A Simple Experiment Proves π = 4

[Lloyd]

Pi is not 4 and will never be. Some years ago the Texas State Legislature--that grand bastion of intellectual knowledge-- tried to pass a law decreeing that Pi was 4. Didn't work then either. The collective faculties of all the universities in Texas came down on them like a duck on a june bug.

Please give this up. It makes the proponents of the EU/PC look like dolts.

The New Insights and Mad Ideas board isn't part of EU. It's just a place for everyone to present their own ideas on anything.

If the Texas legislature tried to pass a law saying pi=4, then there must be something to it. They surely wouldn't try that just to be crazy. MM says the equivalence only applies to circular motion, not to static circular dimensions. He has presented considerable explanation along with math. So, to challenge him, you need to quote his math and explain where his error is.

[Grey Cloud]

Pi is just the name we assign to 22/7 - straight or curved; static or in motion. If Mathis has discovered something which equals 4 then, by definition, it is not Pi. It's like 'proving' that 1 kilometre is not 1000 metres.

[LongtimeAirman]

.
Hi Lloyd, Thanks for popping in.

Review. Steven Oostdijk has provided two tracks with straight lengths 55.3cm and 70.4cm, maintaining a length ratio of 3.14 to 4. This has allowed him to mark off the unit lengths, 0 thru 4 and PI on the 70.4cm straight track. The shorter length, 55.3cm, is laid into a circle (any resemblance to a helix is ok, the outcome is the same) and marked into quarters. Two balls of equal velocity enter the tracks and hit their marks and track ends simultaneously. The motion of the balls show the two tracks to be the same length – 4.

I'll answer questions. Sorry if I get a bit redundant.

jacmac. The static physical length of a curve is equal to its length. Does rolling a ball through it change that?

That's the point of the experiment. Motion through a curve makes the curve (4/3.14) longer.

jacmac.If you roll a circle down the tube( like a tiny ring) I predict it will not make the turn into the loop. It will fall over.

The experiment is simple enough to try yourself. I believe there is always a rolling contact. The sphere, or ring must bank a bit. We could use balls with stripes or patterns to examine whether any additional rotations are present.

jacmac.There are other forces a work which you choose to attribute to some kind of magic math.

No magic math here, just static length or motional rate times time equal distance.

jacmac. I do not buy it. No aha here!

I may go out of business, but I’ll keep trying.

Zyxzevn. But seriously. I can see the ball move slower in the curved path, just measure it.

Correct. It's been shown that for balls in motion, the circular path is as long as the straight, 4 units. Rate times time equal distance show the two velocities are the same. The curved path only appears slower than the straight path because the motion reveals that for objects in motion, the curved distance is greater.

Zyxzevn. It has to be slower, because the ball's rotation changes in direction. This causes friction. And the ball is pressed towards the side of the path, causing even more friction.

Friction is not an issue here, it would be cumulative and obvious.

Zyxzevn. Besides that the length of both paths are not clear.

The track lengths are clear enough to demonstrate a straight/curve distance metric difference greater than 20%.

Zyxzevn. Another experiment would be a rotating wheel, and holding it against a flat surface.
Now we have again a rotating movement versus a linear movement.
If the wheel goes faster than the surface, you would be right.
And as everyone understands, it goes the same speed.

Stick to the current experiment or modifications to it.

Grey Cloud. Pi is just the name we assign to 22/7 - straight or curved; static or in motion. If Mathis has discovered something which equals 4 then, by definition, it is not Pi.

Pi is defined as the circumference divided by the diameter. For geometry that's close to the ratio 22/7. For motion, with diameter of 2, the circumference is 8, and PI=4.

Grey Cloud. It's like 'proving' that 1 kilometre is not 1000 metres.

Yes, Miles discusses one such problem, More on the Running Track. http://milesmathis.com/track.pdf Miles shows show that both the distances and velocities are being miscalculated in the curves on normal running tracks. Using Miles' paper, the layout of a 400M Olympic track, and excel, I calculated the 200M race is 232M, and the 400M is 463M. http://milesmathis.the-talk.net/t220-mo ... track#1497
.

[Zyxzevn]

The ball in the curved path does go slower. That is exactly what you measure here.
There are several things that can make a ball go slower.
Just denying friction, does not make it go away.
The elasticity of the track also absorbs some of the kinetic energy of the ball.

I think the burden of proof is on your side here.
You only have to test the speed of the ball as it comes out of the curved path versus the
speed of the ball in the straight path.
You can also make 3 circles, the ball will really be slowed down.
I must add that the ball will move to the side of the track, and follow a slightly longer path too.

The rotating motion of a wheel is similar to that of the shown experiment.
I added it so you can understand the consequences of what you are stating with pi=4.
Take a wheel with circumference 3.14.
Tip: It's diameter will be 1.
Now rotate the wheel one rotation over a flat surface.
It will go 3.14 meters.
So the rotation of the wheel does not change the distance.
That is because the way it is.

[jacmac]

Longtime Airman, you are saying the moving ball in the curve travels less distance over time, thus pi is 4.
Nonsense.
Lets review(again).
The length of the curved tube stays the same as without the ball, CHECK.
The surface of the steel ball does not change because it curves, CHECK
The ball goes slower in a curved tube than a straight tube, CHECK
There is a time delay, CHECK

What has caused this ????

False assumption:
Something in geometry changes, therefore,
PI changes to 4.

(Insert here old computer programming saying: GARBAGE IN, GARBAGE OUT)

NONSENSE.

[Zyxzevn]

I forgot to add a way you can cheat this experiment:
The height of the paths.
If a ball goes higher it loses kinetic energy but gains gravity potential energy.
In the curved path it must go on a higher path, because it goes around the corner.

You can even cheat Pi to 5 by slightly tilting the table so the ball in the curve goes even higher.

These problems are additionally to the rotation-friction, the surface friction, the elasticity of
the tubes etc.

[Zyxzevn]

If the Texas legislature tried to pass a law saying pi=4, then there must be something to it.

It shows how bad the maths education is in the USA..

It is very different in Japan for example:
Japanes have geometry puzzles in their temples
See also pdf
Sangaku with 8 circles From this long list of Sangaku
Can you solve it? Are you smarter than a Japanese schoolchild?

[LongtimeAirman]

A Simple Experiment Proves π = 4
http://milesmathis.com/pi7.pdf

Zyxzevn. The ball in the curved path does go slower. That is exactly what you measure here.
There are several things that can make a ball go slower.
Just denying friction, does not make it go away.
The elasticity of the track also absorbs some of the kinetic energy of the ball.

Airman. We can all see that even though the ball clearly travels slower through the tube, there are just 2 speeds. Velocity in the loop and velocity in the straight. Velocity in the loop is slower compared to the straight section, but distance for the loop turns out to be correspondingly longer (4/PI to be exact). We can analyze the video frame by frame, each ball against the unit markers to determine whether there is any funny stuff or cumulative reduction in speed. Show me the friction.

Zyxzevn. I think the burden of proof is on your side here.
You only have to test the speed of the ball as it comes out of the curved path versus the
speed of the ball in the straight path.
You can also make 3 circles, the ball will really be slowed down.
I must add that the ball will move to the side of the track, and follow a slightly longer path too.

Airman. I disagree. Steven’s experiment stands on its own. It clearly shows that the distance associated with curved motion is 4/PI longer than the static geometric curve length. The results are easy to understand given Miles’ prediction and plenty of supporting theory. Anyone spending time with the experiment is free to come up with their own improvements. Disprove the experiment or not.

Zyxzevn. The rotating motion of a wheel is similar to that of the shown experiment.
I added it so you can understand the consequences of what you are stating with pi=4.
Take a wheel with circumference 3.14.
Tip: It's diameter will be 1.
Now rotate the wheel one rotation over a flat surface.
It will go 3.14 meters.
So the rotation of the wheel does not change the distance.
That is because the way it is.

Airman. You insist on departing Steven’s experiment. You are correct, wheels and cars travel ahead at the same speed. How does that disprove Steven’s experiment?

Anyway, you just picked up a screw in your tire tread. You have one more rotation till blowout. You and the car do indeed move ahead 3.14 (your quoted circumference) but at the same time the screw will move a distance of 4.

I’m delighted to direct you to:
The Cycloid and the Kinematic Circumference
http://milesmathis.com/cycloid.pdf

Cycloid.jpg (9.83 KiB) Viewed 8966 times

MM wrote.If you roll a wheel on the ground one full rotation, it will mark off a path on the ground that is 2πr in length, as most people know. That length has been assigned to the circumference of the circle or wheel, which assignment is correct as far as it goes. My papers have not questioned that. However, if you do the same thing but follow the motion of a given point on the wheel (point A in the diagram above, for instance), it draws the red curve. That is called the cycloid. Obviously, the red curve is not the same length as the line on the ground. It is considerably longer, being 8r in length. That is 21% longer than the circumference.

Back to Steven Oostdijk's PI=4 experiment.

jacmac. Longtime Airman, you are saying the moving ball in the curve travels less distance over time, thus pi is 4.

Airman. I don’t think so. The time in the curve equals the time it takes to get to the end of the straight (instead of the PI mark). The fact that the two times are equal allows us to see the curved and straight moving distances are actually the same.

jacmac. Nonsense.
Lets review(again).
The length of the curved tube stays the same as without the ball, CHECK.
The surface of the steel ball does not change because it curves, CHECK
The ball goes slower in a curved tube than a straight tube, CHECK
There is a time delay, CHECK

What has caused this ????

False assumption:
Something in geometry changes, therefore,
PI changes to 4.

(Insert here old computer programming saying: GARBAGE IN, GARBAGE OUT)

NONSENSE.

Airman. Garbage in? You had me wrong with traveling less distance over time in the curve. Miles explains it much better than me. I’m trying to learn it better by discussion.

What time delay?

The wall curvature provides the turning force, but the energy cost to the ball appears to be no greater than the straight track’s rolling contact.

Zyxzevn. I forgot to add a way you can cheat this experiment:
The height of the paths.
If a ball goes higher it loses kinetic energy but gains gravity potential energy.
In the curved path it must go on a higher path, because it goes around the corner.

Airman. Now you’re talking about cheating? After the ramp’s gravity acceleration the tracks are strictly on a flat tabletop.

Zyxzevn. You can even cheat Pi to 5 by slightly tilting the table so the ball in the curve goes even higher.

Airman. You need to do the experiment yourself. Film it and see an analyst, so you can examine each frame. Stop making stuff up.

Zyxzevn. These problems are additionally to the rotation-friction, the surface friction, the elasticity of the tubes etc.

Airman. Disprove the experiment. Show us the friction, not your imagination.

Thanks for sharing the Sangaku info.
.

[jacmac]

I said:

There is a time delay, CHECK

My bad. I should have said the ball travels less distance in the curve.

Airman:

We can all see that even though the ball clearly travels slower through the tube, there are just 2 speeds. Velocity in the loop and velocity in the straight. Velocity in the loop is slower compared to the straight section,

Yes I agree.
Also,any friction is minor and can be overlooked for this discussion. IMO

I say the slower velocity in the loop is caused by the rotation of the ball being pushed off its desire to roll in a straight line.(inertia) This push to the side results in a change in the spin axis within the ball itself. The ball is FORCED to turn. This force causes the velocity to drop. While at the same time, the track of the contact of ball to tube moves up the side of the tube to a new equilibrium level( like a luge sled). At that new level I think the ball behaves as moving in a straight line and does not loose more velocity. I think the velocity loss occurs in the beginning of the curve as the ball moves up the side of the tube.

Airman

The fact that the two times are equal allows us to see the curved and straight moving distances are actually the same.

No. You are contradicting yourself.
Airman

We can all see that even though the ball clearly travels slower through the tube

The two times are equal, the ball in the tube is slower, It travels less distance.
The length of the curve is less, the ball travels less distance.
Pi is conserved.

[LongtimeAirman]

jacmac.
I said:
There is a time delay, CHECK

My bad. I should have said the ball travels less distance in the curve.

Airman:
We can all see that even though the ball clearly travels slower through the tube, there are just 2 speeds. Velocity in the loop and velocity in the straight. Velocity in the loop is slower compared to the straight section,

Yes I agree.

Airman. Don't agree with me by misquoting me. You left out a pertinent half of the sentence.

We can all see that even though the ball clearly travels slower through the tube, there are just 2 speeds. Velocity in the loop and velocity in the straight. Velocity in the loop is slower compared to the straight section, but distance for the loop turns out to be correspondingly longer (4/PI to be exact).

Correction needed. “tube” should also be replaced with “loop” in the first sentence.

I believe the rule is - for any given period of time, the distance traveled through the straight equals the distance traveled through the curve; however, the equality requires use of the curve metric, PI=4.

Also, “clearly travels slower” is false. It’s falling for an illusion. Like changing the angle of view (foreshortening) apparently makes a length shorter. It only looks slower because we are comparing it to our PI=3.14 geometry metric understanding. PI=4 does take some getting used to.

jacmac. Also,any friction is minor and can be overlooked for this discussion. IMO

Airman. Safe enough given the tabletop experimental confines.

jacmac.
I say the slower velocity in the loop is caused by the rotation of the ball being pushed off its desire to roll in a straight line.(inertia)
This push to the side results in a change in the spin axis within the ball itself.
The ball is FORCED to turn.
This force causes the velocity to drop.
While at the same time, the track of the contact of ball to tube moves up the side of the tube to a new equilibrium level( like a luge sled).
At that new level I think the ball behaves as moving in a straight line and does not loose more velocity.
I think the velocity loss occurs in the beginning of the curve as the ball moves up the side of the tube.

Airman. I like most of your description.

To repeat, (thank you), this experiment allows us to directly compare motion in the two tracks using the standard relationship: velocity = change in distance over change in time.
Since timeLoop=timeStraight,
(distLoop/velLoop)=(distStraight/velStraight),
This is true when:
distLoop=distStraight,
velLoop=velStraight,

There is no velocity loss. It is an illusion. Any appearance of slowing is matched by the fact that the curve is longer than it appears.

jacmac.

Airman
The fact that the two times are equal allows us to see the curved and straight moving distances are actually the same.

Airman. Yes.

jacmac. No. You are contradicting yourself.

Airman
We can all see that even though the ball clearly travels slower through the tube.

Airman. Distance along the curve must be gauged against a known fixed distance before the curve metric is understood. Steven’s experiment does that. The loop velocity just appears to be slower, it is not. Both velocities are equal (1.2m/s at PI=4), both distances are equal (70.4cm at PI=4).

jacmac. The two times are equal, the ball in the tube is slower, It travels less distance.
The length of the curve is less, the ball travels less distance.
Pi is conserved.

Airman. Hypnotic - I'm getting sleepy - but false.
.

[jacmac]

Airman says:

Any appearance of slowing is matched by the fact that the curve is longer than it appears.

Ok. I get it. If you measure the loop with a cloth ruler(because they bend so nicely) the length it appears to be when empty is not the same as it is when there is a steel ball rolling through it. Wonderful. Who knew !

Jack

[JouniJokela]

This is all over complicated;

The experiment is valid, and proves that Velocity = Angular velocity.

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

Or even simpler; rotation speed;
https://en.wikipedia.org/wiki/Rotational_speed
is same as the tangential speed / (speed of straight line)
https://en.wikipedia.org/wiki/Speed#Tangential_speed

The "official" difference between velocity and speed being the idea of vector (velocity=value + direction) or just a value (speed).

The equation is "tangential speed = 2 x pi x radius x cycle" or
"Omega-rad = speed / radius".

Both equations says clearly that the experiment result "4" is CORRECT. The only thing which can be argued is, if this 4 can be called a "pi".
I would not call it Pi, as it would confuse the most people cause they are used to think the 2-dimensional diameter-circumference-ratio of a circle.

But as it's a "tangential-speed"-"rotation-speed"-ratio of a motion, I would say "Kinetic-pi" is 4.

This arguing here is btw. similar, as the arguing about if the sun rotates around the earth or the Earth around the sun.

Because these both arguments are correct, and the merely difference is ONLY where the cordinate system is placed. And though the the location of the coordinate system does simplify math in certain cases, an thus makes it easier to understand causalities, it's completely possible to solve the retrogade motion of Mars perfectly correctly with the coordinate system which is fixed in your belly button. The math is just "slightly" more complicated.

But then, it's much easier to talk things like "left" and "right" when the coordinate system is in your navel.
It makes no sense for Galileo to talk about the motions of solar-system with a person who is only interested about the woman on his LEFT side.
There won't be any reasonable dialogue. Thus, Galileo made a dialogue of his own.

It makes absolute no sense to speak from "Kinetic-pi" with 2-dimensionlly thinking persons.

[LongtimeAirman]

.

JouniJokela. This is all over complicated;

The experiment is valid, and proves that Velocity = Angular velocity.

Airman. Hello JouniJokela. Wrong conclusion.

The subject deserves attention. One simply cannot equate linear (tangential) and angular (rotational) velocities.

Miles shows that both current equations are false in his paper.
Angular Velocity and Angular Momentum
http://milesmathis.com/angle.html

He provides the relationship between angular velocity and radius.

MM wrote:

ω = √[2r√v2 + r2) - 2r2]
r = √[ω4/(4v2 - 4ω2)]

Not as simple as the current equation, but much more logical. Instead of strange scaling, we get a logical progression. As r gets larger, the angular velocity approaches the tangential velocity. This is because with larger objects, the curve loses curvature, becoming more like the straight line. With smaller objects, the curvature increases, and the angular velocity may become a small fraction of the tangential velocity.

JouniJokela.
It makes absolute no sense to speak from "Kinetic-pi" with 2-dimensionlly thinking persons.

Airman. I’d sure hate being hit by "Kinetic-pi". Miles uses “Kinematic”. Among other things, Wikipedia defines kinematics as a field of study often referred to as the "geometry of motion".
.

[Zyxzevn]

Airman.

All other parts of your theories have been debunked in different ways.
Sadly Miles does not understand mathematics at all, he mixes all kinds of stuff up.
One needs a bit of understanding of mathematics to see through his mistakes.
I am helping you with that a bit.
And looking at the results of these longs posts, it seems clear that I have corrected
many of Miles mistakes. And those lead to the conclusion that PI is indeed 3.1415....

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.

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.

You don't understand that something could be wrong, that is clear from your responses.
Both in theory and in practice, you fully believe Miles.

Even the greek, as everyone educated in math can tell you that
everything that Miles has stated about Pi is wrong (including all the listed examples).

Sadly he does not see it, and clearly you do not understand it.

What is clear for me is that Miles level of understanding of mathematics is very low.
And that it is attractive for people that do not understand mathematics either.
And this seems common in the USA, which in my opinion has the worst education of the modern world.

Why does Miles say he knows it better?
From my mathematical background, it is clear to me that Miles never really understood the maths.
Probably he wanted things to be in simple numbers, in simple structures.
So with his creative and poetic mind he created his own world of physics.

And that is how I think we should see his work.
As creative and poetic.

Not as realistic or accurate.
For that he does not understand maths good enough.

[Zyxzevn]

Because Miles is not very good in math, I added the
"Cycloid" calculation:



a= 0..PI
y= r-r*cos(a)
x= a*r-r*sin(a)

dy/da= r*sin(a)
dx/da= -r*cos(a)+ r

dL= sqrt( dx^2+ dy^2)
dL/da = sqrt( r²*sin²(a)+ r²*cos²(a)+ r² - 2*r*r*cos(a) )
dL/da = sqrt( r²( 1 ) + r² - 2*r²*(cos(a)) )
dL/da = r* sqrt( 2+ 2*cos(a) )

Wolfram alpha:
integral ( sqrt(2+2*cos(x)) ) = 2*sqrt( 2*cos(x) + 2)*tan(x/2)

So:
L(a) = integral (a=0..PI, dL/da) =
L(0)= 2*sqrt( 2*cos(a)+ 2)*tan(a/2) = 2*sqrt( 2+ 2)*0
L(PI) = 2*sqrt( 2*(-1)+ 2)*(tan(PI/2) = 2*sqrt( 0)*Inf

Because it is infinite, we need a limit.
And according to Wolfram Alpha we see that:
Lim( a->PI)= 2*sqrt( 2*cos(a)+ 2)*tan(a/2)= 4.
We have to take this distance twice for a full turn.

So the length of the path that an object in the wheel takes,
while rotating on the road for a distance of exactly 2*PI,
is exactly 8,
BECAUSE PI=3.1415..

And there lies the problem with Miles.
He is confused with maths, because he does not understand it.
So he mixes things with each other.
PI does not change because it is moving,
instead you get the above difficult formula.
Which is clearly to difficult for Miles to understand.
His paper does not contain any maths at all.
I even would suggest to remove math from his URL, and
rename to it to "milesis.com".

Again for clarity:
Maths works BECAUSE
PI = 3.1415...