Comment on The SAT Question Everyone Got Wrong

• FiskFisk33@startrek.website ⁨10⁩ ⁨months⁩ 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 ⁨10⁩ ⁨months⁩ ago

    This is the comment that finally enlightened me

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  • Bloodyhog@lemm.ee ⁨10⁩ ⁨months⁩ 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 ⁨10⁩ ⁨months⁩ ago

    This finally made it click. Thanks

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  • ThrowawayPermanente@sh.itjust.works ⁨10⁩ ⁨months⁩ ago

    Thank you

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• protist@mander.xyz ⁨10⁩ ⁨months⁩ 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 ⁨10⁩ ⁨months⁩ ago

    I just watched the video, that’s really interesting.

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• NocturnalMorning@lemmy.world ⁨10⁩ ⁨months⁩ ago

  Watch the video, it’s explained.

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  • SpaceNoodle@lemmy.world ⁨10⁩ ⁨months⁩ ago

    This should have been an article. What’s the summary?

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    • protist@mander.xyz ⁨10⁩ ⁨months⁩ 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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      • SpaceNoodle@lemmy.world ⁨10⁩ ⁨months⁩ ago

        I read an article about it. Everybody is doing a shit job of describing what happens. The outer circle naturally makes a full rotation as it travels around the inner one, as the path it follows goes around a full 360°, so that counts as one of the rotations it ends up making, which is in addition to the 3 due to travel around the circumference.

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    • schmidtster@lemmy.world ⁨10⁩ ⁨months⁩ ago

      Add the radius together. If the circle is inside. A-B 3-1 = 2.

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      • protist@mander.xyz ⁨10⁩ ⁨months⁩ ago

        Does not compute

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      • SpaceNoodle@lemmy.world ⁨10⁩ ⁨months⁩ ago

        [deleted]

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• Hugin@lemmy.world ⁨10⁩ ⁨months⁩ 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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