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Circle A is 1/3 of the radius of Circle B.Attachment 533313
If circle A revolves its circumference around the circumference of Circle B (which remains staionary), how many times will Circle A rotate on its journey? The circumference of a circle is 2 * Pi * r or Pi * Dia.
The same question, slightly rephrased, is posed in this picture (where Circle B remains stationary):
The circumference of A must be 1/3 of B, so three revolutions. My backup answer is avocado green
??? Three ???
Using pi multiplied by D to get the circumference of each circle and that r = R/3 the two equations seem to cancel each other out with only “3” being left…
… but it is late, I’m practically in bed and I did that totally in my head so I’m probably wrong…
I've heard this exact problem being discussed recently. Perfect timing!
The SAT Question Everyone Got Wrong - YouTube
4. A does an extra revolution around its own axis of rotation in addition to its own circumference around B's circumference.
Circle Revolutions and the Coin Rotation Paradox
super! Thanks, I never quite had a good explanation of a sidereal day but now I see it’s linked to this problem, makes it much easier to explainQuote:
Originally Posted by taz01
That's where I saw it today. Thought y'all might like a puzzle. :DQuote:
Originally Posted by taz01
Just a footnote to this puzzle: one of the comments under the video said:
"Thinking about this yesterday and I realized the extra rotation becomes intuitive if you shrink the large circle down to a point, and rotate around that. Even though the diameter of the circle it's rotating around is zero, the "small" circle still has to make a full rotation to return to its starting point."
That's a great explanation!