2 Circles Math Problem That Everyone Answered Incorrectly in SAT Exam
video description
I see silly debates about the term revolving, nuances between rotating and revolving, and solution is 1, blabla, it's the classic denial and the debate you're having is about the two meanings of revolving in astronomy and nothing else, the Earth does a revolution on itself in one day, and around the sun in one year, and it's not the same thing at all, but it's not really related to the debate here. Others do revolutions in their bed or on forums.
(I believe revolution means back to the same position, and that is politically very accurate)
One guy said something useful i'll use that.
If a small guy was pushing that boulder in some neighbored hell of Sisyphus, he would see the -lower point- of the wheel, when that radius angle would point to the center of the gravity of that hell, and he would indeed count 3 rotations, we can see that also in the video, and that would respect the ratio circumferences.
And from an outside point of view, a copernicus or whatever gallilean referencial where you could spot 3 invariable stars for your stellar navigation, avoiding wormholes, even if quantum sillysm would have made gap progress, ok from the fix point of view of the computer screen, where the lower point would point always -down the screen- it will turn 4 times from an absolute point of view, which is often better view, it is in adequation with the distance of that C circle and so on.
So the 3 rotations would be correct from the view point of someone pushing along the boulder, which will be biaised by the fact he's turning too, and his sense of what is -down- will not be absolute. Even if it's concretly when the little mark on the wheel to spot that point would touch the ground.
I'm starting to feel dizzy myself, maybe everything is a lie and those circles can be put flat, there would be no debate since the bottom perspective would not exist, it's maybe better for our mental health and the distances will match the common sense answer, err sorry, the scientifical logic of majority, so we should declare strongly that there is no debate with those flat circles, and call them truth.
The answer is 3, i repeat 3, not 42.
Take that flat earth. Is Sisyphus in the comments? Correcting the same mistakes, again, and again.
Date: 2023-11-15
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Comments and reviews: 29
Logical
Not convinced yet. You are creating a problem with your thinking rather than solving one. Since the traveled path is curved, you can't assume as if circle A is traveling on a straight line. Circle A traveling on a straight line would complete a full circle once point A comes back to its original position (being the lowest point, however, when traveling on a curved surface, the frame of reference is constantly changing, thus, point A's -lowest- position should never be irrelevant to and independent from the frame of reference (the big circle. Point A's lowest position (or original position) has now changed according to the frame of reference and should only be determined once point A makes contact with its frame of reference (the big circle in this case. I don't care if it traveled more than one circle in comparison with the same motion on a flat frame of reference because the extra rotation brings it back to its original position, not the abstract original position you created based on a 'straight line' frame of reference. If you used the same logic to explain relativity theory, you'll make many mistakes and create a big mess. Circle A is only making a full rotation when the same point comes in contact with its frame of reference not when it abstractly become the lowest point in a standard, flat, frame of reference. It is obviously traveling on a curved path and so cannot follow the standard rules of a straight path. I think there's a reason why relativity theory confuses most people. It is difficult to understand that there is no direction, speed, movement, time, space, without a frame of reference. Everything is relative and so is circle A to circle B. You have unknowingly changed the frame of reference of circle A here and came up with a 4th rotation when in fact there were only 3 rotations relative to circle B. When you walk on the face of earth you are walking on a curved surface, and so you can't apply the laws of a flat surface to your equations. That's why satellites have to adjust for the curvature of earth's surface when giving GPS information to your phone. Your vehicle isn't traveling on a flat surface that is made up of straight grid lines, the lines are curved and so is your motion. Please reconsider another video upload.
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Not convinced yet. You are creating a problem with your thinking rather than solving one. Since the traveled path is curved, you can't assume as if circle A is traveling on a straight line. Circle A traveling on a straight line would complete a full circle once point A comes back to its original position (being the lowest point, however, when traveling on a curved surface, the frame of reference is constantly changing, thus, point A's -lowest- position should never be irrelevant to and independent from the frame of reference (the big circle. Point A's lowest position (or original position) has now changed according to the frame of reference and should only be determined once point A makes contact with its frame of reference (the big circle in this case. I don't care if it traveled more than one circle in comparison with the same motion on a flat frame of reference because the extra rotation brings it back to its original position, not the abstract original position you created based on a 'straight line' frame of reference. If you used the same logic to explain relativity theory, you'll make many mistakes and create a big mess. Circle A is only making a full rotation when the same point comes in contact with its frame of reference not when it abstractly become the lowest point in a standard, flat, frame of reference. It is obviously traveling on a curved path and so cannot follow the standard rules of a straight path. I think there's a reason why relativity theory confuses most people. It is difficult to understand that there is no direction, speed, movement, time, space, without a frame of reference. Everything is relative and so is circle A to circle B. You have unknowingly changed the frame of reference of circle A here and came up with a 4th rotation when in fact there were only 3 rotations relative to circle B. When you walk on the face of earth you are walking on a curved surface, and so you can't apply the laws of a flat surface to your equations. That's why satellites have to adjust for the curvature of earth's surface when giving GPS information to your phone. Your vehicle isn't traveling on a flat surface that is made up of straight grid lines, the lines are curved and so is your motion. Please reconsider another video upload.
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Math
You are incorrect! One revolution for the small circle is where the rotating circle makes a full 360 degrees revolution around its own axis. By adding the larger circle you've created a reference point that is not valid. If you were sitting on the outer edge of the little disc you'd see you've gone only three full times around the small disc's axis (the only valid reference point respecting the small disc when posing the question how many revolutions did the small disc make) Let's Imagine if the larger circle were flattened out so that it's circumference length is 2pi)R is laid out in a straight flattened distance. The smaller circle would only make three full revolutions (from point of contact to point of contact) along that distance. In turning the smaller wheel around a larger circle changes the position of the smaller circle with respect to the original reference point which is only valid from outside the reference point of the small disc. So moving the small disc along the curvature of the larger circle creates a false impression of how many degrees the smaller disc turned around its own axis. The amount of times the small circle actually revolves around its own axis as it proceeds around the larger circle is only three times. You can prove this analytically since the larger circle has a circumference length of 2pi)R and the smaller circle 2pi)R/3 the ratio is 3, which yields the number of full 360 degree turns along the length 2pi)R. This same invalid argument could be made for the Earth's orbit. If we stood above the plane of the solar system we'd say the Earth rotated more times than 365 given one revolution around the sun. However, we live on the Earth and the fact remains there are only 365 days to a year.
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You are incorrect! One revolution for the small circle is where the rotating circle makes a full 360 degrees revolution around its own axis. By adding the larger circle you've created a reference point that is not valid. If you were sitting on the outer edge of the little disc you'd see you've gone only three full times around the small disc's axis (the only valid reference point respecting the small disc when posing the question how many revolutions did the small disc make) Let's Imagine if the larger circle were flattened out so that it's circumference length is 2pi)R is laid out in a straight flattened distance. The smaller circle would only make three full revolutions (from point of contact to point of contact) along that distance. In turning the smaller wheel around a larger circle changes the position of the smaller circle with respect to the original reference point which is only valid from outside the reference point of the small disc. So moving the small disc along the curvature of the larger circle creates a false impression of how many degrees the smaller disc turned around its own axis. The amount of times the small circle actually revolves around its own axis as it proceeds around the larger circle is only three times. You can prove this analytically since the larger circle has a circumference length of 2pi)R and the smaller circle 2pi)R/3 the ratio is 3, which yields the number of full 360 degree turns along the length 2pi)R. This same invalid argument could be made for the Earth's orbit. If we stood above the plane of the solar system we'd say the Earth rotated more times than 365 given one revolution around the sun. However, we live on the Earth and the fact remains there are only 365 days to a year.
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justgivemethetruth
Firstly, the question did not have a -none of the above- choice, so 3 is the answer, and here is why.
Think of the center of the circle as the Sun. Then think of the smaller circle as the Earth. In the origin position you look up from the Sun toward the Earth and you see the words Circle A written horizontally across the Earth. A full revolution relative to the Sun would be when the Earth is again in the position where you can read Circle A horizontally. we call that 1 day. More specifically we call that 1 -Solar- day. When we do this experiment, the Circle A Earth takes 3 days to come back to the same place relative to the sun. so the -Solar year- is 3 Solar days. The Sun appears at high noon three times. Now, what this guy is talking about is called a Sidereal day, that is the Circle A Earth rotating relative to a fixed point an infinity distance from the center of Circle B - lets say directly down from the bottom or the video. From the point of view of very, very far distance down from the bottom of the video, Circle A does not do a full Solar rotation. but this full Sidereal rotation really leaves Circle A at - in that day. This is the paradox here. Since the answer 3 was given, that is the correct answer. 4 would also be correct, maybe more correct, I don't know, but it doesn't matter since 3 was the only listed answer there. ;-)
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Firstly, the question did not have a -none of the above- choice, so 3 is the answer, and here is why.
Think of the center of the circle as the Sun. Then think of the smaller circle as the Earth. In the origin position you look up from the Sun toward the Earth and you see the words Circle A written horizontally across the Earth. A full revolution relative to the Sun would be when the Earth is again in the position where you can read Circle A horizontally. we call that 1 day. More specifically we call that 1 -Solar- day. When we do this experiment, the Circle A Earth takes 3 days to come back to the same place relative to the sun. so the -Solar year- is 3 Solar days. The Sun appears at high noon three times. Now, what this guy is talking about is called a Sidereal day, that is the Circle A Earth rotating relative to a fixed point an infinity distance from the center of Circle B - lets say directly down from the bottom or the video. From the point of view of very, very far distance down from the bottom of the video, Circle A does not do a full Solar rotation. but this full Sidereal rotation really leaves Circle A at - in that day. This is the paradox here. Since the answer 3 was given, that is the correct answer. 4 would also be correct, maybe more correct, I don't know, but it doesn't matter since 3 was the only listed answer there. ;-)
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Kestrel
And no, no, Circle A does NOT travel around imaginary Circle C; it travels around the periphery of Circle B. The periphery of Circle A travels along the periphery of Circle B, a distance of 2pr.
Imaginary Circle C does play a role in the perception of what occurs, but it creates an optical illusion which leads people to the incorrect conclusion of 4 revolutions, whereas the correct answer is actually 3 revolutions (or, more generally (r/(r/3) revolutions.
Start with the definition of a revolution: Circle A completes a revolution once it completes a full 360 turn about its own axis of rotation. When traveling along a straight path, the orientation of Circle A's axis of rotation is fixed. However, when Circle A travels along the curved surface of Circle B, the entire system that is Circle A is rotating. When the entire system of Circle A rotates, that means that Circle A's axis of rotation itself revolves, which affects when Circle A actually completes that 360 degree turn about that revolving axis of rotation. I have provided a more thorough explanation of the illusion and the actual point of completion of revolutions in the link in my post below.
On a related note, it astounds me the lengths to which people contort logic to try to substantiate a conclusion just because someone else asserts that it is correct.
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And no, no, Circle A does NOT travel around imaginary Circle C; it travels around the periphery of Circle B. The periphery of Circle A travels along the periphery of Circle B, a distance of 2pr.
Imaginary Circle C does play a role in the perception of what occurs, but it creates an optical illusion which leads people to the incorrect conclusion of 4 revolutions, whereas the correct answer is actually 3 revolutions (or, more generally (r/(r/3) revolutions.
Start with the definition of a revolution: Circle A completes a revolution once it completes a full 360 turn about its own axis of rotation. When traveling along a straight path, the orientation of Circle A's axis of rotation is fixed. However, when Circle A travels along the curved surface of Circle B, the entire system that is Circle A is rotating. When the entire system of Circle A rotates, that means that Circle A's axis of rotation itself revolves, which affects when Circle A actually completes that 360 degree turn about that revolving axis of rotation. I have provided a more thorough explanation of the illusion and the actual point of completion of revolutions in the link in my post below.
On a related note, it astounds me the lengths to which people contort logic to try to substantiate a conclusion just because someone else asserts that it is correct.
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Mark
I showed this problem to my non-technical wife who came up with a completely off-the-wall image that appears to give the correct answer:
Imagine the 2 circles as a figure of 8 railway track. Circle-A is a station with a circular platform at which sits a train with a length exactly the same as the length of the platform. The train sets off around Circle-B. One third of the way round, the end of the train has left the station. After 3 'lengths', the head of the train is at the railway cross-over, but it has NOT YET entered the station. After travelling ONE MORE train length, the train is back at the starting point. Therefore FOUR lengths.
My own visualisation is to start off with the obvious: Circle-A rolling along a line the length of Circle-B, ie three times. Now, imagine Circle-A with a roller-skate and trundle it along the perimeter of Circle-B. Note how it rotates exactly once. Thus, rolling along Circle-B's perimeter is the sum of these two: four.
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I showed this problem to my non-technical wife who came up with a completely off-the-wall image that appears to give the correct answer:
Imagine the 2 circles as a figure of 8 railway track. Circle-A is a station with a circular platform at which sits a train with a length exactly the same as the length of the platform. The train sets off around Circle-B. One third of the way round, the end of the train has left the station. After 3 'lengths', the head of the train is at the railway cross-over, but it has NOT YET entered the station. After travelling ONE MORE train length, the train is back at the starting point. Therefore FOUR lengths.
My own visualisation is to start off with the obvious: Circle-A rolling along a line the length of Circle-B, ie three times. Now, imagine Circle-A with a roller-skate and trundle it along the perimeter of Circle-B. Note how it rotates exactly once. Thus, rolling along Circle-B's perimeter is the sum of these two: four.
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------
The problem lies in -revolve- definition being ambiguous.
Many people would interpret as -How many times does point P touches circle B- which would be three, rather than -How many times point P reaches the lowest position with respect to our eye-.
First scenario refers to -revolving with respect to the big circle B- while the second scenario refers to -revolving with respect to the Euclidean coordinate system-.
Indeed, as some points out, if we flatten the circle B and let A rolls on the straight line, it will revolve 3 times with unambiguous rotation. However when the surface is circular, it adds one more revolution if we view the surface from a third stationary view point, while the revolution number is still 3 from the view point of a 2D creature living in the surface, namely circle A itself.
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The problem lies in -revolve- definition being ambiguous.
Many people would interpret as -How many times does point P touches circle B- which would be three, rather than -How many times point P reaches the lowest position with respect to our eye-.
First scenario refers to -revolving with respect to the big circle B- while the second scenario refers to -revolving with respect to the Euclidean coordinate system-.
Indeed, as some points out, if we flatten the circle B and let A rolls on the straight line, it will revolve 3 times with unambiguous rotation. However when the surface is circular, it adds one more revolution if we view the surface from a third stationary view point, while the revolution number is still 3 from the view point of a 2D creature living in the surface, namely circle A itself.
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ind1jch
3 rotations is the correct answer if circle B rotates for circle A to travel around B.
There is not enough information in the question, so either 3 or 4 is the correct answer.
Divide the circumference of the larger circle by the circumference of the smaller.
(2-3r-pi) / (2-1r-pi) = 3
This is further evidenced in your video at the 1: 25 mark when the smaller circle literally makes three rotations around the larger one.
When you measure from the center point of the smaller circle to calculate distance traveled, you are creating a new circle that is 4/3, not 3/3. For rotations, such as gearing, the distance traveled calculation occurs where the two circles touch - along their circumferences.
Thanks for the great puzzle!
Enjoy!
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3 rotations is the correct answer if circle B rotates for circle A to travel around B.
There is not enough information in the question, so either 3 or 4 is the correct answer.
Divide the circumference of the larger circle by the circumference of the smaller.
(2-3r-pi) / (2-1r-pi) = 3
This is further evidenced in your video at the 1: 25 mark when the smaller circle literally makes three rotations around the larger one.
When you measure from the center point of the smaller circle to calculate distance traveled, you are creating a new circle that is 4/3, not 3/3. For rotations, such as gearing, the distance traveled calculation occurs where the two circles touch - along their circumferences.
Thanks for the great puzzle!
Enjoy!
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Mike
The way I see it, when the point in contact with the larger circle (you called it 'lower point') comes in contact with the larger circle again, the smaller circle has rotated 1 and 1/3 revolutions. Then as it continues to the next time this point touches the larger circle, the small circle has rotated 2 and 2/3 revolution. And finally when it contacts the larger circle for the third time back at the starting point, the small circle has rotated 3 and 3/3 time, or 4 times.
This particular point on the smaller circle does not draw a simple circle around the larger one, but rather a complex sort of cycloid. Which is why it's total distance traveled is larger than the circumference of the larger circle.
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The way I see it, when the point in contact with the larger circle (you called it 'lower point') comes in contact with the larger circle again, the smaller circle has rotated 1 and 1/3 revolutions. Then as it continues to the next time this point touches the larger circle, the small circle has rotated 2 and 2/3 revolution. And finally when it contacts the larger circle for the third time back at the starting point, the small circle has rotated 3 and 3/3 time, or 4 times.
This particular point on the smaller circle does not draw a simple circle around the larger one, but rather a complex sort of cycloid. Which is why it's total distance traveled is larger than the circumference of the larger circle.
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education
I can see why some are disapointed by the wording of the question. From a mathematical perspective Rotation and Revoloution are not the same thing the Earth rotates on its axis and revolves around the Sun. What the question is actually after is how many times circle A rotates while making 1 complete revolution around circle B, the answer is it makes 4 complete rotations around its axis.
Imagine instead of circle B it's triangle B with sides equal to 1x circumferance of A - circle A does 1 complete rotation from the top down 1 side - 1/3rd to go around the first corner, another 1 to get to the next corner, another 1/3rd, another 1 then another 1/3rd to get to the top - 4 rotations in all.
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I can see why some are disapointed by the wording of the question. From a mathematical perspective Rotation and Revoloution are not the same thing the Earth rotates on its axis and revolves around the Sun. What the question is actually after is how many times circle A rotates while making 1 complete revolution around circle B, the answer is it makes 4 complete rotations around its axis.
Imagine instead of circle B it's triangle B with sides equal to 1x circumferance of A - circle A does 1 complete rotation from the top down 1 side - 1/3rd to go around the first corner, another 1 to get to the next corner, another 1/3rd, another 1 then another 1/3rd to get to the top - 4 rotations in all.
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Christophe
intuition tells me this supposedly logical and mathematical demonstrations are plain wrong! if you were correct, then revolving circle A inside circle B would end up with 2 revolutions for the same length to be travelled? this is just insane, unless you consider that the -inner- perimeter of a circle is half the length of the -outer- perimeter: -): -D please, do your math before asserting such facts, 4 is the correct answer just because it is 3 self-revolutions + 1 revolution around de circle B
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intuition tells me this supposedly logical and mathematical demonstrations are plain wrong! if you were correct, then revolving circle A inside circle B would end up with 2 revolutions for the same length to be travelled? this is just insane, unless you consider that the -inner- perimeter of a circle is half the length of the -outer- perimeter: -): -D please, do your math before asserting such facts, 4 is the correct answer just because it is 3 self-revolutions + 1 revolution around de circle B
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Saikat
This is a beautiful question. But literally every possible numerical real number as answer is correct as per the question because the reference frame, where the observer is, is not defined in the question. If there is a reference frame with respect to which the circle B and observer is fixed, with respect to the observer the correct answer is 4. But if the intersecting point of circle B and A and observer is fixed with some reference frame, the correct answer is 3 with respect to the observer.
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This is a beautiful question. But literally every possible numerical real number as answer is correct as per the question because the reference frame, where the observer is, is not defined in the question. If there is a reference frame with respect to which the circle B and observer is fixed, with respect to the observer the correct answer is 4. But if the intersecting point of circle B and A and observer is fixed with some reference frame, the correct answer is 3 with respect to the observer.
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Saikat
This is a beautiful problem. Bro, I got my answer 3 (with unknown confusion which I understood after I saw your video) and after I saw your logical solution, I understand my mistake and I'm now confident that the answer is 4. Your video contents are very much good bro. One thing that I believe is we can never be confident with a wrong answer. Have you mistake what everyone did bro? And one more thing that before giving a wrong answer how can I be sure that I'm not confident with the answer?
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This is a beautiful problem. Bro, I got my answer 3 (with unknown confusion which I understood after I saw your video) and after I saw your logical solution, I understand my mistake and I'm now confident that the answer is 4. Your video contents are very much good bro. One thing that I believe is we can never be confident with a wrong answer. Have you mistake what everyone did bro? And one more thing that before giving a wrong answer how can I be sure that I'm not confident with the answer?
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Nafis
At 2: 50 you can see the tip of the radius of circle A has -touched circle B and is normal to Circle B's circumference-, which is coincident with your straight line example at 3: 08. Keyword here: normal to the surface. While at 4: 03 you can clearly see the circle A's radius is not normal to the other circle's cirfumference, indicating it hasn't yet completed it's full revolution. You're not accounting for the fact that the path is circular, not a straight line. Nice vid tho.
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At 2: 50 you can see the tip of the radius of circle A has -touched circle B and is normal to Circle B's circumference-, which is coincident with your straight line example at 3: 08. Keyword here: normal to the surface. While at 4: 03 you can clearly see the circle A's radius is not normal to the other circle's cirfumference, indicating it hasn't yet completed it's full revolution. You're not accounting for the fact that the path is circular, not a straight line. Nice vid tho.
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Christian
If circle A rolls for a certain distance on a straight line, it will roll for that distance plus an extra angle on circle B. So we expect that circle A will revolve more than 3 times around circle B. In particular because of the relation between the two radius of the circles, the extra angle is pi/3 for every revolution. So circle A revolves 4 times before reaching the initial position. So none of the given aswers is correct. This is a very interesting subject!
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If circle A rolls for a certain distance on a straight line, it will roll for that distance plus an extra angle on circle B. So we expect that circle A will revolve more than 3 times around circle B. In particular because of the relation between the two radius of the circles, the extra angle is pi/3 for every revolution. So circle A revolves 4 times before reaching the initial position. So none of the given aswers is correct. This is a very interesting subject!
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Wisenheimer
You are not solving this problem correctly. The answer is three. When you do your demonstration, you don't take perspective into consideration. In reality, the camera should be kept horizontal to the POINT OF CONTACT. as such, as the circle travels around the larger circle, the camera will complete one revolution, if the proper perspective is maintained. You are mistakenly adding this revolution to the solution, rather than to the change in perspective.
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You are not solving this problem correctly. The answer is three. When you do your demonstration, you don't take perspective into consideration. In reality, the camera should be kept horizontal to the POINT OF CONTACT. as such, as the circle travels around the larger circle, the camera will complete one revolution, if the proper perspective is maintained. You are mistakenly adding this revolution to the solution, rather than to the change in perspective.
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Antonio
At 2: 16 perimeter of A is in touch with perimeter of B, not C. Center of un A, i n C never touches perimeter of A or B, it's just location of Center of mass.
2: 36 -lower point- is better yo call initial point as the perimeter of B si curve un less considered as big as earth planet. 3: 03 asum on earth -lower point- points Center of earth. 3: 11 at one turn, -lower point- points to center of earth in B, not lower as un a plane surface. Rotation= 3
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At 2: 16 perimeter of A is in touch with perimeter of B, not C. Center of un A, i n C never touches perimeter of A or B, it's just location of Center of mass.
2: 36 -lower point- is better yo call initial point as the perimeter of B si curve un less considered as big as earth planet. 3: 03 asum on earth -lower point- points Center of earth. 3: 11 at one turn, -lower point- points to center of earth in B, not lower as un a plane surface. Rotation= 3
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Arun
If we consider this as linear, it will be more easy to solve. One big line equal to circumference of big circle and another line about that equal to one third of the length. It takes 3 rotation to complete. Note that we have to come to the starting point. To be exact the starting point of small line is in the 2/3 point of big line. In order to get to the start point, it need to travel one more time. So, that makes 4 rotations.
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If we consider this as linear, it will be more easy to solve. One big line equal to circumference of big circle and another line about that equal to one third of the length. It takes 3 rotation to complete. Note that we have to come to the starting point. To be exact the starting point of small line is in the 2/3 point of big line. In order to get to the start point, it need to travel one more time. So, that makes 4 rotations.
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Twoofee
Depends on the perspective of the question. Image three little dudes (and one dudette) was pushing circle A around circle B. They would obviously only see circle A turn 3 times, and that would be the correct answer if that was the assumed perspective.
Of course, we all knew that this was suppose to be tricky. So the assumed perspective was obvious to guess, but nevertheless it was still a guess.
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Depends on the perspective of the question. Image three little dudes (and one dudette) was pushing circle A around circle B. They would obviously only see circle A turn 3 times, and that would be the correct answer if that was the assumed perspective.
Of course, we all knew that this was suppose to be tricky. So the assumed perspective was obvious to guess, but nevertheless it was still a guess.
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SgtSupaman
I got it correct by the test's answers. So, why does it make a difference for the small circle to move around the big circle than when the two circles remain stationary and rotate together? Because, if the two simply rotate in place, they are like gears, where the small one will rotate 3 times for every 1 rotation on the large one. This is the exact same motion from a different perspective.
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I got it correct by the test's answers. So, why does it make a difference for the small circle to move around the big circle than when the two circles remain stationary and rotate together? Because, if the two simply rotate in place, they are like gears, where the small one will rotate 3 times for every 1 rotation on the large one. This is the exact same motion from a different perspective.
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LARRY
Are we talking COMPLETE ROTATIONS of circle A as it travels around (and in contact with ) circle B? The answer is 3. If a vertical line is drawn through the center of circle A with an arrow at the top the base of the line will contact circle B, 3 times. If you are talking about how many times the line will return to vertical (arrow pointing up) then it is 4 times.
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Are we talking COMPLETE ROTATIONS of circle A as it travels around (and in contact with ) circle B? The answer is 3. If a vertical line is drawn through the center of circle A with an arrow at the top the base of the line will contact circle B, 3 times. If you are talking about how many times the line will return to vertical (arrow pointing up) then it is 4 times.
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Sai
The answer None of the above is right. But I think you have a misconception here. It was asked number of revolutions, not number of rotations. In that case, no. of revolutions is 1 as it revolved only once around circle B. Isn't that a point to be considered? Please explain if my understanding is incorrect. Hoping to view the response in your next video.
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The answer None of the above is right. But I think you have a misconception here. It was asked number of revolutions, not number of rotations. In that case, no. of revolutions is 1 as it revolved only once around circle B. Isn't that a point to be considered? Please explain if my understanding is incorrect. Hoping to view the response in your next video.
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sash
To see the genius beauty of this problem just do this:
Instead of rolling small circle around big one just statically move it around big circle and see how it makes a rotation in opposite direction to rolling it. That's what adds 4th rotation to the answer. So the answer is always radius difference ratio (k)+1 so in this puzzle 3+1.
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To see the genius beauty of this problem just do this:
Instead of rolling small circle around big one just statically move it around big circle and see how it makes a rotation in opposite direction to rolling it. That's what adds 4th rotation to the answer. So the answer is always radius difference ratio (k)+1 so in this puzzle 3+1.
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Abhijit
For those who are confused by linearizing the path and then getting answer 3 here is the explanation
While you are trying to linearized the path problem is distance travelled by center and point of contact are not same you will not get a rectangle but a trapizium so you guys calculation is coming wrong as you took it rectangle
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For those who are confused by linearizing the path and then getting answer 3 here is the explanation
While you are trying to linearized the path problem is distance travelled by center and point of contact are not same you will not get a rectangle but a trapizium so you guys calculation is coming wrong as you took it rectangle
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Dan
I've seen this question posed at a few websites (including MindYourDecisions) so let me complement you on taking the time to not graphically demonstrate the problem with solution, but to also verbalize the explanation so much better than anyone else. For what it's worth, you earned yourself a bookmark (and a thumbs up) on my PC.
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I've seen this question posed at a few websites (including MindYourDecisions) so let me complement you on taking the time to not graphically demonstrate the problem with solution, but to also verbalize the explanation so much better than anyone else. For what it's worth, you earned yourself a bookmark (and a thumbs up) on my PC.
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Clovis
I came up with 9. 11 rotations. Let's call the radius of Circle A(1) and the radius of Circle B(3. That's gives circle a's radius 1/3 the length of circle b's radius. Now do your equation for circumference for each circle and divide circle a's circumference into circle b's circumference and you'll get 9 rotations.
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I came up with 9. 11 rotations. Let's call the radius of Circle A(1) and the radius of Circle B(3. That's gives circle a's radius 1/3 the length of circle b's radius. Now do your equation for circumference for each circle and divide circle a's circumference into circle b's circumference and you'll get 9 rotations.
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Gary
I did it.
and get 2,
If you put the small circle INSIDE the big circle, and go clockwise like here, then the small circle goes counterclockwise
3-1 =2
or is it.
4 - 1 is three?
I think uU can find the answer under -Smoke & Mirrors. -
-
or.
I mean spin the big circle and.
reply
I did it.
and get 2,
If you put the small circle INSIDE the big circle, and go clockwise like here, then the small circle goes counterclockwise
3-1 =2
or is it.
4 - 1 is three?
I think uU can find the answer under -Smoke & Mirrors. -
-
or.
I mean spin the big circle and.
reply
Krishnan
Take a thin thread and wrap the small circle A three times along the circumference. Measure the length. Now same way wrap the big circle B with a thread one round and Measure the length. Now you see both lengths are same. So where does the fallacy lie?
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Take a thin thread and wrap the small circle A three times along the circumference. Measure the length. Now same way wrap the big circle B with a thread one round and Measure the length. Now you see both lengths are same. So where does the fallacy lie?
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Pandit
Your explanation that that the distance traveled by circle A (circumference of C ) = n-2-(3. 14)-(r/3) seems to be not correct as it contradicts with your 2nd explanation where you said that it would have been true for linear motion not angular motion
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Your explanation that that the distance traveled by circle A (circumference of C ) = n-2-(3. 14)-(r/3) seems to be not correct as it contradicts with your 2nd explanation where you said that it would have been true for linear motion not angular motion
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Ryad
Hey Ammar. what happens if you pin the circles down like gears and then turn the small circle so the big one turns underneath it. How many times will you need to turn the small circle so that the big circle gets to the same point?
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Hey Ammar. what happens if you pin the circles down like gears and then turn the small circle so the big one turns underneath it. How many times will you need to turn the small circle so that the big circle gets to the same point?
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