merjet

Aristotle's wheel paradox

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Chickweed is the correct choice of words, as in, "Mervin is feeding pretty chick's over 21, weed and champagne, pronounced chawm panya."
 

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2 hours ago, anthony said:

Aristotle's wheel paradox

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Aristotle's Wheel

Aristotle's wheel paradox is a paradox or problem appearing in the Greekwork Mechanica traditionally attributed to Aristotle.[1] A wheel can be depicted in two dimensions using two circles. The larger circle is tangent to a horizontal surface (e.g. a road) that it can roll on. The smaller circle has the same center and is rigidly affixed to the larger one. The smaller circle could depict the bead of a tire, a rim the tire is mounted on, an axle, etc. Assume the larger circle rolls without slipping for a full revolution. The distances moved by both circles are the same length, as depicted by the blue and red dashed lines. The distance for the larger circle equals its circumference, but the distance for the smaller circle is longer than its circumference: a paradox or problem.

The paradox is not limited to a wheel. Other things depicted in two dimensions show the same behavior. A roll of tape does. A typical round bottle rolled on its side does -- the smaller circle depicting the mouth or neck of the bottle.

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

SHOW me the "slippage".

We've done so over and over again.

Quote

You guys would be lost without an inner track, there is no "track" in the diagram and no possible slippage.

The diagram at Wikipedia has been altered recently, most likely by your fellow moron Merlin, trying to cheat reality. It's not working.

Quote

HOW does the small circle rotate once, precisely equal to the large circle's single rotation? It rotates relatively slower. At least 4 times I've explained that, not once has anyone acknowledged or argued it.

Asked and answered, explained and illustrated, in multiple ways, over and over again. You are not cognitively capable of grasping it. The problem exceeds your visuospatial/mechanical reasoning abilities.

J

 



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Sooo. That is a representation of two car wheels on one side of a car, attached to a chassis? Classy. It would be more illustrative if we could see a Rolls Royce body. Are the larger and smaller wheels really just one wheel?

Where's the car jack and the spare? It's a joke officer. There's nothing in the glove compartment and that smell is just rubbing alcohol I put in my ears after showering. What? Well yeah. I had a bit of an ear ache. Hic! 

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52 minutes ago, Max said:

 

Note that the original text states: The wheels roll without slipping for a full revolution. In the new version the lines are no longer continuous, but dotted, and moved to the upper side to remove any notion of rolling over a support, that was clearly implied in the original version (rolling without slipping!). The small wheel in the new version no longer rolls at all. Those changes are a bit too obvious. We were all these pages discussing the original version, to refer now to a changed version is a bit disingenuous, it's like moving the goalposts.

It really doesn't change anything, other than making it even harder for Merlin or Tony to grasp what's going on. They're intent on framing the setup in terms that they seem to hope will result in others being as cognitively limited as they are.

It's like, "But if we take away X from the original, and we make Y metaphorical or nonexistent, then you guys are just like me, right, and you can't see the slippage, right? Since theres  no longer a line or surface that the inner wheel is supposed to roll on,  you no longer have a means of reference for comparison, and therefore you can't honestly claim to see slippage! So now you're just as limited as I am!"

They don't like the reply, which is that We can still see the slippage because they haven't succeeded in removing our reference for comparison, which is the line on which the large wheel rolls. I, and I'm sure many others, can track subdivisions on the small wheel and the distance that they travel in comparison to the bottom line (For an example of something like what my mind sees, see the illustration that I posted back on page 32 or 33, or around there somewhere, the one with the yellow squares on wheels).

To me, and to most people, this type of thinking and visualizing is very easy stuff. Not so for Merlin and Tony. They don't and can't see and comprehend what we can, and they refuse to believe that we can. It's all very upsetting to them.

J

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On 11/12/2018 at 11:13 AM, anthony said:

Bob: Nothing changes if there is to be a 'track' the inner wheel is on, or if the line is an imaginary 'path'. You get the same result with two surfaces, or one. Set up or picture an experiment with any bottle (best, because it has a protruding "inner circle", the neck and cap seen from the side). Construct two parallel tracks for the bottle to rest on. One higher than the other to finely adjust for the differing diameters. When the bottle is evenly balanced and leveled on both tracks, roll it along them and observe that both bottle and neck will roll evenly, with no skipping, slipping or jamming. (I'm sure if it's not balanced well, it will veer off course)..

Tony says the lid does NOT over-spin it’s track.

 

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53 minutes ago, Jonathan said:

It really doesn't change anything, other than making it even harder for Merlin or Tony to grasp what's going on. They're intent on framing the setup in terms that they seem to hope will result in others being as cognitively limited as they are.

It's like, "But if we take away X from the original, and we make Y metaphorical or nonexistent, then you guys are just like me, right, and you can't see the slippage, right? Since theres  no longer a line or surface that the inner wheel is supposed to roll on,  you no longer have a means of reference for comparison, and therefore you can't honestly claim to see slippage! So now you're just as limited as I am!"

They don't like the reply, which is that We can still see the slippage because they haven't succeeded in removing our reference for comparison, which is the line on which the large wheel rolls. I, and I'm sure many others, can track subdivisions on the small wheel and the distance that they travel in comparison to the bottom line (For an example of something like what my mind sees, see the illustration that I posted back on page 32 or 33, or around there somewhere, the one with the yellow squares on wheels).

To me, and to most people, this type of thinking and visualizing is very easy stuff. Not so for Merlin and Tony. They don't and can't see and comprehend what we can, and they refuse to believe that we can. It's all very upsetting to them.

J

I think they could if they tried.

But they don’t want to try because they’re not motivated to posses the truth, they want to “win.” That’s what’s holding up their personal growth at the moment.

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1 hour ago, Jon Letendre said:

Tony says the lid does NOT over-spin it’s track.

 

Nice example of an instructive illustration with very simple means. It's sooo obvious!

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On 11/16/2018 at 2:31 PM, Max said:

Excerpts in quotes and blue text below.

"So you admit that it is a solution."

Wrong. I said you believe it, not I believe it.

"There is nothing to understand."

So you don't understand it. Try harder. Maybe someday you will. 

"Therefore the notion of slippage is essential for understanding and solving this paradox."

Wrong. I gave two solutions, neither of which invoke slippage. Also, the Wikipedia article says the larger circle rolls without slipping. Get it? No slippage!

"Wrong. As I’ve shown above, the “translation solution” isn’t a solution, it’s just stating one half of the paradox problem."

Wrong. The problem as stated says nothing whatever about the necessary properties of translation nor even mentions translation.

"You can’t expect me to “answer”, as you didn’t ask me anything in that post."

Wrong. I quoted your using "support" and I asked "Its support??" Then I repeated a formula from August 6 challenging anybody who read it to quantify the three terms on the right side of an equation, shown again below. I'll even pre-fill the 3rd term for you with what you have asserted. 

2*pi*R = Rotation + Translation + Slippage
2*pi*R =  _____   +    _____    + 2*pi*(R – r)

Fill in the blanks. Is that so difficult?
 

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12 hours ago, Max said:

Nice example of an instructive illustration with very simple means. It's sooo obvious!

Yes, but the question is, how will Tony and Merlin avoid grasping it?

Will Tony say that he was referring to bottles, not to straws and lids, and especially not to masking tape (!), so therefore the principle has been altered in Jon's video, so it's a scam and illusion? The masking tape plays a big part in creating the overspin, which wouldn't be there otherwise?

Also, you can see Jon's hand in the video. There's no hand in the original description of the "paradox," nor in the one that Merlin probably replaced the original with at Wikipedia, so therefore his hand has tainted the experiment. The presence of the hand eliminates the possibility of slippage of the straw on its surface, thus putting all of the slippage on the lid and its surface. Tsk tsk. That wasnt in the original setup!

We have to refuse to consider any means of either measuring slippage or isolating it, because if Tony and Merlin can't see and comprehend it, then it isn't there, despite the fact that others can see and comprehend it.

Illusions and scams! Your videos and your reality are all illusions and scams. The only thing that is real and is the truth is cycloids, even though Merlin can't plot them or trace them. The cycloids that Merlin imagines but which he can't produce in reality are arbitrarily the only concept excluded from being illusions and scams.

J

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On 11/17/2018 at 1:44 PM, Jonathan said:

[More psychologizing nonsense and lies from the obnoxious reality-faker.]

 

On 11/17/2018 at 1:54 PM, Jonathan said:

[More psychologizing nonsense and lies from the obnoxious reality-faker.]

 

On 11/18/2018 at 11:09 AM, Jonathan said:

[More psychologizing nonsense and lies from the obnoxious reality-faker.]

 

On 11/18/2018 at 11:21 AM, Jonathan said:

[More psychologizing nonsense and lies from the obnoxious reality-faker.]

 

On 11/18/2018 at 3:39 PM, Jonathan said:

[More psychologizing nonsense and lies from the obnoxious reality-faker.]

Ha ha ha ha ha ha ha ha. 

Tony and I aren't duped by your con art videos and drawings, and it's clearly very upsetting to you. You get riled and post multiple times, the posts filled with vicious personal attacks and devoid of reason. They consist of psychologizing and insulting they who challenge your nonsense and don't swallow your faking reality. Every one of your con art videos and drawings has a horizontal surface tangent to the smaller circle that you allege it literally slips on. It isn't merely to show motion relative to a real surface. We can easily see that without your fakery. No, you put the extra surface there to serve your personal agenda. You treat it as real as the surface below the larger circle or wheel. You epitomize faking reality. In reality a wheel on a car or truck does not have a horizontal surface tangent to and supporting the rim. Invoking said surface is your "crutch", and without it you are too lame-brained to deal with reality. Your accusing me of "cheating and altering reality" is gross hypocricy that stems from your failure to grasp reality without faking it.

Your arbitrary assertion that "the smaller circle/wheel slips" is nothing better than a sloppy metaphor from your diseased imagination unhinged from reality.

Your faking reality has been exposed. Beep, beep. Vrooom.

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20 hours ago, Peter said:

The jet on the moving tarmac idea was ingenious. It shows that in the real world more factors, like thrust or a cat batting the tinker toy Legos. are involved.   

Peter, It is an interesting exercise, testing one's (sometimes) faulty premises involving identity and causality. Q. When is a jet plane like a horse and wagon? A. Their sets of wheels. Both are unconnected from the power train. Their wheels, very simply, provide a rolling platform and no more. Momentum comes through engine thrust or horse-power, not wheel power. Unlike what we are better used to of autos and bicycles, and a direct drive to the wheels. The red herring in this 'paradox' is (dis)information about a rolling conveyor belt -- which leads one to think about the wheel rotation and the runway's and wheels' effect on the plane's velocity, etc., and likely, wrong conclusions.

In a related second part, one's informed knowledge is that an airplane's lift and flight are solely dependent on airspeed, not (directly) ground speed. Therefore, sneaking in a mention of the wheels and the runway is misleading and superfluous info. Here again, there is a nice blend of observed, abstracted knowledge and 'educated' knowledge, integrated with no contradictions.

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2 hours ago, merjet said:
   17 hours ago,  Jonathan said: 

[More psychologizing nonsense from the obnoxious reality-faker.]

 

Oh, no! I've been accused, by a Rand-follower, of the dreaded Objectivist Sin of "psychologizing"!

I suppose that I'm supposed to crumble, and wallow in guilt.

But, wait. What is "psychologizing"?

Saint Ayn defines it thusly: "Psychologizing consists in condemning or excusing specific individuals on the grounds of their psychological problems, real or invented, in the absence of or contrary to factual evidence."

Hmmm. So, my comments about Tony and Merlin are not applicable, since I haven't been condemning or excusing them, nor have I done so on the grounds of their psychological problems, but rather I have been objectively judging their ability to cognitively function in specific regard to visuospatial/mechanical reasoning, and I haven't done so in the absence of factual evidence, nor contrary to it, but rather have based my judgments specifically on the factual evidence.

Merlin, I know that, as a Rand-follower, you probably think that the accusation of "psychologizing" is a powerful weapon in your arsenal. Well, sorry, but it's not. Judgments of your cognitive impairment based on overwhelming evidence (38 pages worth now) don't magically become "psychologizing" just because you dislike the factual reality that the judgments represent.

You are, in fact, visuospatially/mechanically inept.

And here's yet more evidence of your visuospatial/mechanical incompetence:

2 hours ago, merjet said:

Tony and I aren't duped by your con art videos and drawings...and don't swallow your faking reality. Every one of your con art videos and drawings has a horizontal surface tangent to the smaller circle that it "slips" on. It isn't merely to show motion relative to a real surface. We can easily see that without your fakery. No, you put the extra surface there to serve your personal agenda. You treat it as real as the surface below the larger circle or wheel. You epitomize faking reality. In reality a wheel on a car or truck does not have a horizontal surface tangent to and supporting the rim. Invoking said surface is your "crutch", and without it you are too lame-brained to deal with reality. Your accusing me of "cheating and altering reality" is gross hypocricy that stems from your failure to grasp reality without faking it.

Your arbitrary assertion that "the smaller circle/wheel slips" is nothing better than a sloppy metaphor from your diseased imagination unhinged from reality.

Your faking reality has been exposed. Beep, beep. Vrooom.

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Check out the edit history at Wikipedia:

https://en.wikipedia.org/w/index.php?title=Aristotle's_wheel_paradox&action=history

Merjet, Merjet, Merjet.

He's obsessed with it. He seems to think that if he alters the "paradox" at Wikipedia, especially by visually eliminating the Mechanica's reference to the upper line that the smaller circle contacts throughout its motion, then that's the final authority. It trumps reality.

The Wikipedia page is no longer about "Aristotle Wheel Paradox," but has now become "Merlin's Personal Attempt to Distort the 'Paradox' So That He Can Feel That He Won Over at OL."

J

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41 minutes ago, Jonathan said:

Check out the edit history at Wikipedia:

https://en.wikipedia.org/w/index.php?title=Aristotle's_wheel_paradox&action=history

Merjet, Merjet, Merjet.

He's obsessed with it. He seems to think that if he alters the "paradox" at Wikipedia, especially by visually eliminating the Mechanica's reference to the upper line that the smaller circle contacts throughout its motion, then that's the final authority. It trumps reality.

The Wikipedia page is no longer about "Aristotle Wheel Paradox," but has now become "Merlin's Personal Attempt to Distort the 'Paradox' So That He Can Feel That He Won Over at OL."

J

I'm reminded of Michael Mann's contortions clinging to his Hockey Stick model.

Ellen

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5 hours ago, merjet said:



>>  = me 

>   = merjet

black = me

 

 

> >So you admit that it is a solution."

>  Wrong. I said you believe it, not I believe it.


No, that is not what you said. You said:

> I get it. You believe there is only one correct solution -- merely because you like it. There are many proofs of the Pythagorean Theorem. Is only one of them correct merely because you like it best?

That implies that you believe that there is more than one correct solution, and that implies again that you admit that the mentioned solution is correct, otherwise you’d said “you believe the wrong solution”.


>> Therefore the notion of slippage is essential for understanding and solving this paradox."

> Wrong. I gave two solutions, neither of which invoke slippage. Also, the Wikipedia article says the larger circle rolls without slipping. Get it? No slippage!

The fact that the article mentions that the larger circle rolls without slipping is already an indication that the notion of slippage is important (why mention it otherwise?). Moreover, the original Wikipedia article you linked to in your first post stated: The wheels roll without slipping for a full revolution. That was much better than your new version, as it showed immediately the crux of the paradox, namely the supposition that both wheels at the same time can roll without slipping, which is impossible.


>> "Wrong. As I’ve shown above, the “translation solution” isn’t a solution, it’s just stating one half of the paradox problem."

> Wrong. The problem as stated says nothing whatever about the necessary properties of translation nor even mentions translation.

As if the wordtranslation” would be essential! The article mentions “The distances moved”, which of course implies translation. The paradox is that those distances seem to be different while they must of course be equal. That story of the cycloids is completely unnecessary, as the only thing you conclude from that story is that the center(s) of both wheels travel over the same distance. You don’t need any cycloid to “prove” such a trivial thing. In your second “solution” you just state the same, without the whole cycloid circus. Further, you still haven’t really solved the paradox, you’ve only “proved” that those two distances must be equal. Well, we knew that all along, as that is part of the paradox statement.

What still has to be shown is, why the supposition that both wheels roll without slipping (explicit in the original version, implicit in the new version) is wrong. The answer is of course that when one wheel (the large one or the small one) rolls without slipping, the other wheel automatically must be slipping to travel the same distance, to make up for the difference in traced circumferences.

 

>> "You can’t expect me to “answer”, as you didn’t ask me anything in that post."

>Wrong. I quoted your using "support" and I asked "Its support??" Then I repeated a formula from August 6 challenging anybody who read it to quantify the three terms on the right side of an equation, shown again below. I'll even pre-fill the 3rd term for you with what you have asserted. 

That is disingenuous, “its support?” is not a serious question. You meant apparently those formulae, but there you didn’t ask anything. Sorry, but I can’t know what you’re thinking if you don’t express yourself clearly.

 

> 2*pi*R = Rotation + Translation + Slippage
2*pi*R =  _____   +    _____    + 2*pi*(R – r)

Fill in the blanks. Is that so difficult?

Not at all. First, those variables are not independent, we're talking about the (center of the) circles, not about a point on the circles.

For the large wheel (radius R) that rolls (one revolution) without slipping: Translation = Rotation = 2πR

For the small wheel (radius r) that rolls and slips, while the large wheel rolls without slipping: Translation = rotation + slippage = 2πr + 2π(R-r) = 2πR, as you’d expect.

Simple comme bonjour!

 


 

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6 hours ago, merjet said:

"So you admit that it is a solution."

Wrong. I said you believe it, not I believe it.

"There is nothing to understand."

So you don't understand it. Try harder. Maybe someday you will. 

"Therefore the notion of slippage is essential for understanding and solving this paradox."

Wrong. I gave two solutions, neither of which invoke slippage. Also, the Wikipedia article says the larger circle rolls without slipping. Get it? No slippage!

"Wrong. As I’ve shown above, the “translation solution” isn’t a solution, it’s just stating one half of the paradox problem."

Wrong. The problem as stated says nothing whatever about the necessary properties of translation nor even mentions translation.

"You can’t expect me to “answer”, as you didn’t ask me anything in that post."

Wrong. I quoted your using "support" and I asked "Its support??" Then I repeated a formula from August 6 challenging anybody who read it to quantify the three terms on the right side of an equation, shown again below. I'll even pre-fill the 3rd term for you with what you have asserted. 

2*pi*R = Rotation + Translation + Slippage
2*pi*R =  _____   +    _____    + 2*pi*(R – r)

Fill in the blanks. Is that so difficult?
 

Merjet, The entire 'paradox" comes tumbling down when a viewer recognizes one fact. 

EVERY point and every size of circle inside the wheel will travel the same (pink dotted line) distance; and equal to the wheel's travel (blue line)

A -> B is a CONSTANT (For a given circle).

E.g. A point at 2 o'clock on the big wheel's outer rim when rotated once, ends up in the same position, AND the same (pink/blue dotted line) length of travel. O .... O Put your point anywhere else inside, the same thing.

I don't know how long those visuo-spatial experts need to see this.

Once realized, Bang! goes the 'paradox'. There is no problem or paradox, the diagram is true to reality.

The dotted Pink line *always* equals the dotted Blue line. For any specific point and for every inner circle.

What does one infer from that realization? a.The circumference of the small wheel is VALIDLY lesser than its distance traveled. That's the observable reality of any circle or wheel's motion.

b. The 'trick' which throws everyone off, was the 'suggestion' by Aristotle's shrewd line placements, that there is a relation between small circle circumference and its distance moved -- just as there is for the large circle [1 : 1]. For the former, there is NOT.

c. The large wheel's distance is what counts, inner wheels are subordinate.

d. A second "track" now becomes null and void.

e. And anyone is wasting his efforts trying to force the inner wheel to fit its rotation, somehow, into this longer path of travel, longer than its circumference.

What these guys are doing, is trying to shoehorn facts of reality into a mechanical method (skidding, sliding, etc.on a track). 

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2 hours ago, Jonathan said:

Check out the edit history at Wikipedia:

https://en.wikipedia.org/w/index.php?title=Aristotle's_wheel_paradox&action=history

Merjet, Merjet, Merjet.

He's obsessed with it. He seems to think that if he alters the "paradox" at Wikipedia, especially by visually eliminating the Mechanica's reference to the upper line that the smaller circle contacts throughout its motion, then that's the final authority. It trumps reality.

The Wikipedia page is no longer about "Aristotle Wheel Paradox," but has now become "Merlin's Personal Attempt to Distort the 'Paradox' So That He Can Feel That He Won Over at OL."

J

Indeed. And it's a pity that he's messed up this Wikipedia page with those useless cycloids, giving "solutions" that aren't.

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Tony wrote:

”Bob: Nothing changes if there is to be a 'track' the inner wheel is on, or if the line is an imaginary 'path'. You get the same result with two surfaces, or one. Set up or picture an experiment with any bottle (best, because it has a protruding "inner circle", the neck and cap seen from the side). Construct two parallel tracks for the bottle to rest on. One higher than the other to finely adjust for the differing diameters. When the bottle is evenly balanced and leveled on both tracks, roll it along them and observe that both bottle and neck will roll evenly, with no skipping, slipping or jamming. (I'm sure if it's not balanced well, it will veer off course)..”

Tony thinks the straw is NOT skidding it’s track...

 

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17 minutes ago, Jon Letendre said:

Tony thinks the straw is NOT skidding it’s track...

Correct. That is indeed what Tony believes. And Merlin does, too. Our recognition that it does skid while it rolls, and our proof of its skidding -- our physical presentations of the skidding -- are a "scam," a "con job" and an "illusion."

Hahahaha!

J

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2 hours ago, Jonathan said:

Correct. That is indeed what Tony believes. And Merlin does, too. Our recognition that it does skid while it rolls, and our proof of its skidding -- our physical presentations of the skidding -- are a "scam," a "con job" and an "illusion."

Hahahaha!

J

Let’s take the Hurricane twice around IMI, a 1.1 mile go-kart track.

The guys who pass me are old men, in their sixties! But riding modern setups. I am on my stock original 1987 HONDA CBR600F HURRICANE. 2nd gear only.

 

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At the risk of adding to the length of this thread....

Draw a horizontal straight line with end points A and B.

Draw a circle (or wheel) sitting on point A. Put an X on the circle where it coincides with point A.

Make line AB longer than the circumference of the circle.

Problem:  Rotate the circle so X again comes down on line AB at point B. Remember line AB is longer than the circumference of the circle. Skidding, slipping, sliding, etc are not allowed.

Maybe Merlin the magician can do it. I doubt anyone else can.

 

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19 minutes ago, jts said:

At the risk of adding to the length of this thread....

Draw a horizontal straight line with end points A and B.

Draw a circle (or wheel) sitting on point A. Put an X on the circle where it coincides with point A.

Make line AB longer than the circumference of the circle.

Problem:  Rotate the circle so X again comes down on line AB at point B. Remember line AB is longer than the circumference of the circle. Skidding, slipping, sliding, etc are not allowed.

Maybe Merlin the magician can do it. I doubt anyone else can.

 

I fear they can’t process that, jts. Humbly, I have some suggestions for improvements.

 

Choose a plastic lid.

With tape measure or ruler, obtain its diameter.

Multiply the diameter by 3.14. Now you know the lid’s circumference.

Make two pencil marks, A and B, on a table. Line AB should be unmistakably longer than the circumference.

Put an X on the lid and place the X at point A.

Problem:  Rotate the lid so X again comes down on line AB at point B. Remember line AB is longer than the circumference of the lid. Skidding, slipping, sliding, etc are not allowed.

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 That’s a great teaching suggestion, jts.

The lid is the “small wheel” or “inner circle.”

It doesn’t reach B. It can’t, because it lacks circumference to reach B, just like the “inner circle” lacks circumference to roll the whole length of the dotted lines. But the inner circle DOES get there, so the lid HAS to get there. How? By skidding. You still have the lid in your hand, it didn’t reach B, get a good grip on it, hold it tight, now push and slide that motherfucker across the table to point B. THAT’s how the inner circle makes it all the way. It doesn’t skid only at the end, like I just told you to do, but it is skidding a little bit all the way along since starting at A.

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