## 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

Maol. Well, this certainly solves the paradoxical question of "What is the radius of a square?"

Airman. Pi are square.

Maol. Well, and I'm sure you easily see, Pi are square solves for the radii of a rectangle, which is sort of an ellipse with corners, like the difference between the tracks at Indy and Talladega, but only to an approximation, or several approximations, as required. Pi are cubed then solves for the multi-inclusive radii of an ellipsoid and requires more approximations, many more.
Maol

Posts: 284
Joined: Fri Mar 11, 2011 1:40 pm

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

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

Airman said. That’s what the experiment shows. We have two apparently different constant velocities: circular - 94.3cm/s; and straight - 120cm/s; that are both equal to 120cm/s when pi=4.

lw1990. Are you serious right now
They 'appear' to be different velocities because they are.
Your false idols of Mathis and his student have made you a foolish believer in the superstition of pi=4
By convincing you that the very real phenomenon of speed of the ball does not matter, but whatever bull they feed you, like 'distance warping magic' affects the experiment instead.

How do we know that a ball in any given experiment is traveling at any given speed, how do we know it is not just 'appearing to do so'? This is the kind of problem you get when you invent things with no basis in reality.

Airman. To calculate velocity, one needs to know distance and time.

Straight paths allow the single dimensional equation, (rate)*(time) = distance.
Unfortunately, the formula doesn’t “fit” curves, since curves are two dimensional.

Pi = Circumference/diameter, was invented in order to solve that. Pi=3.14 is the curve to linear metric that allows us to measure any curved path as a linear distance.

Steven’s experiment includes that. The circular track length is based on diameter 17.6cm.
Pi * diameter = 3.14 * 17.6cm = 55.3cm.

A steel ball is launched at 120cm/s into the circular track and completes it at a constant speed 0.5867 seconds later. The circular track velocity is thus: distance/time = 55.3cm/0.5867s = 94.3cm/s

Another steel ball is launched at the exact same time and initial velocity into a separate straight track, four diameters long (4*17.6cm), 70.4cm. Both balls travel for the same amount of time. The straight track velocity was a constant 120cm/s.

Two apparently different velocities: circular - 94.3cm/s; and straight - 120cm/s.

You might say there’s no problem here. The velocities cannot be equal because the distances 55.3cm and 70.4cm are different. If you watch the experiment (hypothetical you) you might even believe, as most would agree, the ball appears to travel slower through the circular track. The time may be the same but the two distances are different.

There’s a big problem. Steven was kind enough to include the 55.3cm distance (the Pi mark) on the straight track. When the ball in the circular track completes its circle, the straight track ball should be at the Pi mark, and not at the 4 mark, as is clearly shown in the video. A dilemma. This violates the known geometrical distance calculation (pi = 3.14 = 55.3cm/17.6cm = circumference / diameter). Repeat, geometry is broken here.

The two balls: 1) started with the same initial velocity; 2) experienced no significant friction; and 3) traveled the same amount of time. It’s not unreasonable to suspect that the two distances and velocities are actually the same.

A new motion metric is needed. The same experiment that demonstrates a failure in pi=3.14 geometry also shows us the correction, replace 3.14 with 4. We then see that the two distances and velocities are equal (70.4cm and 120cm/sec).

For objects in curved motion. Pi=4.

We should observe that we’ve always been underestimating certain distances and velocities. The ball is traveling ((4-3.14)/4) or 21 percent further and faster through the circular track than we thought.

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

Maol. Well, this certainly solves the paradoxical question of "What is the radius of a square?"

Airman. Pi are square.

Maol. Well, and I'm sure you easily see, Pi are square solves for the radii of a rectangle, which is sort of an ellipse with corners, like the difference between the tracks at Indy and Talladega, but only to an approximation, or several approximations, as required. Pi are cubed then solves for the multi-inclusive radii of an ellipsoid and requires more approximations, many more.

Airman. It’s not easy, but I think I see. Pi are hypercubed diagonalizes the universe, allowing us to solve for the radius in any corner of space and time. Thanks.
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LongtimeAirman

Posts: 233
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### Re: A Simple Experiment Proves π = 4

There’s a big problem. Steven was kind enough to include the 55.3cm distance (the Pi mark) on the straight track. When the ball in the circular track completes its circle, the straight track ball should be at the Pi mark, and not at the 4 mark, as is clearly shown in the video.

It is not a dilemma if the speed of one ball is slower than another ball, even if the speed slowly decelerates through the track, this still means normal physics is happening and nothing is broken or wrong. The experiment does not even come close to showing a shred of evidence that the speeds of the two balls are identical throughout the track. If it did, you might have a point, but it absolutely does not.

You're calculating 'velocity' based on a start distance and end distance of marks on the track, rather than calculating if there's actually a change in velocity while going through the track (like deceleration or even acceleration difference). Without those facts, it is pointless to compare the tracks. It's like saying if I go 60 mph at the start of a racetrack in my car, and you do the same, but then I accelerate to 70 mph in the middle of the track, while you don't, then when I finish first, it's because you went a longer distance. You'd never be able to figure out why I finished first by just measuring my start point and an end mark and calculating an 'overall velocity', since you don't know if I accelerated, all you can assume is that 'I didn't travel as far', then invent an idiotic answer like some curved space distance magic.

There is a whole lot of horrible science here, but let's start with the fact that you don't measure velocity through the track except the overall start point-end mark velocity because you can't fathom a reason why the speed would change within the two different tracks. Science doesn't give one shit what you can or can't fathom, measure it anyway, or don't bother to make stupid claims like pi=4.

Let's simplify again, to make this painfully clear.
Imagine you have two identical straight tracks, both balls are fired through them at the same time at the same exact initial speed, but one ball reaches the end of a track before the other by some significant distance.
Your immediate hunch would be that somehow, the speed of one ball differed through the track at some point, even though you don't know what caused it or when it happened, it may have even been throughout the entire track after the starting point. The point here is that you have to measure the speed of the balls throughout the track to find out why, you don't just go and assume that one track is sitting in a distance-warp-blackhole-field that made it travel less distance or greater distance ,like some asshole would, you put your science cap on and measure it.

This is the exact same scenario, except they looped the track to make you forget about doing that. Just because there is a loop, does not mean it's okay to skip the whole 'speed measurement' aspect and jump straight into reinventing geometry, you stupid, stupid, sheep.
lw1990

Posts: 101
Joined: Fri Oct 14, 2016 8:56 am

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

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Airman wrote. There’s a big problem. Steven was kind enough to include the 55.3cm distance (the Pi mark) on the straight track. When the ball in the circular track completes its circle, the straight track ball should be at the Pi mark, and not at the 4 mark, as is clearly shown in the video. A dilemma. This violates the known geometrical distance calculation (pi = 3.14 = 55.3cm/17.6cm = circumference / diameter). Repeat, geometry is broken here.

lw1990 wrote.
It is not a dilemma if the speed of one ball is slower than another ball, even if the speed slowly decelerates through the track, this still means normal physics is happening and nothing is broken or wrong. The experiment does not even come close to showing a shred of evidence that the speeds of the two balls are identical throughout the track. If it did, you might have a point, but it absolutely does not.

You're calculating 'velocity' based on a start distance and end distance of marks on the track, rather than calculating if there's actually a change in velocity while going through the track (like deceleration or even acceleration difference). ...

There is a whole lot of horrible science here, but let's start with the fact that you don't measure velocity through the track except the overall start point-end mark. ...

... The point here is that you have to measure the speed of the balls throughout the track to find out why, ...

Airman. Steven uses 13 marks – a baker’s dozen – in order to calculate, compare and monitor for a change of speed in the two tracks. Not, you might notice, just the “overall start point-end mark”.

The circular track length of 55.3cm is marked into quarters (0,1,2,3,4) (5 marks inclusive). The straight track has 6 marks, (-1,0,1,2,3,4) with unit separations of 17.6cm; 17.6 the straight track also has a “PI mark” at 3.14 showing where the circular track’s original 55.3cm distance would end. The -1 (-17.6cm) and 0 marks allow one to calculate and compare each ball’s observed initial velocity of 120cm/s. A time vs distance plot of the balls’ path through the track markers are shown.

The horizontal values 0.0000s, 0.1467s, 0.2933s, 0.4400s, 0.5867s, are the observed times the steel balls crossed their marks (0,1,2,3,4) in both tracks. The corresponding distances are indicated on the plot lines.

Five measured points for each track lets us calculate 4 interval (quarter track) velocities. The velocity calculation for each interval is given by:

velocity = change of distance over the change in time, or
velocity(current) = (currentPosition – previousPosition)/(currentTime-previuosTime)

Circular track:
(0,1). 1st interval. (13.8-0)/(0.1467-0) = 94.3cm/s
(1,2). 2nd interval. (27.7-13.8)/(0.2933-0.1467) = 94.3cm/s
(2,3). 3rd interval. (41.5-27.7)/(0.4400-0.2933) = 94.3cm/s
(3,4). 4th interval. (55.3-41.5)/0.5867-0.4400) = 94.3cm/s

Straight track:
(0,1). 1st interval. (17.6-0)/(0.1467-0) = 120cm/s
(1,2). 2nd interval. (35.2-17.6)/(0.2933-0.1467) = 120cm/s
(2,3). 3rd interval. (52.8-35.2)/(0.4400-0.2933) = 120cm/s
(3,4). 4th interval. (70.4-52.8)/0.5867-0.4400) = 120cm/s

As you can see, our two apparently different velocities of 94.3cm/s and 120cm/s occurred over each of our quarter intervals

All velocities, including our initial velocities are 120cm/s when Pi=4.

We also have a camera with frame rate. Measurement marks may be placed along the entire length of transparent tubing. Make that a future refinement. It isn’t necessary, the demonstration is clear.

My previous post referred to constant velocities. That’s what these plots show. There are no decelerations observed. Any friction present is acting over both tracks equally and is at least an order of magnitude less than the observed curve-to-linear (pi=3.14) metric error.

Pi=4 for bodies in curved motion.
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LongtimeAirman

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

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

As you say, there are two different velocities through the track - to every single person outside the mathis cult, this means that one ball is traveling at a different speed than the other ball.

Why do you claim that this is not true? Because you can't fathom why one ball would be slower than the other, so you invent a reason - the pi=4 thing. Science doesn't give a shit what you can't conceive of, sheepish fool.

The claim that pi=4 solves the 'mystery' of the results of the experiment is not part of the experiment, you tacked that idiotic speculation onto the experiments results, the experiments results itself just shows one ball has a slower speed than the other ball, indicated by your own graph. If pi=3.14, as we all know it does, there is a speed difference between the balls throughout the track, period. If pi=4, then the speeds are the same, but there is absolutely no reason at all to assume pi=4 for a curved track, just because it makes the speeds the same and that's what you think should happen. Science doesn't give a shit what you sheepish idiots think about what should happen in the experiment, or that the balls should go the same speeds in your tiny little brains. It just models reality, not what you want to see happen.

In order to show that one ball is traveling a further distance in the same amount of time, balls have to go the same speed - apples to apples, yet reach different distances. The velocities (speeds) are not the same, so your argument is flawed (that's a kind word, more like completely f#*!ing stupid). Note: going the same speed yet reaching different distance is impossible, as shown by literally every moving object in history, so convincing others of your completely Stupid claim is going to be hard to do in general, and have success limited only to other sheepish people.
lw1990

Posts: 101
Joined: Fri Oct 14, 2016 8:56 am

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

lw1990 wrote:The velocities (speeds) are not the same, so your argument is flawed (that's a kind word, more like completely f#*!ing stupid). Note: going the same speed yet reaching different distance is impossible, as shown by literally every moving object in history, so convincing others of your completely Stupid claim is going to be hard to do in general, and have success limited only to other sheepish people.

Oh I don't know... I don't think it is sheepish at all to have the courage to state that pi = 4 when motion is involved. It can be unpleasant as is clearly apparent from reading this thread

It goes like this folks.
Pi = 3.14 in Euclidian geometry.
But Euclidian geometry doesn't work when movement, hence time, is involved.

So Miles uses something called cycloid mathematics. You will read there 'that the length of half an arc of cycloid is 4r and a complete arc is 8r'. And since pi is the ratio of the circumference and the diameter, it follows that... pi = 4. Been known since the 16th century. Not new.

I know it can be hard to wrap our head about it at first. But we can do it. It's worth the effort

P.S. There is also something called Manhattan geometry you can look into. It states that the circumference of a circle is(C(O,r,d)=8 x r. But that one is too strong for me. It is apparently useful math for some folks though.

Melusine

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Location: Maryland, USA

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

lw1990. As you say, … there are two different velocities through the track - this means that one ball is traveling at a different speed than the other ball.

lw1990. Why do you claim that this is not true? Because you can't fathom why one ball would be slower than the other, so you invent a reason - the pi=4 thing.

Airman. Steven’s experiment shows us exactly what is happening:

Length. Two tracks, side-by-side; 1) circular and 2) straight; cut to two different lengths:
1) 55.3cm=3.14 * 17.6cm and 2) 70.4cm=4 * 17.6cm; and marked into quarters (0,1,2,3,4).

Motion. Two balls are released into the tracks; same initial velocities – 120cm/s; same start(0.0000), middle (0.1467s, 0.2933s, 0.4400s,) and stop(0.5867s) times; Speeds are constant throughout the experiment; 1) 94.3cm/s and 2) 120cm/s; indicating no apparent friction in either track.

Yes, it seems we have two speeds.

We also have synchronized motion (ball start/stop times) across geometrically unequal distances. According to geometry (pi=3.14), the straight ball should have been at the Pi mark when the curve ball completed its circle, not the 4 diameter mark.

You insist that different speeds explain everything. Why can’t I just accept that speeds are different through curves and straights?

More than 20% different? With a ratio involving 3.14 and 4? They started at the same speed, and their track speeds remained constant. Friction’s been eliminated. Motion thru both tracks are synchronized. But why call it a slowdown? A constant velocity difference ratio of 20% without a change in time isn’t a slowdown, it’s a distance scaling change.

And so the solution is simple. The experiment shows us a direct comparison of curved and linear motion that happens to conflict with our current understanding of geometry. A new motion metric where we are shown that both distances are equal (70.4cm) and both velocities are equal (120cm/s). For bodies in motion pi=4.
lw1990. The experiment does not even come close to showing a shred of evidence that the speeds of the two balls are identical throughout the track. If it did, you might have a point, but it absolutely does not.

Airman. I showed you the evidence that the balls’ velocities were constant around the track and you refuse to consider it.

Honestly, I’m been grateful for the discussion. But your contributions are reduced to invective and insult the idea of a forum.

We have a simple experiment demonstrating new physical motion - and you refuse to hear it. You could do real science by investigating and debunking the real thing and not waste your time here.

Let’s just agree to disagree.
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LongtimeAirman

Posts: 233
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### Re: A Simple Experiment Proves π = 4

lw1990 wrote:
But Euclidian geometry doesn't work when movement, hence time, is involved.

Yes it does, do you see trains crashing into each other because their travel times are computed using normal velocities??

Euclidean geometry works well to design train tracks on the ground. But it doesn't work to design train schedules because it doesn't take velocity or acceleration into account. Besides, trains don't usually go around in circles.

lw1990 wrote:Btw I'm glad that there are a couple of vague concepts you're throwing around, and that one is 'too strong' for you.

The need for cyloid mathematics became apparent in the 16th century. Galileo and Descartes worked to develop it, amongst many others.
Manhattan geometry is more recent. Minkowski did extensive work on it in the 19th century. You might like it, it doesn't deal with trains but with taxicabs. Another practical application is in calculating positional distributions of hexamers in gene splicing. Those are not vague concepts.
Manhattan geometry is 'too strong' for me because i'm not interested in studying it. That's probably why Steven O.'s experiment is too strong for you. You're not interested in studying it. Clearly.

Melusine

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

@Airman, sorry I insulted you, but it is just so aggravating because this seems so simple, not worthy of 5 or 6 pages of discussion but a single reply and everybody should understand

The speeds of the balls have to be constant and the same around the track, not just constant yet different.
Both balls start out 120 cm/s as you say,
One ball becomes 94.something cm/s as you say,
This means it is not 'constant', it changed. It may remain 94.something cm/s through the track from there on out, but it did not remain a constant 120 cm/s as it started out. You can't say that it could become some other value, yet remains the same; common sense.

In order for a ball to go from 120 cm/s to 94.something cm/s it has to decelerate (slow down), for some reason.
What this reason is, we don't have a concrete idea for yet, although many have been proposed.
The reason the proposed answer of pi=4 or distance-warping doesn't make any sense is because we already know the speeds changed. If the speeds didn't change, then it would make more sense that some distance magic happened, but the speeds change, meaning one ball can travel a further distance in a certain timeframe because it's going faster through the track, no need for the voodoo magic of pi=4 to exist at all to explain this.

What is going on here is that a few people don't know for certain why the ball is decelerating to 94.something in the curved track. Merely not knowing why doesn't mean that you can ignore the facts; one of the facts being that the balls are going different speeds through the track, not different distances. Instead of reconciling this fact, some lazy thinking happened and in order to make the balls appear to be going the same speed, as some people want to believe should happen, they changed the mathematical variable pi only for one track and not the other, in order to manipulate the results and force the speeds to be the same on paper, when they are not in reality. This is not rational. If you have a measuring tape for one track, and a different measuring tape for the other track, and both measuring tapes are based on different length marks, you can't compare measurements between the track because you aren't comparing 1 to 1, apples to apples, pi to pi, you are changing things around on paper and your results will be nonsense.

it is very simple - if the curved track ball was truly going a further distance, it would be able to keep its 120 cm/s speed and still take longer to reach an equivalent mark on the track. There would not be a speed differentiation because it would simply have more track to go on. This is very obviously nonsensical/irrational, since the tracks are the same length (if the experiment was set up right). The obvious answer then, is exactly what the experiments results show - one ball decelerates to 94.something cm/s , the other does not, and the difference in speed explains the reason one gets to a certain mark faster than the other - normal science. It can be a bummer that the world is not full of alice in wonderland magic, but we have to just accept it. There's plenty of awesome things left to investigate anyway.
Last edited by lw1990 on Fri Oct 28, 2016 1:31 pm, edited 2 times in total.
lw1990

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Joined: Fri Oct 14, 2016 8:56 am

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

Two posts containing ad hominem attacks have been removed from this thread.
The poster has been informed of the TB Forum's position on personal attacks.
viewtopic.php?f=11&t=4

So I hope that no forum members will be intimidated by the threat of personal attacks and also that no forum members will be tempted to respond in kind.
The simple rule of thumb is - attack the idea not the presenter of the idea.

nick c
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Location: connecticut

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

We actually discussed this topic a few years back here: Mathis and pi

Basically, Mathis assumes circular motion as a continous zigzag movement. This assumption correctly gives a square circumference to a circular path. I'll argue the motion constitutes continous and smooth steps of diagonals, like the circumference of a polygon. Except it's an integrated circular path (detailed polygon). This path is smaller than the aforementioned square.

As for the video (maybe it already has been mentioned), I believe the bent tube will add a slight amount of friction to the motion due to the radial redirectioning. The original rolling motion of the ball will meet some resistance from the tube walls, at some points counter-roll the motion. If the ball had color patterns, this would show up. If the tube was very elastic, the ball would clearly lose energy to tube deformation.

Someone should do an experiment in an empty parking lot. Steering wheel in a set position and with constant (measured) speed. Measure path radius and round time. Probably need another person to set out marks for the path. Compare measurements to calculations with traditional and proposed values of pi.

Siggy_G
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Location: Norway

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

This discussion is getting ridiculous.

It is CERTAIN that PI=3.14...

It does not matter what movement there is.
Nor what experiment there is.
PI does NEVER change!

I have explained many ways to calculate PI.
All these DIFFERENT ways, give the same answer PI=3.14....

For me anyone claiming something different is similar
to someone claiming earth is flat.

I am sorry that the understanding of maths and physics is so low for some people that they actually
think that Mathis might be valid.

If you think Mathis might be valid, learn some maths by a good teacher.
I am sorry for the people that FELL for the WRONG mathematics by Mathis.
He is simply very poetic, but not a good mathematician.

The defence of Mathis is to introduce very COMPLEX maths, and make it seem simple
by assuming some FALSE things. Two wrongs do not make something right.
Making FALSE assumptions do not make some COMPLEX maths simple. It makes it FALSE.

I think a threat like this should be removed/deleted, because it does make the EU seem silly.
This is not a "new insight" or a "mad idea".. it is a totally WRONG idea.

--------------------------------------------------------------------

Now that is out of the way, we can analyse the track problem...

The track problem is the bad understanding of physics by LongTimeAirman.
I asked him about the SPEED of the ball AT EVERY part of the track,
and explained how he could measure it.
I am dissapointed that he did not do it.
It is clear that the SPEED is lower in the curved track.
There is no discussion about it.
LongTimeAirman, even thinks that it might slow down due to the track being longer because it is curved,
for some magic reason. Which if you think about it, is really silly.

And looking at the video, we can see that the ball does not slow down suddenly.
Our eyes would see that sudden speed-adjustment.
So LOGICALLY the ball must slow down gradually.
And that means that the ball encounters some kind of resistance.

So from these simple observations we can both see that LongTimeAirman is wrong,
and that he does not understand physics either.

I am ok if LongTimeAirman wants to discuss what causes the resistance/speed reduction,
I can see that he find it difficult to understand.
I am also OK to explain to him how you can calculate PI. (See beginning thread).
And how you can use PI=3.14.. to do complex maths.

But all the talk about PI is pure TROLLING by LongTimeAirman,
because PI has nothing to do with it, and PI never changes.

So from now on I will report any future post that claims that PI=4, as TROLLING.

If this goes on I would even advice to BAN ALL posts referring to MATHIS.
More ** from zyxzevn at: Paradigm change and C@

Zyxzevn

Posts: 860
Joined: Wed Dec 11, 2013 4:48 pm

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

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Siggy_G. We actually discussed this topic a few years back here: Mathis and pi
viewtopic.php?f=8&t=3183

Airman. Thanks for the reading material, what an eye-opener. I wasn’t a member yet and hadn’t seen it. Mathis and pi is a sensitive issue here and I think I understand that and a few of the earlier responses in this discussion much better now.

Thanks too, in a cosmic sense. I see TB member StevenO was also part of the discussion.
viewtopic.php?f=8&t=3183&start=15#p34628
StevenO wrote: Re: Mathis and pi

Hi Siggy,

As I stated before, to get a good grasp of this dynamic circle vs. geometric circle problem, you should really study Miles' papers on the calculus. The mistakes in the calculus spill over to a lot of area's in physics and lead to many misconceptions. A math description is always less complete than the actual physics.

Airman. After reading that whole discussion I don’t know if you did or not. You may have won the discussion at the time, unfortunately the whole Mathis and pi thing has developed into a schism. This board has suffered because of it.

That discussion is history. Everyone needs to move on.

StevenO went and created an actual demonstration of the dynamic circle vs. geometric circle problem. I daresay you played a part in StevenO’s motivation (hence cosmic).

Siggy_G. As for the video (maybe it already has been mentioned), I believe the bent tube will add a slight amount of friction to the motion due to the radial redirectioning.
The original rolling motion of the ball will meet some resistance from the tube walls, at some points counter-roll the motion. If the ball had color patterns, this would show up. If the tube was very elastic, the ball would clearly lose energy to tube deformation.

Airman. "(maybe it already has been mentioned)" – yes, I’ll review:

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

StevenO‘s experiment “shows that, while Pi as a distance is 3.14, Pi as a distance/time is 4”

Two transparent pvc tube tracks, side-by-side;
Length. 1) circular and 2) straight; cut to two different lengths:
1) 55.3cm=3.14 * 17.6cm and 2) 70.4cm=4 * 17.6cm; and marked into quarters (0,1,2,3,4).
Motion. Two balls are released into the tracks; same initial velocities – 120cm/s; same start(0.0000), middle (0.1467s, 0.2933s, 0.4400s,) and stop(0.5867s) times; Speeds are constant throughout the experiment; 1) 94.3cm/s and 2) 120cm/s; indicating no apparent friction in either track.

Airman. About the apparent speed difference (94.3cm/s and 120cm/s) between the two tracks I wrote:
More than 20% different? With a ratio involving 3.14 and 4? They started at the same speed, and their track speeds remained constant. Friction’s been eliminated. Motion thru both tracks are synchronized. But why call it a slowdown? A constant velocity difference ratio of 20% without a change in time isn’t a slowdown, it’s a distance scaling change.

And so the solution is simple. The experiment shows us a direct comparison of curved and linear motion that happens to conflict with our current understanding of geometry. A new motion metric where we are shown that both distances are equal (70.4cm) and both velocities are equal (120cm/s). For bodies in motion pi=4.

I agree the experiment could be improved. I’ve remarked that colored marbles can be used to see whether any strange rotations are present. Nevertheless, for those who will see, it is clear. The fact of the matter is that this wonderful, world changing demonstration was created by a TB member as a result of discussion here.

For bodies in curved motion (accelerations comprised of orthogonal velocities) Pi=4
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LongtimeAirman

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

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

Miles says:
It doesn't seem right
that just turning a tube into a circle would make it longer. It looks at first like when you lay the tube
out straight, it is pi diameters long, but when you curve it into a circle, it magically becomes 21%
longer. Well, it doesn't really become longer, and we know that since we can straighten it back out and
it is still pi diameters long. But something about curving it changes it. It doesn't change the length, it
changes the distance that has to be traveled.

" it doesn't really become longer"
"It doesn't change the length"

" it changes the distance"

There is your basic situation; length no longer equals distance when length is put in a circle.
I am impressed with the wonders of mathematics.

When I was younger, I ran track at school. When I ran straight my body was vertical(not counting a slight forward lean). When I ran the curves I had to lean to the left and it was more difficult to maintain the same speed as running straight.

What I did not know then was the curved part of the track got longer when I ran on it.
Thank you for clearing that up for me ! Now I understand everything.

Jack
jacmac

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

Siggy_G wrote:Someone should do an experiment in an empty parking lot. Steering wheel in a set position and with constant (measured) speed. Measure path radius and round time. Probably need another person to set out marks for the path. Compare measurements to calculations with traditional and proposed values of pi.

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.

Melusine

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