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
Comment on The SAT Question Everyone Got Wrong
___f____g___@lemmy.ca 11 months agoWouldn’t it be 3 = 6π/2π ?
protist@mander.xyz 11 months ago
___f____g___@lemmy.ca 11 months ago
I just watched the video, that’s really interesting.
NocturnalMorning@lemmy.world 11 months ago
Watch the video, it’s explained.
SpaceNoodle@lemmy.world 11 months ago
This should have been an article. What’s the summary?
protist@mander.xyz 11 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
SpaceNoodle@lemmy.world 11 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.
schmidtster@lemmy.world 11 months ago
Add the radius together. If the circle is inside. A-B 3-1 = 2.
Hugin@lemmy.world 11 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.
FiskFisk33@startrek.website 11 months ago
if the path had been straight yeah, but the path itself rotates 360 degrees, which gives us an extra rotation
DontRedditMyLemmy@lemmy.world 11 months ago
This is the comment that finally enlightened me
Bloodyhog@lemm.ee 11 months ago
Now that is mind-bending trickery! Having a degree in applied matha millennia ago did not help…
vrighter@discuss.tchncs.de 11 months ago
This finally made it click. Thanks
ThrowawayPermanente@sh.itjust.works 11 months ago
Thank you