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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 along a straight line, so it’s (6π/2π) + 1
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
First you said add the radii together, then you gave an example subtracting them, but either way this is incorrect. You divide the larger radius by the smaller radius and add 1
Not quite. With radius 2 and 3 circles, the outer circle would take 2.5 rotations to complete the revolution. You have to set the first circle radius to 1 (divide both radii by the lesser) and then add the radii to calculate the relative circumference of the circle drawn by the motion of the center of the outer circle, so the answer would be calculated like:
Wouldn’t it be 3 = 6π/2π ?
if the path had been straight yeah, but the path itself rotates 360 degrees, which gives us an extra rotation
This is the comment that finally enlightened me
Thank you
This finally made it click. Thanks
Now that is mind-bending trickery! Having a degree in applied matha millennia ago did not help…
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 along a straight line, so it’s (6π/2π) + 1
I just watched the video, that’s really interesting. Thanks for the explanation
Watch the video, it’s explained.
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This should have been an article. What’s the summary?
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
Add the radius together. If the circle is inside. B-A 3-1 = 2.
Does not compute
It’s in the video.
A circle with a radius of 2 and a circle with a radius of 3 would be 5 rotations.
First you said add the radii together, then you gave an example subtracting them, but either way this is incorrect. You divide the larger radius by the smaller radius and add 1
Not quite. With radius 2 and 3 circles, the outer circle would take 2.5 rotations to complete the revolution. You have to set the first circle radius to 1 (divide both radii by the lesser) and then add the radii to calculate the relative circumference of the circle drawn by the motion of the center of the outer circle, so the answer would be calculated like:
2/2 + 3/2 = 5/2 = 2.5
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…?
Its not even remotely what you said. Its A/B+1 or A/B-1 for an interior loop.
edit: I didn’t need to be this aggressive. It’s VAGUELY what you said. its (A+B)/B. You have missed the /B part… which is A/B + 1.
in the example you gave, for radius 2 and 3… it would be 3/2 + 1 or 2.5. Not 5 (off by a factor of 2 because /B)
They explain multiple ways to do it in the video. A circle with a radius of 2 and a circle with a radius of 3 would be 5.
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