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Comment on The SAT Question Everyone Got Wrong

I did not watch this video but did read about this math. Visualize the larger circle unwrapped into a flat line, and the smaller circle sliding along the length of the line so its bottom point is fixed to the line. You’ll see the small circle never rotates. Now slide the small circle with a point fixed onto the large circle in the same way, and you’ll see the small circle makes one complete rotation. That rotation happens in addition to the rotations you get from dividing the larger circumference by the smaller circumference, so the answer is 4 in this case

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YoBuckStopsHere@lemmy.world ⁨2⁩ ⁨years⁩ ago
Satellite operators have to use this equation for orbits.

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___f____g___@lemmy.ca ⁨2⁩ ⁨years⁩ ago
Wouldn’t it be 3 = 6π/2π ?

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- FiskFisk33@startrek.website ⁨2⁩ ⁨years⁩ ago
  if the path had been straight yeah, but the path itself rotates 360 degrees, which gives us an extra rotation
  
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  - DontRedditMyLemmy@lemmy.world ⁨2⁩ ⁨years⁩ ago
    This is the comment that finally enlightened me
    
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  - Bloodyhog@lemm.ee ⁨2⁩ ⁨years⁩ ago
    Now that is mind-bending trickery! Having a degree in applied matha millennia ago did not help…
    
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  - vrighter@discuss.tchncs.de ⁨2⁩ ⁨years⁩ ago
    This finally made it click. Thanks
    
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  - ThrowawayPermanente@sh.itjust.works ⁨2⁩ ⁨years⁩ ago
    Thank you
    
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- protist@mander.xyz ⁨2⁩ ⁨years⁩ ago
  That’s what you’d think, but there’s an extra rotation involved in the act of the small circle moving around the larger circle rather than a long a straight line, so it’s (6π/2π) + 1
  
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  - ___f____g___@lemmy.ca ⁨2⁩ ⁨years⁩ ago
    I just watched the video, that’s really interesting.
    
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- NocturnalMorning@lemmy.world ⁨2⁩ ⁨years⁩ ago
  Watch the video, it’s explained.
  
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  - SpaceNoodle@lemmy.world ⁨2⁩ ⁨years⁩ ago
    This should have been an article. What’s the summary?
    
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    protist@mander.xyz ⁨2⁩ ⁨years⁩ ago
    I summarized it above, there’s an extra rotation included when the outer circle moves along the inner circle, essentially falling a bit with every roll forward. If the outer circle rolled along a straight line of the same length as the circumference of the inner circle, it would only roll 3 times, but moving around the circle instead adds exactly one extra rotation. That other gent says this is used in calculating orbits too, where you’re also moving forward while constantly falling
    
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    schmidtster@lemmy.world ⁨2⁩ ⁨years⁩ ago
    Add the radius together. If the circle is inside. A-B 3-1 = 2.
    
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- Hugin@lemmy.world ⁨2⁩ ⁨years⁩ ago
  The center travels 2π per rotation but need to travel 8π because the path of the center of the small circle is a circle 4r the radius of the large circle plus the radius of the small circle. It would be three if the center of the small circle traveled along the edge of the larger circle but it’s edge to edge.
  
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