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Aristotle's wheel paradox
• If you roll a rigid wheel a distance of its circumference, each inner circle must also go that same distance
wait..but how?
• If you roll a rigid wheel a distance of its circumference, each inner circle must also go that same distance
wait..but how?
Resolution:
• Consider the 2 points 𝐵 & 𝑆 (big/small)
• Each travels 2πR horizontally (R=rad. of B)
• 𝑆's Cycloid path is *shorter* than 𝐵's
⇒ The closer 𝑆 is to the center, the shorter and more direct the path
∴ 𝑆 goes 2πR horizontally b.c it takes a shorter path
• Consider the 2 points 𝐵 & 𝑆 (big/small)
• Each travels 2πR horizontally (R=rad. of B)
• 𝑆's Cycloid path is *shorter* than 𝐵's
⇒ The closer 𝑆 is to the center, the shorter and more direct the path
∴ 𝑆 goes 2πR horizontally b.c it takes a shorter path
I noticed after the fact that the main gif is somewhat misleading
So I plotted the cycloids along the wheel, which makes the resolution to the paradox much easier to see.
So I plotted the cycloids along the wheel, which makes the resolution to the paradox much easier to see.
