Aristotle's Wheel Paradox - To Infinity and Beyond

Use a piece of string

Its Aristotle's wheel paradox

I knew this must have something to do with the continuum hypothesis. I wish I was smart enough to solve it. it often keeps me up at night

My math is not mathing 😢

Infinite number of skips = no skips!

It’s all how you look at; and there are an infinite number of ways to look at it.😂

Thanks for the amazing simple explanation!

So then wouldn’t it be more correct to say that it’s a 0-3 and 0-2 ration rather than a 1-1 ratio? The top of the triangle being 0

the outer circle is traveling faster than the inner circle so it’s easy to calculate distance/time = circumference

THANK YOU!!

Thanks from France, french husband 😂 vidéo looks a lot more understandable now!
Bisous chez vous 😁

¡Gracias!

No.

Just physically separate those two wheels and you will get the result.

I slipped on a banana, let's talk about it for fifteen minutes...

the fact that galelio actually discovered calculus after this is crazy, but it just didn't catch on and was eventually lost until newton rediscovered it

This is time travel

O no she is married 😢,hmm okay okay

Thanks for explaining 😁😁

Tu es up and atom?

Not even wrong.

you spent a lot of time amplifying the misunderstanding... so much so that you may have increased the misunderstanding...

I always get triggered any time someone misrepresents infinity. To be fair it's not a video about that. But always finding a number closer to zero, and there being no closest number to zero isn't what makes the reals uncountable.

The wheel is doing the movement that is sinusoidal and the small circle is traveling the smaller curved line that become more of the line of the inner circle they are not traveling the same line the inner one is traveling paralel line. lines all of them that can be wrote as the one-to-one dot connections. So as the question ware whether they are of the same amount of dots yes all of the lines are of the same amount of dots it just depend how big dot segment is for different lines also as dots can be infinitely small then we can have large num of still finite but close to infinite of dots that will not actually vary in size that much to be noticeable to humans. The another point is that if we consider object like dot its the 0 dimension polygon and also 3 dimensional 0 dimension polyhedron. And the circle is 1 side polygon and ball is 1 face polyhedron.

Also their sinusoids are not the same and the length that first one is traveling is not the same as length that inner one is traveling. Simple way to solve the problem is make 3 random dots on the wheel and then notice how long they will pass. they are all traveling the same length as they are all traveling with the circle are traveling different sinusoide different radius from center of circle.

you can just say that even if the amount of the fruits are equal but that does not make orange and apple the same fruit

Just put the elastic band on both outer surface of circle. If we rotate the circle with one fixed end the smaller circle elastic band stretches more so... Smaller circle perimeter stretches (Ignore Grammatical mistakes😅)

2d move. different square

So what whs the answer?

This is the dumbest explanation of all time

Great video. But I still don't understand why the circumference seem to be equal. The explanation you gave seems to define a mathematical framework to understand the problem but I don't see how the actual question was answered.

If the wheels and lines had teeth like gears, would the wheels turn or lock?

Superb video!

My brother just broke his phone saying it's apples and oranges there's noooo pears........made me have to watch this video

I dont think it is being dragged. To drag is an action than can be used when the two circles are dragged without rotating. I would not call it dragging. What would I call it? I dont know, I dont think we have a word for this.

The solution is in the outer circle that encompasses the two wheels.

The two wheels are directly proportional to the outer circle divided by their diameters ..

Or in your demo of laying the wheels out in straight lines, encompassed within a triangle. The relationship between the lines are directly proportional to the apex, divided by their lengths..

If you measure both lines, where both lines lengths are in proportion with one another, you will see they intersect at the same lengths, respective to there proportions of length to the apex.

i finally see it.... the wheel's true "travel distance(recardless of size" is on its center point.... that why the shapes of the wheels circles being drawn straiten as you approch the center point... its so clearly obvious to me now but was very puzzling at first.... the larger the diameter of the wheel the further or longer its trajectory will be between two points but for the wheel itself .. ITS distance traveled must be measured from the center point to be TRUELY ACCURATE TO DISTANCE FROM POINT A TO POINT B... problem solved whether you understand it or not...

You just described stagger on a race car!

How many tangents can she go off on without solving or addressing a problem ? Answer... Create a paradox where there isn't one!

If both wheels travel different path and lenght at the same time is time stretching here? Same time diferent velocity and lenght

Could the "inner circle is dragging or skipping" be proven by an ancient mathematician by putting a string on the outside of the big wheel and attached smaller wheel and then trying to roll it out on the planks where you painted the hexagon goo? The inner string should get stretched and break if it isn't very strong, but the outer string should just comfortably roll out without any tension.

Just a side note.. similar to "analogue compared to digital" numbers...

So what's the solution of the paradox?

Why i never understand ...i hear bad the words of English...each has its accent.and its proper phonetics it same many languages not one...i know english but i never van follow speaking ..i can't distinguish between phonems....

This is too simple., the inner circle is skidding consistently. The best way to illustrate is to use an extreme large circle and extreme small inner circle. Mark paint the inner circle with dots to detect skidding. The motion of the inner circle is affected by large circle as they are connected in one motion.

Still dont get it, the smaller circle clearly is not dragging or skipping at all.

Ok... I'm not a mathematician but I've been thinking a lot about this over the last few days.

I think everyone has got this wrong!

Imagine if the smaller wheels drawn on the large wheel were actual wheels that you could push out from the larger one & were, therefore, capable of independent movement when the larger wheel was doing its rotation. They would obviously cover the same distance as the large wheel but would do that with many more rotations of independent movement.

If that were plotted on some paper & the small wheel was, say, half the circumference of the larger, it would show two complete rotations to the larger one's one.

I think it's the fact that you are looking at what the smaller wheel does as part of the bigger, & the whole thing as a single entity that is causing the problem?

I'm probably totally wrong but just putting it out there....

This video was wheely fun to make!


I'll show myself out...