Smart Princeton Math People

<p>Hello, I am not applying to Princeton, not because I don't want to, but because I am sure I wouldn't get it. However I do need your help. On a recent math team problem at our school, many of the kids felt the answer was something, but it turned out to be something completely different, and I am having trouble understanding why the correct answer is correct, here is the problem, I hope you could help explain it:</p>

<p>The circumference of the larger crcle is two times that of a smaller circle, if the smaller circle is rolled around the edge of the larger circle, how many rotations does the smaller circle make. The imgae that was with it was two circles side by side, one smaller than the other, they were tangent to each other, and they were not inside eachother. So when rolling it has to go around the outside of the larger.</p>

<p>Here is what I did, but was wrong: C1 = 2(PI)r C2 = (C1)/2 = (PI)r
(C1)/(C2) = (2PIr)/(PIr) = 2. The correct answer is supposed to be 3, why?, thanks for your help.</p>

<p>Hm that's an interesting problem. I got 2 as well. I don't see how it can be three.</p>

<p>just to add something to it, my bc calc teacher actually cut out circles for this, and it does come out to 3, but she didn't know how to do it mathematically, but the answer definately is 3, if anyone knows why please reply</p>

<p>Interesting.......i think it has to be 2. R u sure whether u r telling the complete Qs?</p>

<p>Here is the actual question: Problem 3-3. One circle has half the circumference of another. How many rotations about its own center will the smaller circle make in rolling exactly once around the larger one, in the manner shown? the picture is like i said above, two tangent circles, one smaller than the other, b/c the circumferences are 1/2, and my teacher did make a scale model and showed that it was 3, but we don't know how to derive it mathematically, and yes, it makes no sense, yet it must</p>

<p>This is actually more of a physics problem, not math. The number of revolutions the circle makes multipled by 2pi equals its angular displacement. The mistake that all of you are making is that the linear distance traveled by the small circle is related to the angular displacement of its center, not the edge. The linear distance traveled by the small circle is 2pi*3r (r being the radius of the small circle, which is half of the radius of the larger circle). This is equal to its radius times its angular displacement, theta. The r's cancel, and you get theta = 6pi. To convert this to revolutions, divide by 2pi (one revolutions is 2pi radians). That's three revolutions. Ta-da.</p>

<p>Its not 2, its always x+1, even with questions in Physics involving gears.</p>

<p>i've always thought of it like x for rotating around its own axis + 1 for rotating around the axis of the bigger circle.</p>

<p>ForeverZero- Why did u multiplied it by 3r? Why not 2r?</p>

<p>Because the linear distance that the rotating small circle moves is the distance that the center of the circle moves. The path of the small circle can be seen as a circle that is generated by its center around the larger circle. The linear distance of the small circle would essentially be the circumference of a circle with a radius of 3r. So 2pi*3r would be the linear distance. Do a few simple conversions, and you get the number of revolutions to be 3.</p>

<p>One thing not to do is to IM princeton students asking for help. Don't assume everyone here is good at math. In fact, I don't intend to take math ever here.</p>

<p>I'm not a math guy and some random applicant IMed me one day asking for help. Needless to say, I was not happy to help him at all.</p>

mzhang, what is your intended major and what classes did you take this semester?</p>

<p>EEB 211: The biology of organisms
WRI 109: culture and memory (wri seminar)
CHI 103: intensive elementary chinese (for native speakers)
FRS 149: active geological processes (frosh seminar with all-expenses paid trip to sierra nevadas and death valley)</p>

<p>Intended major: anything from EAS to EEB to HIS</p>