## A Simple Experiment Proves π = 4

Beyond the boundaries of established science an avalanche of exotic ideas compete for our attention. Experts tell us that these ideas should not be permitted to take up the time of working scientists, and for the most part they are surely correct. But what about the gems in the rubble pile? By what ground-rules might we bring extraordinary new possibilities to light?

Moderators: MGmirkin, bboyer

### Re: A Simple Experiment Proves π = 4

Melusine wrote:If you do this experiment, you will find that the path drawn by a wheel of the car is a circle with a circumference of 2πr with π = 3.14. No big surprise here.

However, if you were able to track a particular point on this wheel (the air valve or a chalk mark), you would find that for each full rotation of the wheel, the point follows a cycloid curve of length 8r. So the total distance covered by that point is 8r x the number of rotations of the wheel along the circular path.

You can find an animated illustration of this on the cycloid page at Wikipedia.

Edit... of course, to clarify, r in the first part is the radius of the circular path. r in the second part is the radius of the wheel.

I find this confusing. The cylcoid describes a point on a circle that is rolling. So there is both rotational and linear motion. It does not describe e.g. a car going around in a fixed circle on a fixed track.
5boxen

Posts: 3
Joined: Fri Oct 07, 2016 1:41 pm

### Re: A Simple Experiment Proves π = 4

.
Cycloids are not clear examples of curved motion. Calculating their paths, however, do require two variables and time (total of 3 variables).
.................

A circle is more than a circle when it is being created by an object moving through space. Curved motion means that an object is subject to two orthogonal velocities*.

"Here is a video showing how the motions of the circle correspond with the motion on the two axes. Hosted on Vimeo, the link should take you there directly."

https://vimeo.com/189106809

.

* Oops, no, not subject to orthogonal velocities, but subject to forces which result in orthogonal velocities.

I'm still learning too.
.
LongtimeAirman

Posts: 233
Joined: Sun Nov 03, 2013 7:59 pm

### Re: A Simple Experiment Proves π = 4

5boxen wrote:
Melusine wrote:If you do this experiment, you will find that the path drawn by a wheel of the car is a circle with a circumference of 2πr with π = 3.14. No big surprise here.

However, if you were able to track a particular point on this wheel (the air valve or a chalk mark), you would find that for each full rotation of the wheel, the point follows a cycloid curve of length 8r. So the total distance covered by that point is 8r x the number of rotations of the wheel along the circular path.

You can find an animated illustration of this on the cycloid page at Wikipedia.

Edit... of course, to clarify, r in the first part is the radius of the circular path. r in the second part is the radius of the wheel.

I find this confusing. The cylcoid describes a point on a circle that is rolling. So there is both rotational and linear motion. It does not describe e.g. a car going around in a fixed circle on a fixed track.

I agree it is confusing because then the mind is left to wonder at what point do we need to leave the 'regular' world where pi is 3.14 and enter the world of cycloid math where C = 8r.

I think the wheel of a car defining a circular path in a parking lot is akin to a pen drawing a circle on paper. Only the end result is taken into account. Factors such as the speed of the car and the diameter of the wheel are irrelevant.
However, when you consider a particular point on the wheel, the size of the wheel in relationship to the final circular path on the parking lot becomes important, so cycloid math is needed.

LongtimeAirman wrote:Here is a video showing how the motions of the circle correspond with the motion on the two axes. Hosted on Vimeo, the link should take you there directly.

https://vimeo.com/189106809

Thank you Airman. This is very helpful in better visualizing why the cycloid is the way it is.

Melusine

Posts: 27
Joined: Mon Jun 01, 2015 8:18 am
Location: Maryland, USA

### Re: A Simple Experiment Proves π = 4

Steven Oostdijk's
A Simple Experiment Proves π = 4
http://milesmathis.com/pi7.pdf
MM wrote: It doesn't change the length, it changes the distance that has to be traveled.

jacmac. length no longer equals distance when length is put in a circle.
I am impressed with the wonders of mathematics

Airman. Yes it sounds contradictory; but length and distance aren’t really the same.

Length is a fixed quantity depending on one’s metric. Usually involving a change in X and Y. A geometric fact. I suppose pi=3.14 will always be the tool of artists and engineers in creating curves and surfaces. There’s no reason for that to change.

Distance refers to how far an object travels. velocity*time=distance. We are adding time and motion to the mix.

One might say distanceStraight still equals lengthStraight; I also have no problem with nails on chalkboard.

We’ve always assumed that pi=3.14 gave us all we needed to convert curves into distances; we were wrong. If you're going to equate length to distance in the curve, Steven’s experiment shows us that

distanceCircumference=lengthCircumference*(4/Pi)

Extraordinary Experiments (StevenO) wrote:
The ratio of circumference/diameter is 3.14 but the ratio of angular velocity/linear velocity is 4*diameter instead of PI*diameter

Being a runner, you may appreciate Miles’
MM wrote: NEW PAPER, added 9/10/16, More on the Running Track. http://milesmathis.com/track.pdf This is to clarify my recent addendum to my paper on pi=4. I show that both the distances and velocities are being miscalculated in the curves on normal running tracks.
.
LongtimeAirman

Posts: 233
Joined: Sun Nov 03, 2013 7:59 pm

### Re: A Simple Experiment Proves π = 4

The only increase that running the curve adds to the distance was not mentioned by Miles.
Running parallel to the lines on a straightaway is equal to the line distance and it is easy to stay in your lane.
Running outside your lane line on the curve is required. Stepping on the line is a disqualification. Some runners can stay closer to the line than others. Moving out from the curve line adds radius, thus adds circumference, thus increases distance. (wow, Look I just did MATH)

Been there done that.

Almost everything that Mr. Mathis said is absurd.

It is all semantic B.S.

Jack
jacmac

Posts: 562
Joined: Wed Dec 02, 2009 12:36 pm

### Re: A Simple Experiment Proves π = 4

jacmac wrote. The only increase that running the curve adds to the distance was not mentioned by Miles.
Running parallel to the lines on a straightaway is equal to the line distance and it is easy to stay in your lane.
Running outside your lane line on the curve is required. Stepping on the line is a disqualification. Some runners can stay closer to the line than others. Moving out from the curve line adds radius, thus adds circumference, thus increases distance. (wow, Look I just did MATH)
Been there done that.

Almost everything that Mr. Mathis said is absurd.

Airman. Ok.

Discussion seems one-way at times.

Here are my calculations for actual distances for a 200M track along lane center-lines based on the new motion metric.

It's surprising. The curved distance doesn’t count on the radius. It does take some getting used to.
.
LongtimeAirman

Posts: 233
Joined: Sun Nov 03, 2013 7:59 pm

### Re: A Simple Experiment Proves π = 4

.
The vimeo link showing Curved Motion above isn’t working.

Pi_Cartesian_Cycle
by Dragon Face
.
LongtimeAirman

Posts: 233
Joined: Sun Nov 03, 2013 7:59 pm

### Re: A Simple Experiment Proves π = 4

Pheeeew ... 6 pages of theory and talk ... physics is about experiment ...

I suggest one simple experiment which will resolve this whole issue ....

Repeat the original experiment but using glass tubing ... second best would be metal ... or even acrylic ..

Due to the softness of the original tubing the added centrifugal force pushes the ball deeper in , resulting in slowing the ball more , it's like riding a bicycle on sand , it's hard work because the surface gives .

Also if the circular tube is not very securely fixed , the passage of the ball will impart a slight movement of the tube , this will slow the ball too.
oz93666

Posts: 195
Joined: Sun Jan 19, 2014 3:12 pm

### Re: A Simple Experiment Proves π = 4

oz93666 wrote:Pheeeew ... 6 pages of theory and talk ... physics is about experiment ...

I suggest one simple experiment which will resolve this whole issue ....

Repeat the original experiment but using glass tubing ... second best would be metal ... or even acrylic ..

Due to the softness of the original tubing the added centrifugal force pushes the ball deeper in , resulting in slowing the ball more , it's like riding a bicycle on sand , it's hard work because the surface gives .

Also if the circular tube is not very securely fixed , the passage of the ball will impart a slight movement of the tube , this will slow the ball too.

This was already replied to by Steven on his Youtube channel, there is no appreciable friction in this kind of tubing.

The point is that a ball going straight has 1 motion forward, 1 spin.

A ball through a circle has 2 motions forward, a curve is a summation of 2 motions (or better said , 2 directions) a ball going straight only has 1 direction. This difference causes the effect demonstrated by this experiment.

The ball through the circle goes > and ^ , the ball straight only >

This why the kinematic ratio of a circle's circumference to its diameter is 4.

Regards,
Daniel
- Shoot Forth Thunder -

D_Archer

Posts: 1206
Joined: Sat Apr 18, 2009 4:01 am
Location: The Netherlands

### Re: A Simple Experiment Proves π = 4

D_Archer wrote:
This was already replied to by Steven on his Youtube channel, there is no appreciable friction in this kind of tubing.

how did he reply? how does he know there's no appreciable friction ?
D_Archer wrote:The point is that a ball going straight has 1 motion forward, 1 spin.

A ball through a circle has 2 motions forward, a curve is a summation of 2 motions (or better said , 2 directions) a ball going straight only has 1 direction. This difference causes the effect demonstrated by this experiment.
The ball through the circle goes > and ^ , the ball straight only >
This why the kinematic ratio of a circle's circumference to its diameter is 4.

Are you saying the ball exits the curved path with roughly the same velocity , and that the path it travelled is effectively longer ... when we can clearly see the path it travels in the video , a circle.
oz93666

Posts: 195
Joined: Sun Jan 19, 2014 3:12 pm

### Re: A Simple Experiment Proves π = 4

Consider the rolling ball in the tube , it's axis of spin is parallel to the table and at right angles to the direction of movement .
As the it enters the curved section of the tube (tube in the plane of the table ) , it's axis of spin will now change and no longer be parallel to the table , what effect will this have ? a force is required to do this .As it moves around the curve the orientation of the axis of spin is constantly changing , to do this requires a force , will this slow the ball?
When it exits the curve , (if the tube were to continue) the spin axis would revert back to parallel to the table.
oz93666

Posts: 195
Joined: Sun Jan 19, 2014 3:12 pm

### Re: A Simple Experiment Proves π = 4

oz93666 wrote:
D_Archer wrote:
This was already replied to by Steven on his Youtube channel, there is no appreciable friction in this kind of tubing.

how did he reply? how does he know there's no appreciable friction ?

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

D_Archer wrote:The point is that a ball going straight has 1 motion forward, 1 spin.

A ball through a circle has 2 motions forward, a curve is a summation of 2 motions (or better said , 2 directions) a ball going straight only has 1 direction. This difference causes the effect demonstrated by this experiment.
The ball through the circle goes > and ^ , the ball straight only >
This why the kinematic ratio of a circle's circumference to its diameter is 4.

Are you saying the ball exits the curved path with roughly the same velocity , and that the path it travelled is effectively longer ... when we can clearly see the path it travels in the video , a circle.

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.

oz93666 wrote:Consider the rolling ball in the tube , it's axis of spin is parallel to the table and at right angles to the direction of movement .
As the it enters the curved section of the tube (tube in the plane of the table ) , it's axis of spin will now change and no longer be parallel to the table , what effect will this have ? a force is required to do this .As it moves around the curve the orientation of the axis of spin is constantly changing , to do this requires a force , will this slow the ball?
When it exits the curve , (if the tube were to continue) the spin axis would revert back to parallel to the table.

The only force provided is the starting force from falling down (ie gravity).

I would think the spin axis being parallel to the table or not has no appreciable effect on the travelling sphere, this would be a gravity issue, but being flat and on such a small scale and time, gravity can be neglected, but yes this maybe could be written out further (mathematically) or tested in some way, with heavier balls...(but that would increase friction)

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.
---

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).

Regards,
Daniel

ps. http://milesmathis.com/pi7.pdf
- Shoot Forth Thunder -

D_Archer

Posts: 1206
Joined: Sat Apr 18, 2009 4:01 am
Location: The Netherlands

### Re: A Simple Experiment Proves π = 4

D_Archer:
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,

Yes, when the ball is in the curve the track or path of contact is up on the side of the tube.
Imagine a Luge sled going through a fast curve, and the sled is up on the side of the chute.
To the person in the sled (just like the ball) the sensation will be of going in a straight line forward, BUT UPHILL.
That is why it takes longer than a straight downhill run.

This is all FUN TRICKS WITH MATH IMO.

Jack
jacmac

Posts: 562
Joined: Wed Dec 02, 2009 12:36 pm

### Re: A Simple Experiment Proves π = 4

oz93666 wrote:As it moves around the curve the orientation of the axis of spin is constantly changing , to do this requires a force , will this slow the ball?

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.

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.
It is a path that only leads to confusion and disappointment
More ** from zyxzevn at: Paradigm change and C@

Zyxzevn

Posts: 891
Joined: Wed Dec 11, 2013 4:48 pm

### Re: A Simple Experiment Proves π = 4

Zyxzevn wrote:
oz93666 wrote:As it moves around the curve the orientation of the axis of spin is constantly changing , to do this requires a force , will this slow the ball?

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.

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.
It is a path that only leads to confusion and disappointment

But there is no appreciable slowing down measured...

Same question for you as oz >
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).

Regards,
Daniel
- Shoot Forth Thunder -

D_Archer

Posts: 1206
Joined: Sat Apr 18, 2009 4:01 am
Location: The Netherlands

PreviousNext