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Aristotle's Wheel Paradox | STEM Montessori Toy
Regular price$20.95
Description
Description
There is a dilemma represented in this wooden puzzle that will have you wondering how it can be possible. You won't be the first. Aristotle took a whack at this in the Aristotelian Mechanica, as well as in the Mechanica of Hero of Alexandria and Galileo gave it a try as well. See what you can make of it...
Not everyone agrees that Aristotle invented this little paradox, but everyone agrees that it would be just like him to come up with something like this. The paradox involves two different-sized wheels, one inside another. The two rotate in sync and you can see as you turn the wheels to travel the length of the opening in the puzzle that the etched line on the wheels turns one time, thus the circumference of each wheel has rotated over an equal length.
Both wheels use exactly one circumference to trace the same amount of distance - the length of the space in the puzzle. But, clearly one circumference is smaller than the other. Either that means that the wheels have the same circumference, which they don't, or that different circumferences "unroll" to the same length, which they can't.
That can't possibly be right.... The smaller radius can't possibly be equal to the larger one, so what's going on?
To further illustrate the paradox, I have included an separate copy of the inner wheel. We know that when attached to the bigger wheel that it turns one rotation to cover the length of the opening starting at the hash mark. But now take the small wheel and position it at the same starting point and rotate one revolution.... it does not travel the same distance! Such a dilemma.... Can you explain it??
This wooden model made in our Hudson Florida shop nicely presents this paradox in a physical format that will likley leave you or friends or students struggling for an explanation. Great fun for thinkers!
Measures about 11" x 3.5"
Not everyone agrees that Aristotle invented this little paradox, but everyone agrees that it would be just like him to come up with something like this. The paradox involves two different-sized wheels, one inside another. The two rotate in sync and you can see as you turn the wheels to travel the length of the opening in the puzzle that the etched line on the wheels turns one time, thus the circumference of each wheel has rotated over an equal length.
Both wheels use exactly one circumference to trace the same amount of distance - the length of the space in the puzzle. But, clearly one circumference is smaller than the other. Either that means that the wheels have the same circumference, which they don't, or that different circumferences "unroll" to the same length, which they can't.
That can't possibly be right.... The smaller radius can't possibly be equal to the larger one, so what's going on?
To further illustrate the paradox, I have included an separate copy of the inner wheel. We know that when attached to the bigger wheel that it turns one rotation to cover the length of the opening starting at the hash mark. But now take the small wheel and position it at the same starting point and rotate one revolution.... it does not travel the same distance! Such a dilemma.... Can you explain it??
This wooden model made in our Hudson Florida shop nicely presents this paradox in a physical format that will likley leave you or friends or students struggling for an explanation. Great fun for thinkers!
Measures about 11" x 3.5"
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Personalize it!
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Product Specifications
- Dimensions
- 11.0 × 3.0 × 0.5
- Materials
- Wood
- Age Range
- Teens (13-18 years), Adults (18+ years), Kids (6-8 years), Tweens (9-12 years), Seniors (65+ years)
- What's Included
- Wood base (1), Round piece (1), Instructions sheet (1)
- Gift Occasions
- Christmas, Birthday, Holidays, Back to School
- Personalization Available
- Yes
- Category
- Educational Learning Tool
- Availability
- In Stock
Personalize It!
Did you know we can add a custom laser engraving to every puzzle and game? Well, we can. Add a personal touch to your gift with a name or message.
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Frequently Asked Questions
What is Aristotle's Wheel Paradox?
What is Aristotle's Wheel Paradox?
It is a wooden model of a classic geometry paradox that has puzzled thinkers for centuries.
What is the paradox?
What is the paradox?
Two different-sized wheels, one inside the other, rotate in sync. As they roll along the opening, each wheel appears to cover the same distance in one turn, which would suggest the two different circumferences unroll to the same length.
How does the model show it?
How does the model show it?
An etched line on the wheels lets you watch each wheel turn exactly once as it travels the length of the opening, so you can see the puzzle play out in your hands.
What is the extra inner wheel for?
What is the extra inner wheel for?
A separate copy of the inner wheel is included. Roll it on its own from the same starting point and it does not travel the same distance, which sharpens the question.
What is the historical background?
What is the historical background?
The model notes that Aristotle considered it in the Mechanica, as did Hero of Alexandria, and Galileo took a turn at it as well.
Is there a single answer?
Is there a single answer?
It is presented as a thinking challenge meant to spark discussion, designed to leave you, friends, or students working out an explanation.
What size is it?
What size is it?
It measures about 11 by 3.5 inches.
What is it made of?
What is it made of?
It is a wooden model.
Who is it for?
Who is it for?
It suits students, teachers, and anyone who enjoys a good thinking challenge.
Where is it made?
Where is it made?
It is made in our Hudson, Florida shop by Creative Crafthouse.
Can I personalize Aristotle's Wheel Paradox?
Can I personalize Aristotle's Wheel Paradox?
Yes. Aristotle's Wheel Paradox can be personalized with a custom laser engraving. Add a name, date, or short message when you order. See our laser engraving page for details and examples. For a custom logo or artwork, request a quote for custom work.
How fast does it ship?
How fast does it ship?
Standard orders ship from our Florida workshop within 1 business day. Personalized orders ship within 2 business days.
