A Simple Experiment Proves π = 4

[oz93666]

Because he specifically bought this type of tubing to make sure friction is not an issue..

??? really??? !!! this is very soft and flexible tubing if a ball is pressed harder into it's surface it will sink deeper in , guaranteed

Steven measured frame by frame and indeed there was no slowdown (same velocity), and thus yes because of the extra direction the path is effectively longer..

This defies the evidence of our own eye !! we can clearly see on the video the ball moves in a circular path , I suggest you are allowing a theoretical notion to override the evidence of your own eyes

The spin is not constantly changing, the ball spins one way only, you may have point that after falling down at the start of the curve the ball has to change orientation and cling to the side of the tube, but that is 1 moment and as measured that 1 moment did not slow down the ball, it is continues motion.

The orientation of the spin axis is constantly changing as it moves around the curved path , this requires a force , and perhaps work ... the ball in the curved path is not with it's spin axis at 90* to the table , this would require zero gravity or infinite centrifugal force , the angle is somewhere between 0 and 90 ( dependent on the speed of the ball ,hence on it's path around the curved path, the axis is constantly changing orientation.
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Can you see or do you agree that to make a curve any object has to make 2 directions? This is the simplest explanation of the difference. (to my simple mind).

I think it's better to consider it has one direction , which is changing due to the force from the tube wall.

Below Miles about this experiment.
ps. http://milesmathis.com/pi7.pdf

I was not impressed with that link....The main problem is we've all become armchair scientist ...theorising all day long , non of us (including me) can be bothered to perform the simple experiments , which I'm sure would very quickly clear this matter up ...

Best Regards ...oz

[oz93666]

If you measure the speed, the ball has indeed slowed down, which proves that the
whole idea of "longer path" is wrong. If the path was longer, it would not slow down.

It slows down in the same way as skiers slow down when they make curves on the snow.
Actually it is the best way to reduce speed for skiers.

The idea that PI can be 4 is wrong too, which is proven beyond doubt too.
Because it is a mathematical constant.

I would agree with that , I suggest the reason a skier slows down is the added centrifugal force from turning pushes him deeper in the snow , he's no longer skimming over the top , and is rapidly slowed ... if the skier had hard ice , or we used glass tube in the experiment , there wold be minimal slowing.

Without knowing it, Mathis has been "trolling" many people with his
bad understanding of maths, logic and basic physics.
And anything that he claims should be taken with a grain of salt.

He has got us thinking , which can't be bad.

[D_Archer]

Can you see or do you agree that to make a curve any object has to make 2 directions? This is the simplest explanation of the difference. (to my simple mind).

I think it's better to consider it has one direction , which is changing due to the force from the tube wall

No, a curve is not 1 direction, that is the whole point, it was a rethorical question.

Did you watch the mechanical universe video?* from 11:26 till 11:50 , you can see a circular motion is made by 2 directions.

*http://www.dailymotion.com/video/x2wiyaj

Or the short animation by John McVay > http://milesmathis.com/Pi4.avi

Regards,
Daniel

[Roshi]

What fascinates me about the circle - a perfect circle cannot exist in the physical world. It's is beyond our grasp.

If we would have super advanced tools and the objects in the Universe would be infinitely divisible, and would try to fabricate a perfect circle - either the radius or the circumference would be an irrational number. We could never see the edge of this perfect circle in the physical world.

Am I mistaken in some way? It seems we can only work with the idea of the circle in mathemathics, but in reality we must do with imperfect circles, and that is not because we don't have proper tools, no tool could make a perfect circle.

Or maybe I am mistaken, and this is a false paradox like the one when you always have to go half the distance to somewhere before going the full distance, then half of the half, and so on, and you can never reach the full distance.

On a computer screen a circle is as perfect as it's medium allows: the minimum pixel size. Does the Universe have a minimum size? The Plank length?

[D_Archer]

What fascinates me about the circle - a perfect circle cannot exist in the physical world. It's is beyond our grasp.

If we would have super advanced tools and the objects in the Universe would be infinitely divisible, and would try to fabricate a perfect circle - either the radius or the circumference would be an irrational number. We could never see the edge of this perfect circle in the physical world.

Am I mistaken in some way? It seems we can only work with the idea of the circle in mathemathics, but in reality we must do with imperfect circles, and that is not because we don't have proper tools, no tool could make a perfect circle.

Or maybe I am mistaken, and this is a false paradox like the one when you always have to go half the distance to somewhere before going the full distance, then half of the half, and so on, and you can never reach the full distance.

On a computer screen a circle is as perfect as it's medium allows: the minimum pixel size. Does the Universe have a minimum size? The Plank length?

This is something videogame makers and CG artists know better, in the digital world circles are indeed never real circles, they always have cornes, with enough subdivisions it appears 'round' to our eyes.

The discovery here is that in the real world a circle also only just appears 'round' to make it we do have to make these tiny steps....

Regards,
Daniel

[Zyxzevn]

...if the skier had hard ice , there wold be minimal slowing.

If you turn on ice with skates, you slow down, too. TIP: It is a way to stop.

In the experiment, the rotational momentum of the ball is reversed, while sliding on the slope of the tube.
That means that energy is lost.
This energy is expressed in a slower speed of the ball with the equation: E=0.5*m*v²
And indeed we can see that the ball has lost some speed in the video when it comes out of the tube.
CASE CLOSED

He has got us thinking , which can't be bad.

Trolls can make you think too, but that still makes them trolls and (often) a waste of time.

I am sorry if you like his theories.
I do not mind any theories or whatever idea.
But due the way he introduces them with bad logic and very bad maths,
I find him very trollish.

[oz93666]

Trolls can make you think too, but that still makes them trolls and (often) a waste of time.
I am sorry if you like his theories.
I do not mind any theories or whatever idea.
But due the way he introduces them with bad logic and very bad maths,
I find him very trollish.

I've never said I like his theories , I've called pi=4 'insanity' ....

He's just a very curious case , clearly he has something ...according to his bio awards and scholarships for maths and science... to be able to write a 6,000 pages on our sort of subjects is no mean feat...

I'm not sure what your term troll implies ??? that he knows it's rubbish he's writing ? Is all his scientific work rubbish ?

What motivates him ???

He's also a conspiracy theorist , and I can confirm he has most of that correct!

[jacmac]

oz93666 said:

the ball in the curved path is not with it's spin axis at 90* to the table , this would require zero gravity or infinite centrifugal force

While I agree with your general position and conclusion Pi does not=4 , Your above statement is not correct IMO.

The ball IS with it's spin axis 90* to the table in the curve, until it slows down enough to drop lower.

Have you ever seen a carnival ride where people stand up against the wall of a cylinder, it spins, then faster, until the floor drops down and the people are held in place up against the wall by centrifugal force.
The centrifugal force is NOT INFINITE otherwise the cylinder would explode sending all the people to their doom.

And you say:

The orientation of the spin axis is constantly changing as it moves around the curved path

No, once the ball is fully into the curve the spin axis is steady (90*) to the table; the ball is slowing down due to the change of one direction while also moving straight ahead, so to speak, in the other direction (parallel to the table).
That's what I was saying above with the Luge sled example.
From the PERSPECTIVE of the sled rider engaged with the curve the change in direction would seem to be up, as the G force pushes her down into the sled. (Only a close example as luge is of course downhill)
Jack

[chrimony]

He's just a very curious case , clearly he has something ...according to his bio awards and scholarships for maths and science...

I wouldn't take that at face value. For instance, see this post by a former member and Mathis critic, where it appears Mathis fraudulently claimed to have discovered an error on the PSAT exams that had to be corrected nationwide, which a New York Times article attributes to somebody else.

to be able to write a 6,000 pages on our sort of subjects is no mean feat...

I agree, he's obviously pretty smart. But it seems he'd rather take the shortcut to greatness by declaring himself and his "discoveries" great, despite the obvious flaws pointed out in his work.

He's also a conspiracy theorist , and I can confirm he has most of that correct!

And I can confirm he has most of that incorrect. Now that we've stated our blanket opinions on the subject, I'll point out that discussions of conspiracy theories aren't allowed on the forum, per the rules.

[comingfrom]

Coming into this discussion late, I first read the whole thread.

It appears to me, what the debunkers of this experiment seem to forget, is the reason for this experiment.

The problem in physics already existed.
Using pi=3.14.. to measure the distance of an orbiter, it arrives late.
Even when runners exert extra effort on the curves to counter the centrifugal force, they still arrive late at the end of the curve for the length traveled.
So from celestial mechanics to sports there are problems when using pi = 3.14..

Mathis worked on these problems from a physical theoretical point of view, and arrived at a mathematical solution, which was to use 4 for pi for objects in curved motion.

Steven Oostdijk created this simple experiment to demonstrate.
The experiment shows that Mathis is, in this case, correct.

Some may have, in their mind, debunked this experiment. But then they are still left with the above mentioned problems, and why 4 is used instead of pi for cycloids, or bodies in curved motion.

And to those who might say I am deluded for believing in Mathis, I say, I am glad I made the effort to understand what he is saying.

And to Zyxzevn, with all due respect (for I do respect your intellect and knowledge), turning on skates is not a good analogy here. Turning on skates (or skies) to slow down is a heavy application of friction at the skate/ice interface. The ball in the tube, in the experiment, doesn't have skates. The ball/tube surface interface has no such frictional change. It has been shown that the ball is not being slowed down. It's speed remains constant.

Thanks to all.
Paul

[jacmac]

comingfrom:

Even when runners exert extra effort on the curves to counter the centrifugal force, they still arrive late at the end of the curve for the length traveled.

This is a weird statement. What does "arrive late" even mean ?
Curves take longer because they are harder to run.
Miles and true believers say the DISTANCE is longer.
NONSENSE

[LongtimeAirman]

.
jacmac wrote. Miles and true believers say the DISTANCE is longer.

Steven Oostdijk wrote. There is two things I could suggest to mention in the discussion:

1. Pulling a "velocity" around a circle is not the same as pulling a solid ruler around a circle. The velocity vector will need to be rotated along the path otherwise it would not follow the path. This rotation takes time. So it would not be logical that the length of a circular path measured with a velocity would be the same as measured with a ruler. For all these people shouting that Pi will always remain 3.14, sure, but only for geometric ratios.

2. There was a discussion whether the definition of length would need to change but that is not the case. Measuring the length of the circular path starting with the origin on the path will yield 4 as is shown in the video. It would yield 3.14 measured from the virtual center but only if you ignore the rotating reference frame of the ball (which is interestingly enough actually admitted by the mainstream ).

Airman. I believe the nature of length is different between the geometric and kinematic curved paths. Curved motion involves a rotating reference frame. Geometric circles - with which we currently measure things - does not.
.

[comingfrom]

Thank you, Jacmac.

This is a weird statement. What does "arrive late" even mean ?

Knowing the speed of the runner, and the length of the curve, it can be calculated when they will arrive at the end of the curve. But the calculations predict wrong.

Curves take longer because they are harder to run.

That's why I said, even though the athlete exerts extra effort to compensate.

My statement wasn't so weird.

Miles and true believers say the DISTANCE is longer.
NONSENSE

Travelling in a curve involves adding vectors. These vectors are adding within the same time intervals so it isn't a straight addition, but we need a scaling constant, and we use pi.
Problem is, with objects in motion, using 3.14... for pi doesn't give the correct answer, but using 4 does.

~
I'm not an expert in math, but I was aware that when we first began shooting rockets into space they missed the moon by thousands of miles. NASA engineers have obviously had to make the corrections, or compensations, to the classical equations to get their rockets on target. Unfortunately, till now these corrections haven't made into the textbooks. I believe pi = 4 is just one of these corrections.

And pi still equals 3.14.. for geometry. Nobody is disputing that.

~
And thank you Airman, for your patience and lucid explanations.

~Paul