Скачать или смотреть This Doesn't make ANY SENSE - Aristotle's Wheel Paradox

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Aristotle's wheel paradox, described in the Greek work "Mechanica," posits that two concentric wheels, one larger than the other, when rolled, should travel the same distance, even though the larger wheel's circumference is greater.

Here's a breakdown:

The Setup:
Imagine two concentric wheels, one large and one small, attached to a single axle.

The Paradox:
When the larger wheel rolls a distance equal to its circumference, the smaller wheel, also attached to the axle, should also travel a distance equal to its circumference, even though its circumference is smaller.

The apparent contradiction:
The larger wheel's circumference is greater than the smaller wheel's, yet they both appear to travel the same distance in one full rotation.

The Resolution:
The paradox arises from the fact that the smaller wheel, while appearing to roll, is actually sliding to compensate for the larger wheel's greater circumference.

Analogy:
Think of it like a polygon rolling. As the number of sides of the polygon increases, the "hops" become shorter and more frequent, eventually becoming a smooth slide, as seen in a circle.

In essence:
The paradox highlights the difference between the circumference of a circle and the distance a point on the circumference travels when the circle rolls