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Comment by jraph | Hacker News Reader

Yeah, the SAT question is almost an excuse to speak about this things, and you also get to see an interview with one of the concerned candidates. Very enjoyable video.

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There’s also an interesting note about when the specified answers in the question would have been right, the point of view of the centre circle.

I actually didn't think that part belonged in there. Considering a rotating point of view seemed contrived to me.

Surely the intended meaning of the question belongs in the discussion?

You’re right, it’s contrived. But I automatically tried to compare lengths too. So it’s a good lesson in making sure that your simplification of the question still does what the question asks.

I'm not convinced that the intended meaning was to consider a rotating reference frame. I think it was simply an oversight that the straight-line answer and the around-a-circle answer aren't the same. A rotating reference frame is one way to explain that oversight, but it isn't the only one.

The rotating point of view was the "aha" for me. It's even clearer to me when you look at the 1:1 ratio with two identical coins, where when the rotating coin is upright at the bottom of the rotation, and the coin is right-side-up to the observer but is "top edge to middle coin" instead of "bottom edge to middle coin".

(Specifically, my "aha" was that one rotation of the moving coin in place was not the same as one rotation of the moving coin around the middle coin.)

I should have been more specific. I didn't mind that part as a teaching aid in general, but I thought it was contrived as a possible explanation for what the question authors expected students to visualize when they made the correct answer 3.

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