander around with spinning turntables.
…………………………….

Zyxzevn.

I’ve answered your criticisms.

No you didn't.
Each of the problems are not addressed.
You just denied all the problems.

PI is not gonna change whatever experiment you do.
That is because PI is the circumference of a circle.
It is a mathematical CONSTANT that does not change in whatever universe or system.

Airman. It’s easier doing the experiment than hypothesizing all your problems. Thanks for the discussion. Everyone - including me - appreciates your contributions.
.

[Aardwolf]

If you do it, you will see that the graph of the ball in the curved path goes down a bit.

I don't think anyone is in any doubt that the ball in the circle is travelling slower but isn't that Mathis's point. Forward momentum is lost in the tube as it is in an orbit. To correctly account for the lost forward momentum you should use Pi=4 to calculate the time it takes to travel around the curved trajectory.

[LongtimeAirman]

Hello Aardwolf, I need to think about lost momentum. I would say that the pi calculation is used to determine distance around the circle, not time. Nevertheless I guess I need to think about that too.

Plotting distance versus time for both Pi=3.14 and Pi =4 may help everyone. I should have done this earlier.

Balls enter both tracks at the same initial speed 1.2m/s and hit their 4 marks simultaneously:

1. The ball in the circular track is slower than the straight track. There a friction slowing the ball in the circular track pi/4 when compared to the straight track.

or

2. Both tracks are the same length when the curve is measured with Pi=4.

.

[Aardwolf]

I would say that the pi calculation is used to determine distance around the circle, not time.

In geometry yes, but a space agency would want to know why the craft was late. Using Pi=4 solves the problem.

There a friction slowing the ball in the circular track pi/4 when compared to the straight track.

If it were due to friction it would have a cumulative effect and that plot would be a curve not a straight line.