The SAT Question Everyone Got Wrong
How an SAT question became a mathematical paradox. Head to brilliant.org/veritasium to start your free 30-day trial, and the first 200 people get 20% off an annual premium subscription.
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Huge thanks to Dr. Doug Jungreis for taking the time to speak with us about this SAT question.
Thanks to Stellarium, a wonderful free astronomy simulator - ve42.co/Stellarium
Thanks to Newspapers.com, a database of historical newspapers - ve42.co/Newspapers
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References:
Summary of this problem by MindYourDecisions - • Why did everyone miss ...
More cool math about this problem by Kyle Hill - • The SAT Question NO ON...
Discussion of a solar day by MinutePhysics - • Why December Has The L...
Murtagh, J. (2023). The SAT Problem That Everybody Got Wrong. Scientific American - ve42.co/SATSciAm
United Press International (1982). Error Found in S.A.T. Question. New York Times - ve42.co/SAT-NYT
Yang (2020). What's the hardest SAT math problem that you've seen? Quora - ve42.co/SATQuora
Coin rotation paradox via Wikipedia - ve42.co/CoinParadox
Simmons, B. (2015). Circle revolutions rolling around another circle. MathStackExchange. - ve42.co/CircleRoll
Sidereal time via Wikipedia - ve42.co/SiderealWiki
Solar Time vs. Sidereal Time via Las Cumbres Observatory - ve42.co/SiderealLCO
Images & Video:
Zotti, G., et al. (2021). The Simulated Sky: Stellarium for Cultural Astronomy Research - ve42.co/Stellarium
Newspapers from 1980s - 1990s via Newspapers.com - ve42.co/Newspapers
SAT Practice Test via the College Board - ve42.co/PracticeSAT
Revolution Definition via NASA - ve42.co/RevolutionNASA
Revolution Definition via Merriam-Webster - ve42.co/RevolutionWebster
Earth motion animation via NASA - ve42.co/OrbitNASA
Satellite animation via NASA - ve42.co/SatNASA
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Directed by Emily Zhang
Written by Emily Zhang and Gregor Čavlović
Edited by Peter Nelson
Animated by Ivy Tello and Fabio Albertelli
Filmed by Derek Muller
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Thumbnail by Ren Hurley
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Music from Epidemic Sound
“I was amazed how badly it’s worded,” literally half of the SAT problems.
Y’all are overcomplicating a simple problem as an excuse for flunking out of community college
@@LJ3783I think there’s a greater theme here - there’s a certain hubris to the belief that questions such as this represent “intelligence.” There are…certain large tech companies that exclusively leverage SAT type philosophies in hiring to the exclusion of allowing nuance, and it doesn’t actually work that well in my opinion. Problems in the real world often don’t look like an SAT question and more often there literally isn’t a “correct” answer. If we condition people on these sorts of problems they don’t end up adapting well to an engineering trade off, nor are people who view the world from an SAT lens necessarily good at solving trade-offs in the context of a team. I think this type of criticism is that the SAT quite obviously fails to support its own philosophy of the existence of “correct answers” when the wording is wrong. I don’t say that to explain away my life failures, rather I say that because I have learned the importance of hiring people in a more nuanced way that allows for these different dimensions. Not sure if you’ve ever tried to work with an arrogant math PhD before 😂
@@LJ3783not really. The wording here is objectively bad, and dare I say, wrong.
@@justarandomguy8694I'd say that's the real issue, it comes down to semantics.
@@LJ3783if the wording is bad enough that most everyone got it wrong, then perhaps there needs to be an evaluation instead of brushing it off as semantics. Usually with tests like these it is expected for some people to get it wrong. But not a vast majority. If you say things poorly, then it makes sense that you get misunderstandings. Also, you cannot flunk out of community college if you’re not even in college. These exams are meant to loosely determine how ready you are for college. I’m not sure what your first comment was meant to say
To all the 1st posters: KZhead takes up to 15 minutes to gather data on a video before showing stats. Everyone in the first 15 minutes all think they're first.
😂
Nuh uh
I’m 9 minutes in and I says 12k views and 150 comments
haha
Yeah but I was first before you even wrote this. . .
Having the small circle rotating 3 times with the camera rotating is the best intuitive explanation of what's going on I've ever seen for something like this
It was the perfect explanation
I solved the question at the start of the video by pausing the video. MF I got 4 and then wondering the whole video why did people mark 3💀
@@anonymousguy5694 because they just wanted to answer something and there was no checkbox for the answer 4? so they assumed they are missing something and marked 3.
I didn't watch the video. But it is 3 right? Because the small circle would spin 3.141592653589etc x(radius x2) for about 6.28 before going a full rotation, while the bigger circle would spin closer to a distance equal to 18.84.
@@EmmaSquire-ks9nuWatch it and you’ll see it’s 4. But 3 from the perspective of inside the circle (i think that’s how you word it)
I am currently 6 weeks from earning a Purdue Aerospace Engineering BS, I have completed the requirements for a physics minor, ive taken 2 graduate level astronomy courses and a graduate level Space Traffic Management course that dealt with sidereal time on every assignment, but this is easily the best conceptual explanation of sidereal time I have ever seen. Genuinely incredible educational content, I'm blown away.
Hear, hear!
Keep It Simple Stupid KISS
Damn I wish to do aerospace/astrophysics too
Out of curiousity, how often do people pronounce it side real and how often do you hear cider eel? I'd seen the word before and assumed it was a compound word - and Astrophysicists seem like exactly the kind of people to read a word and understand its meaning before hearing it out loud.
@@rose_allen You're hilarious.
This was a mentally challenging video to watch first thing in the morning. I'm awake now
Wait, it is night
It is 10 PM where I live and now I can't sleep😂
Bruh it’s 16:46 where I am Got back from school and just did some homework now I’m eating snacks then I will play games
You're mentally challenged
@@zayansaifullah2008 same
That part about the circle rotating around the triangle was mind-blowing. You instantly understand why it's not the same if the circle rolls on a flat line or rolls on a curved line
That was the "aha" moment for me too.
This
There were 3 aha moments for me
if you divide the straight line in half and start to roll along it at the "top" to the end you then can make a 180, roll around to the "bottom" and then go in the other direction, make another 180 and keep going until you reach your starting point. These two 180 needed for the direction change add the 4th rotation 🤯
The earth around the sun was a fantastic example for why the frame of reference matters, especially with the graphic
I literally did it in 30-40 seconds while lying in my bed, then I saw that my answer wasn't listed in options, so laughed at myself and watched the video. Soon I realised that i was right
I was so confused because of the word "revolution," "1" is what I thought the answer was because of that
The 1872 novel “Around the World in Eighty Days” had a plot that depended on this kind of situation. Phileas Fogg traveled around the world eastward, against the earth’s rotation. Though initially he thought he’d missed the 80 day deadline by some hours, in fact only 79 days had passed in London. One extra rotation had passed beneath his feet. He won the prize, married the girl and lived happily ever after.
Fun!
That is what first came to mind when I first saw this problem. I didn't immediately jump to 4 as the answer, but I knew 3 wasn't correct.
There's a recent TV version starring David Tennant that I remember that from.
@@Mark73 Really? I might have to check that out
Glad about him.
In college, I took a poetry class and once had an answer marked wrong on a test. Confident in my response, I reached out to the poet themselves, who affirmed I was right and even communicated this to my professor. Despite not being a fan of poetry, that moment made me quite proud!
Did the professor change your grade?
@@QYXPI had a question marked wrong on a chemistry test that the professor refused to accept was actually right. The head of the chemistry department came to our class and embarrassed him in front of everyone showing why I was right and he was wrong.
literature tests: q.e.d.
@@Sciguy95 very cool, but also unprofessional
@@pongmaster123 We don't have the full backstory and never will, it might have been well deserved. Don't feel offended for some random obtuse chemistry teacher that may or may not even exist.
Here’s my guess, if the wheel A is revolving like a wheel then you divide both the circles circumference. Circle A has a radius of X and circle B has a radius of 3X, to find the circumference we multiply the radius by two and then times PI, making Circle A have a circumference of 2XPi and circle B having a circumference of 6X PI, so it should be 3
Exactly! They should open a dictionary. It's easy to solve anything if you change the question to fit your answer. By definition of a revolution, the number 3 is correct. Perfect analogy are gears or a wheel because as circle A the wheel would make only 3 REVOLUTIONS on circle B's circumference line, it literally can't make 4. Just because circle A looks like it made an extra full revolution from our perspective, doesn't mean it did. The only reason it looks like so is because, relative to us, circle A is literally getting pivoted full 360° once every time it travels circle B's full circumference. At 180° point circle A looks to us like a flipped version of what it looks like to circle B. If you make an upright square image travel forward on any circles circumference, it would literally get flipped for us at the half way point without making even a fraction of a revolution, that's why for that circle the image stays upright the whole time.
This explanation is the best i have found. The idea of the distance the centre of the planet circle travels and then deriving ratios makes the most sense to me and your graphics helped me to grasp this. It's fascinating. Not too mention the perspective element influencing the answer!! What i didn't realise is that the extra rotation is accounted for as well if observing from the perspective from the centre of the "sun" circle by the fact that the observer has to rotate once to continuously observe the "planet" circle
I was confused for a second until I realized that if you set the radius of the big circle to 0, or in other words rotate the smaller circle around a point on its circumference, it takes 1 full rotation for the circle to end up back at the start.
this comment helped me solidify ny understanding thank you
Thanks. This is a great way to think about it! ❤❤
Genius comment, thank you!
finally! i got it
That idea helped me as well
Another fun way to conceptualize the N+1 is to ask what happens if the circumference of B is 0. A still has to rotate around that point, one time. Great video.
Brilliant. Wish I'd thought of that!
I thought of it as a circle rolling three times along a straight line, and then one more time as the straight line is curled into a circle itself
That's actually a great example.
Yes because by measuring from the center of the circle, you are offsetting by the value of the radius. So you essentially just add up each circle's radius to get the number of rotations of circle A. So if Circle B's radius was zero, the centre of circle A still has to travel around it's own radius of 1.
this helps a lot!! thanks!
I appreciate every one of your videos, they always make me think, and sometimes make my head hurt. Thank you.
Honestly one of the best random fact and knowledge shows I have seen in quite a while.
I came up with the answer, 3, in a second or two, and then wondered "how could that possibly be incorrect". I spent the next 18 minutes learning how. Great video!
An actual honest response, lol at those who said they instantly concluded it was 4 rotations
It is the kind of problems which when you see the solution you feel dumb because the solution is so obvious
You weren't incorrect
i was surprised cause my intuitive answer was 4 by looking at the circles but it was not an option so i thought 3 XD
The answer is 3 only the video is useless
I loved the "I hope so" answer from Doug at the end. It highlights the most important lesson I learned during my education: "I might be wrong."
I feel like I already had that lesson before education. I feel like the most important lesson for me - that helped me grapple with how to be effectively wrong - is how to think in terms of probability than binaries.
@@hieronymusbutts7349❤
A harder lesson still is, "I might be wrong and I'll never know it." This is why people who fear the Scientific Method really shouldn't. It's also a primer in the Scientific Method, perfectly demonstrating why the goal isn't to prove a hypothesis is correct. Rather, the goal is to prove a hypothesis is NOT correct. Similarly, it demonstrates why the strongest theories are those derived from inductive reasoning (multiple specific cases lead to a generalized conclusion), rather than deductive reasoning (a generalized case leads to multiple specific conclusions).
Agreed! The most important thing I learned when learning math or physics or any objective knowledge is that by admitting the probability your are wrong is the best you can do to advance in those fields. I love to think that the physics, as we human know and define it, is always more correct than before but never (at least in the foreseeable future) completely right.
I always thought this way, but I learned in the working world that if you acknowledge that you could be wrong other people will assume you're wrong.
This concept is quite important while solving Rotation problems in Physics. Instantaneous Centre of Rotation, given that it is pure rolling i.e. there is no slipping at the point of contact. It at this centre of instanteous rolling the entire circle or rigid body is pure rotating. Thanks for sharing.
I've just found your channel and it is really brilliant. Keep up with the good work :)
It makes the story even better to know that one of the students who found the SAT error became a mathematician.
They should have offered him a job making the tests.
The fact that he corrected a mistake from the very test that they use to determine if you were good at math probably is a good point to bring up to get hired or accepted for a job or university Its also nice to see that they aknowledged their mistake, admitted it to everyone in news, and dismissed the question from everyone’s test. They have admitted to everyone their mistake, knowing well that it would impact their reputation for having made the mistake Only 3 people in the whole country sent a letter to correct them, likely not many noticed or cared about the mistake. They could just “ignored it and pretend it didnt happen” like so many goverments and corporations do regularly. Even more so considering people were not sharing everything instantly using internet on a global scale
dude if he became a social worker i'd be more fascinated
@@FlorenceSlugcat Removing the question was improper and created more inaccuracy in the scores. The question was part of the test and consumed time that could have been used on other problems. At least some students failed to answer other questions correctly because they wasted time on this question. For example, a great math student could have spent 5 minutes on this question totally stumped that no correct answer was there. Now, that great math student gets this question thrown out and also gets some other questions wrong because of time. So, any student who answered 3 should have been given full credit. The test makers who allowed this faulty question also administered a faulty correction.
@@jakemccoy I agree the question should have been thrown out. When every student in one of my classes misses a question, I eliminate the item. This rarely happens, however.
I learned about this problem when calculating gear ratios of planetary gearboxes, using exactly same <a href="#" class="seekto" data-time="63">1:3</a> ratios.
Don't read my nameDon't read my name
The same thing happened to me
That was my exact thought was gear ratios lol.
Learned about this when we talked about the moon slowing down its rotation in high school and I realised it still made 1 rotation around its own axis for every lunar month, so it could always show the same face towards Earth.
I was just wondering this. It is only for planetary gears or all gears?
That’s amazing! Given probabilities you would think somebody would accidentally get it correct….
This is really interesting! I initially interpreted it as the revolutions answer (1) and was immediately very thrown off by the answer options. Very cool to learn about this type of math problem!
In 1976 my maths teacher gave us the 2 (identical) coin problem. She insisted the answer was 1. I got 2 coins out and demonstrated that it was 2, but she could not be persuaded. It seems like this was a common mistake amongst teachers of that era.
Literally seeing it in front of her and _still_ insisting it's not true is wild
She sounds like a useless teacher.
@@orangenostril "Your coins must be faulty. The answer *is* 1. Now go and sit down!"
Still true today for many teachers, especially in Asia. Teachers are often drilled to "teach what's correct" but never consider what happens when they are wrong. I've been teaching for the past 10 years and the way I look at teaching is, I don't teach. I share and learn at the same time. I share what I know with my students, and encourage them to seek their own versions of the knowledge, and I feel great when they come back with alternative perspectives to the same subject, or other versions that they've found. Then we explore the differences together. This fosters an atmosphere of collaborative learning and students are much more willing to engage the subject, because they own the learning process. For me, I grow with them.
@@bunface 💖
I have a 1st class degree in Physics and clicked on this thinking it would be simple algebra, I had a huge grin on my face whilst being explained to how I was wrong. I love these kind of videos, I love learning something new. Never stop learning!
the phenomenon he describes is true, but it does not apply to astronomical observation the way he makes it out to be. According to their own theory, the tilted axis of supposed ball earth always faces into the same direction (towards the star polaris) in this 360 degree orbit which supposedly gives us the seasons. That means the earth is independently rotating ACCORDING TO THEIR OWN THEORY which contradicts this presentation completely because in this presentation earth is dependently revolving around the sun as if there was a mechanical connection between sun and earth, like a carousel, which we know from actual reality that it is not like this.
@@theswordofthespiritspeakstoyou Apart from getting everything wrong, it does apply to astronomical objects. I'm not sure if you're being serious though. A lot of people, people who never had a chance at education (surprise surprise), repeat stuff from other people who pretend that they believe "earth is flat" to make money of such people. I personally find it hard to believe that anyone who older than 5 can believe "earth flat".
the typical response of denial or paid actors: personal attack without arguments. You can't even stick with the topic. There is no point in having a conversation with you. Good luck.@@josephh891 btw I am seeing this channel has a few million followers making money off of spreading lies. None of the people I talk to make these amounts of cash! You might want to reconsider your insults, they don't stand the test of time... but then again so does the heliocentric model not
Yeah, I paused the vidoes calculated and divided the circumference(even did it on a calcluator and made myself realise after getting the answer how unecessary that was) and thougth the answer was obviosu and ez. Then after already calling myself dumb I got even more corrected :) But as U said "Never stop learning"
Flat earth websites are largely a creation of the intelligence community. There are legitimate conspiracy inquiries that point the finger at national and international BIG LIES. So one of the ways of getting people to ignore said theories is to "muddy the water" (a CIA term), by confusing the population. Let me give an example. Suppose the JFK assassination was really a plot...a plot by "deep-state" people who wanted JFK dead because his policies were threatening military or financial goals of the deep state. So you create a very slick "Flat earth" website, in which you also show evidence that JFK was murdered by a conspiracy, and you also mention evidence that 9-11 was an inside job, also designed by the deep state. In this way, people who don't like conspiracy theories will conflate "flat earthers" with JFK conspiracy theorists or 9-11 theorists, and just come up with the conclusion, "Hey, those conspiracy theorists are all nuts." thus ignoring two conspiracy theories that have some merit. Believe it or not, there are propagandists who work full time at this sort of thing. That's why it's called the Information Wars.
I wasn’t the best at math in high school not because I didn’t get the right answers but because I could visualize the problem. My problem is I couldn’t show how I got the answer. This one is easy. In my head I just rolled it around and got the right answer. This is geometry for me. Visually simple.
This really hurt my brain until the whiteboard explanation. Now it's so clear!
It will never fail to amaze me how seemingly simple questions can turn out to go against common sense when studied further, and then can be used to add to knowledge and laws that are used to greatly change or enhance our world.
This is why common sense is not a thing
@@GameTimeWhy That's not at all what common sense is. Common sense is an ability to intuitively solve simple everyday problems such as "It is cold outside, I will wear warm clothes" or "it is raining, it is better to dry clothes inside". It is certainly not something you can use to solve complex math.
@@anteshellTrue. The major problem with "common sense" is that too many people equate "I think that...." with "It is common sense that....".
This channel information starts where common sense end. And there are many people who dont have common sense to start with
@@anteshellThis is a a hand-wavy explanation. Common sense is usually used to describe something that should be simple and intuitive and known by many people within a given area. This video shows why common sense doesn't map easily to reality and we should study things further. This also isn't complex math its basic geometry, the fundemental of math.
<a href="#" class="seekto" data-time="260">4:20</a> Fun fact, the SAT actually tells you to assume all diagrams are drawn to scale unless otherwise indicated. Definetally made my life easier when I took it.
Thats convenient. In Jee they purposefully distort it
It didn't help you in the Writing and Language section...LOL, JK😂
@@scramjet7466According to my experience most of them are close, if not to scale. Anyways scale doesn't really matter for the questions in JEE
techgeek2625 was right - whether it was drawn to scale (or not) - it didn't matter in this case. The outcome is always the same. total # of rotations = ratio between inner circle to outer circle + 2πr
@@attsealevel Idk much about the questions of SAT, but judging by the level of SAT Maths, maybe some questions will be easier to solve with diagrams which are to scale.
I love these sorts of things where you can make it as complicated, or as simple as you like.
This was an excellent video. Not only did you explain the coin paradox and sidereal time, but you also showed some of the pitfalls in experimental, survey, and test design.
"I just put 3 down. I figured that's what they wanted". So depressing if you stop and think about it.
That's what the school system teaches you
@@Magst3r1 Which is a good lesson for the real world: Learn to pick your battles. When it's a trivial issue, don't waste your time raising a big stink about any concerns you have. Just do what you're expected to do and move on.
You (as I) initially analyzed from a gear-ratio perspective. The problem is more subtle. (see below addnl comments)
life in general is exactly that. on repeat. this is why most nerds who make it are autistic or agreeable or naiive and basic. others get depressed. and society deteriorates.
except 3 is a correct answer - the problem that the 3 students who "corrected" the SAT - was that they overthought the question - in fact "revolution" as more than one meaning - and i would have interpreted it the way the questioners intended it - on a flat surface - the rolling coin that starts with the head upright - will have made 1 full rotation/revolution/roll (when the circumference has fully played out) when it's upright again - but put it on a curved surface - and that no longer applies when rolling a quarter around a fixed quarter - the coin has NOT made a full rotation when George's head is upright again at the bottom of the fixed coin - if you mentally straighten out the edge of the fixed coin - you'll realize that the head of the rolling coin is UPSIDE DOWN when it's on a straight line if at the start you placed a dot on the edge of the rolling coin where it was touching the other - that dot would not be touching until it has gone all the way around to the top of the fixed coin
<a href="#" class="seekto" data-time="644">10:44</a> The circle traveling on the outside of the triangle helped me visualize the solution best.
As an engineer, I made the same answer mistake just like anyone else till realized yeah it is the center of the circle ⭕️ which + 1 because it is running outside then yeah it makes sense.
I knew this was the case because I visualized it immediately, but I still didn't know the answer until he said it increases the distance traveled by exactly one circumference of the circle, then I was ashamed of myself for forgetting curvature introduces an extra rotation. I had learned this during mechanical engineering school and missed my opportunity to say "I know the answer!"
The part here is that it's rotating around not with it like gears then they both become flat lines and 3 to 1 ratio. How is that to blow ones mind.
Yeah
Love this video. Good explanation of this math magic. Great job.
I spent less than a minute on it and didn't do any maths - I got the number 5 by the sheer practicality of it. I'm happy with myself.
This was a great video! Blew my mind when I realized how I was wrong!! Good to know question wordings can be so important, eh?! 😁😉
I was confident that I was right, but because of that, I was then confident I was wrong
I'm just glad I got the correct wrong answer
same
Are you familiar with Symmetrical Sequence Component theory created by Charles Fortescue in 1928? In this work he proves why 3n+1 harmonics are positive sequence (rotate in the same direction as the fundamental) and why 3n-1 harmonics are negative sequence. This comes down to this very coin paradox problem
what was you trying to imply here bro 🤣
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.
Imo this is a more immediately intuitive explanation than what was in the video!
This is a dumb fake question to convince you that the Earth is turning. These two clowns couldn't solve the time of day.
I also thought of this same explanation
Excellent!
Great visualisation. This should be pinned
"when I first saw this problem, my intuitive answer was B", well my intuitive answer was 4
i've learned more stuff from textbooks or reading on the internet than i have in school. i've seen 'sidereal' for more than a decade and never had any good understanding of what it was nor even how it was pronounced. now i learned both. thanks!!
One way to see the extra rotation -- shrink the inner circle to radius approximately 0, so it's like a thin wire. The circle still has to do a rotation to roll around the wire, even though the wire's circumference is negligible. (The rotation disappears from the "circle's perspective" because the "camera" does that one rotation along with it.)
You’re clever 👌
That’s some pro level thinking🔥
but why is it one? why cant it be anything else?
@@munkhjinbuyandelger10:10
Where is the paradox, when started rotating around same sized coin, point under neck of face picture was touching, after halfrotation at 180 deg where narrator started speaking again, point above head of face picture was touching the stationary coin, that means half rotation, full rotation will be when same point that was touching the stationary coin will again touch it, and in same sized coins, that comes when coin reaches starting point again. So where is paradox?? Cant they see that point that was touching at start, touches the circle again at whole 360 rotation, in same size coins. What is confusion??
Three of them got it right by saying that the question was wrong.
likebot more
1k likes within 5 minutes? Wow!
Also 3 is still a correct answer to the problem it’s just badly worded. So everyone who answered 3 still got it right.
The question is incomplete. It should ask how many rotations does the small circle make, on its centre point, to rotate exactly once around the large circle.
@@stevejones1318they forget an A. If there was one more A in the question, it would be correct.
The explanation you gave just showed your point. Pov determines internal and external proportion. +1 and -1
aaaauuuuggghh!!! i was going crazy because i thought the answer was 4 and it wasnt one of the options. took me waaayyyy too long to realize that the reason everyone got it wrong was that the right answer wasnt one of the options. thanks for making drawing the connection to solar vs sidereal time and the practical applications in GPS time. i really appreciate how you relate the abstract puzzles and theoretical questions to real world situations. but this also opens up a whole can of worms about the equation of time vs the mean solar day and how the shortest day of the year, the day of latest sunrise, the day of earliest sunset are three different days.
High intelligence, low self-confidence. Tragic problem
I paused the video with the question before the multiple choice answers came up. I debated with myself but decided the answer was 1 (because of the term "revolution"). I was disheartened when seeing the choices, deciding it must be 3, and then excited again when you said the answer was not an option. Then disappointed again when you said it was 4, and then excited again when you said 1 was a possible answer . . . a real rollercoaster of a video.
Literally same❤
Exactly. Rotation and Revolution are pretty different imo. Pretty ambiguous
Revolutionary comment
That coin rotated once in the first demo, I don't understand how it was 2? With its head up, it went around once before its head was up again.
Was mostly with ya till 10mins….then i felt like a toddler afterwards 🤦🏼♂️🤷🏼♂️😜
There's been a couple of videos on this particular SAT problem before. I'm an engineer and a bit of a math nerd myself, so I understood the point the other video was trying to make. However, Derek uses both computer graphics and real-world cut-outs to explain things, and that sets this video apart from the others. Very elegant, as always, Derek. Love your vids!
I haven't watched this video yet, but based on the thumbnail, it is one that super annoys me because the answer depends on perspective, how you view the english language. I should go find my comment from the past, but first I should watch the video. I just know I will get annoyed when I do, lol
Thank you, for a great YT comment!
haha, good point@@Redmenace96
@@gruangerhave you watched it yet?
Watched it :) The video didn't annoy me but it is the problem I remember@@Alpha_Online
What an awesome video,full of knowledge and images, lots of explanations,very good job😊
This was fascinating. I would not have caught the error but I imagine there were plenty of others who either thought the answer should have been 4 but didn’t contact the SAT; or thought it was 4 but talked themselves out of it. These three just happened to be both confident enough and motivated to contact the SAT.
Undergraduate astronomy student here. The idea of solar vs sidereal time was something I had heard about before, but never properly understood until now. Thank you for all that you do!
I still don’t understand exactly how the movement of the earth affects the rotation time.
@@temple69 Watch a 3D demonstration of it
But why should we add 1 day for Sidereal year, if Earth may not "slipping"? But it was correct only for slipping case
@@igarazhaQuite the opposite. It works only if there is no slipping. Which is exactly the case with the Earth's movement around the Sun.
Thanks for not misusing any comma.
Another way of solving this could be making a line X, on centre A, parallel to point B and then rotating the circle A with respect to line X, such that line X will be always parallel to point B… it is basically same as solving with respect to point B as you said but I just noticed that while I was observing you demonstrate the question…
I got the answer using the center-distance proof right off the bat!! Thanks for the self esteem boost, really needed that today
It’s so impressive how you made this seemingly basic math question into a really interesting and well thought out video. I hadn’t even considered the idea of a Siderial day, it’s so cool!
Thou ne maketh a full point, anything of mathematics must be really interesting.
Agreed
@@aniketmeshram6598 reconstruct your sentence. Please.
@@bill5197 i mean to say that he/she/pronouns wants to defy this Cosmic phenomena which was discovered by that great mathematician and astronomer who gave us "Zero"
I can't believe how well the explanation is made.
Good
Fggg
Very good
I was trying to picture the circle rolling on the other in my head and was feeling insane because at every point the only version of events that made sense was 4 rotations. I feel proud of myself for that. That'll be the smartest thing I do all year
I approached it as a math equation with the circumference of a circle as 2πr and immediately said 3, but stuck around for the rest of the video. I wonder if this phenomenon confused the heck out of early watch makers?
This got my mind really spinning! 😉 So I did my own little experiment, but using rectangles. I found the number of rotations for same-sized rectangles is the same as for the same-sized sized circles (i.e., the quarters) shown in the video. I used a couple Chipotle napkins that were sitting next to me on the couch lol. The outer napkin rotated 2 full times to get back to the original location. And sure enough, when I figured out how to alter my perspective to that of the inner napkin, there was only rotation from that perspective. This was a fun simple way to reinforce a key principle in this video.
There is an anecdote of a professor in the math department of the university I went, who wrote in a final exam of calculus something like "do you dare to calculate the sum of the series?" to which a student answered "No". The professor said he had to give the student full marks since the answer wasn't wrong, and he started being veeery careful in the wording of the exams
That happened to my junior year English teach in high school (but a year before I took her class). The exam question was "describe the book 'The Scarlet Letter'". As I'm sure you've already guessed, one student wrote a 5 paragraph essay about the size and shape of the book, the various artistic properties of the cover art, the texture of the paper and the font used, etc. According to her, she took it to a faculty meeting for help, and the other teachers concluded that she had to grade it as a correct answer.
Both of your stories are amazing!
once I wrote a paper for a friend who said "I didn't know anything about the breakup of the soviet union, so I asked a friend, and HE said: " then she put my entire paper in quotes, ending with "I couldn't have said it better myself." She got an A.
can't get hung up on small quibbles, quickly scrawl the "F" and move on
I took a 3rd year math course called numerical analysis. We had to "Prove a theorem" on an exam that involved a set of given variables in relation to the error when solving differential equations numerically. The intent of the question was to basically memorize a theorem about the minimum error produced we proved in class and reproduce it on the exam. Except the question said nothing about proving a minimum - it just said prove A theorem. I thought I had understood the process of the theorem so I didn't have to memorize it, but I just couldn't get it to work out to show a minimum. I ended up proving a maximum to the error which was correct (we did not do this in class), and he had to give me full marks as he didn't specify which theorem to prove. I ended up with 100% on the exam, and he learned to more carefully word his questions!
I'll always remember when in my freshman astronomy lab, we directly measured the sideral period of the earth. The rooftop-dome telescope was aimed at a patch of sky with it's tracking motor turned off. Over the course about 20 minutes, each of us would peer through the eyepiece (no computer screens back then) and pick out a star that came into view, quickly making a sketch of it amongst its neighbors. When our chosen star passed behind the crosshair (we made sure no one rotated the eyepiece) we each started our stopwatch. Once everyone had their turn, we labelled each of our watches and put them in a cabinet. Then next night we all returned, and one-by-one, observed our star slide across the view, and stopped our stopwatch when it again went behind the crosshair. Mine read 23 hrs, 56 min, 3.92 sec. Across the class, we were all within a quarter second of the actual value. Yes, really simple (and dependent on there being two clear nights in a row), but how many people can say they've done that?
Yes! Sidereal time! Thanks
Beautiful
me, I've done that with timelapses over 24 hours. really cool stuff.
More schools should do this, and similar experiments that require minimal outlay but reconfirm "known" results. For example, I would expect most schools to be able to find someone due north/south who could set up a vertical pole and measure the length of the shadow at solar noon on a specific day. Which, with some trig, is all you need to confirm that the Earth is curved (at least along a north/ south path), and the circumference (if you assume a sphere).
wow ur ancient, did u shake hands with trexes back in the day?
The way I'd think about it (yes, I figured it was 4) is: if they were cogs, both circles rotating around their axle, the small one would do 3 rotations and the big one would do 1. In order then to fix the large circle, we can imagine rotating the sheet of paper once in the opposite direction, so that the large circle would look still. So that would make it 4 rotations for the small one: 3 in the paper and 1 because the paper itself (the reference system) is rotating.
Fantastic explanation! You are one of the clearest and most creative instructors on KZhead. Thank you for your content.
I love how Derek goes the extra mile and tracks down one of the people that called the problem out, who just so happens to be a mathematician now 😂
Right?! As soon as I saw his title, I was like, ok that checks out lol
At this point, I just assume Derek has a 'Sherlock Holmes'-esque filing cabinet of every mathematician, professor, and scientist he can call on for collabs XD
matched so perfectly, like a well written script from a movie😂
is it really a coincidence that the person who called out the test creators on a math problem is a mathematicion
Always has been
What’s crazy to me is when I tried to solve it, I intuitively did one rotation of the little one on the big one in my imagination and saw it only go a 1/4 of the way. I then thought to myself, “wait that must be wrong”. Mind blown
I did the same thing and guessed 9/2 since it was the closest answer haha
I snipped the small circle into a string and draped it over the larger circle in my mind, giving me the answer of 3
Yea but it's just a visual representation of the problem, you're supposed to use the data given in the problem. The actual size of the "coins" in the image is meaningless
@@oneilljames1 The image is to scale
Use cosine and sine. Set the edge as cosine (0,1) and the center as sine (0,0). 2 Pi is one cosine rotation. 2 Pi is two sine rotations. Cosine as the circumference has four 90-degree rotations and sine as the vertex has eight 90-degree rotations within 2 Pi.
I thought I was wrong when I came up with 4 as answer, but later realized it wasn't in the choices. Reason I came up with 4 is because we're basically calculating the displacement traveled by a rolling circle, and the distance traveled by the center of the small circle is the same as displacement done by any point you pick on its circumference 😆
I loved the chalkboard explanation because it highlights how I saw it all along, which means the answer really is B(3).
They should open a dictionary. It's easy to solve anything if you change the question to fit your answer. By definition of a revolution, the number 3 is correct. Perfect analogy are gears or a wheel because as circle A the wheel would make only 3 REVOLUTIONS on circle B's circumference line, it literally can't make 4. Just because circle A looks like it made an extra full revolution from our perspective, doesn't mean it did. The only reason it looks like so is because, relative to us, circle A is literally getting pivoted full 360° once every time it travels circle B's full circumference. At 180° point circle A looks to us like a flipped version of what it looks like to circle B. If you make an upright square image travel forward on any circles circumference, it would literally get flipped for us at the half way point without making even a fraction of a revolution, that's why for that circle the image stays upright the whole time.
As an aerospace engineer, once I realized this is sort of a trick question, I visualized it as I do with sidereal and solar days. I'm happy you talked about those in the video.
Same thought. How is it possible that not one of the test writers/editors etc. had even the most rudimentary understanding of astronomy? I solved it from the thumbnail, before watching the video and wondered how I could be wrong, since my answer wasn't listed.
I wish Derek had rolled his coins in the other direction to match solar system's rotation. My head is stuck on the astronomical visual (and I have a hard time dropping that out of my head).
ABSOLUTELY NOT A TRICK QUESTION. Saw the answer just by looking at the problem, only to watch the video and see that I was correct. The problem with average minds is that when they become highly educated, the tend to Believe that they are way more intelligent than they really are, when in all actually they are just smarter than than rest of us.......... in one specific area.
@@basildraws it was a trick question they told u it made 1 revolution then they asked u howmany revolutions it made if ppl misread question and answered how many rotations it made well thats like being asked if 2 trains are traveling at x speed and start from station x & y at time x when will they meet and deciding to submit a answer on wind speeds over tracks instead
@@hamasmillitant1 No, it wasn't a trick question. If it had been, then "1" would have been on the list of choices. So even if they HAD intended it that way, they still made a mistake. It's pretty clear they meant for the student to calculate rotations based on the choices given, and it's clear they still failed to calculate the answer correctly themselves. The use of the word 'revolution' instead of 'rotation' is just an ADDED mistake on their part.
I've been amazed over the years how vaguely, or just poorly worded, tests questions or assignment questions are in K-12 education. It's also a problem in higher education. When I was in school I was sometimes frustrated at how the teacher who wrote a poorly-worded question seemed incredulous that anyone would misunderstand. Sometimes the problem was that the teacher was unable to account for more creative thinking than their own.
I find it's especially problematic with multiple choice tests. I grew up in a country where they are barely used at all (only for tests that are meant to give an idea of how students as a whole are progressing. They are more meant to test the school and education system as a whole and the grade doesn't account for much) and when I prepared to take the Cambridge Certificate (basically like TOEFL) most of that time was spent learning how to answer multiple choice questions bc well, all important exams we had ever taken up to that point allowed you to explain your answer and what was graded was the whole answer and as long as what you did made sense and was well explained.
Not sure about others, but this was really bad for me, as I had major issues taking the problems (as i am autistic) extremely literally with very little wiggle room. To others, it may have been very easy to "tell what they meant", not for me though.
But this time it's not about wording it's about a wild paradox!
@@fragophilefiles9976 And wording. As he stated the wording of the question allowed for 3 different answers two of which and arguably the most relevant answer wasn't an option.
The most ironic thing is that the testwriters can make questions as ambiguously worded as possible but as soon as you missed a unit or misused one word you lose a point
I figured 4 right away: 3 turns for the gear ratio, and one more because the small gear is going around the circumference. Then spent half an hour trying to figure out why I was 'wrong'. Even dug out old Meccano gears to confirm I was not mistaken (which let me confirm 2 for a <a href="#" class="seekto" data-time="61">1:1</a> ratio, 3 for a <a href="#" class="seekto" data-time="121">2:1</a> ratio, and 4 for <a href="#" class="seekto" data-time="181">3:1</a>. And then I watched the rest of the video and learned a few other things that made it all worth while. Thanks.
It can be done using concept of rolling in physics Let velocity of centre of smaller circle be v, radius of bigger circle be r, angular velocity of smaller circle be w, no. of revolutions of smaller circle be n Now, the centre of smakler circle is revolving in a circle of radius r+r/3=4r/3 about the centre of larger circle So, time for 1 revolution will be 2π×(4r/3) / v = 8πr/3v =t (let) Since smaller circle is in pure rolling motion, velocity of point of contact with larger circle is 0 So, v=w×r/3 , so w=3v/r So, 2π×n/w = t So, n=wt/2π = 4
The fact that the main issue was a poorly worded question is the exact issue I've had in school with so many tests being poorly written. So often the test writer(s) understand the questions they wrote but they don't have them vetted properly so they can be understood by the test takers.
This so very, very much. The countless pains of trying to figure out whether to answer what's literally being asked instead of answering what would seem to be what the maker of the question wanted to ask. It's ridiculous how such a thing exists so pluralously in tests, questionnaires, forms and medical examination papers etc.
I don't think the question writer knows what a revolution is.
Well I guess if anything it better prepares you for life
That’s not a fact. The main issue, is that the correct answer wasn’t even there. The wording of the question was poor also.
Math word problems are more often English problems which is why they are often criticized as being racist. You shouldn't need to be an English major to sold word problems. They should be written like people naturally speak. And the answer should reflect that as well.
I really liked the graphic when Jungreis was explaining his proof at <a href="#" class="seekto" data-time="589">9:49</a>. The additional +1 radius from the smaller circle added to the larger circle is super clever. Awesome video
Geometry is the best mathematics, and I will never be convinced otherwise.
@@M4TCH3SM4L0N3Instead of adding +1, you can allow the vertex to follow sine or cosine and the circumference to follow sine or cosine. Circumference measurement is one rotation for 2 Pi and vertex measurement is two rotations for 2 Pi. You're just changing the path and starting point of the measurement. He used trigonometry, and could have just kept using it for his proof.
@@ADUAquascaping I understand that you CAN use trigonometry for the proof, and I'm not saying that isn't valuable; I'm simply saying that I prefer the branch of mathematics that only requires a straight-edge and compass and its corresponding axioms and proofs.
@@RepentandbelieveinJesusChrist5 Sad how religion turns you into a mindless drone
This is such a delightful error! Gave me a good chuckle!
I definitely have to watch this at least one more time to really grasp how the perspective of the circle's center causes a differet answer than if viewed from a distance outside the circle
You can also arrive at the N+1 solution by considering the case where the radius of circle B is zero. Circle A would not roll at all but still hinge around the point and make one full rotation.
Great idea!
🤯
Or leave circle A and B attached at the same point and rotate circle B clockwise. This is effectively the same as having circle A orbit circle B without any rotation.
Makes me want to research gears now
We know...
The best thing about Veritasium videos are that they keep giving. The video could have been ended at multiple occasions, but they make an amazing, extensive learning out of it.
I'm really glad Veritasium included the astronomical part. The moment I realized my mistake (which happened when I gave it some more thought after he confirmed that 3 was wrong), I noticed the connection to sidereal days - as a kid, I spent ages wondering why my astronomy books claimed a day was only 23 h 56 minutes long, so that's pretty firmly imprinted on my mind.
Leave it to Veritasium to make a 45-minute fascinating video on a seemingly trivial topic!
I think the explanation here is confusing, its actually pretty simple if we use SUPERPOSITION: take the number of rotation ("revolution" along the circumference flatted out as a line) we call it "linear". and the number of the revolution of center point of circle A along the circumference from start to end (the given is 1). to be less confusing, lets just say the single revolution of the circle A, along B. we call it "given". linear = 3 given = 1 total = 4 this is true for all radii. ex. 2: for 2 coins of the same radius for about 1 revolution. linear = 1 given = 1 total = 2
If you learn real math go to mathologer. Veritasium is rookie compared to him
I knew it was too simple. this was such a good video thanks for broadening my mind.
This is exactly why I have hated every multiple choice exam while at Uni. Which means almost every test. I paused the clip to doodle my way to an answer, saw the circumference ratio as 3, then examined the wording and thought "revolution" kind of means 1, then focused on the path travelled to get back to the "starting point" which meant the r/3+r circle, then got confused about wtf they were actually asking and gave up. Multiple choice tests are only as good as those who write them.
As a machinist, we deal with this quite a lot. When milling around a circular boss, you have to do a calculation how much you need to increase the feedrate to keep the same speed at the outside of the end mill. The same goes for milling inside a hole, except you calculate the smaller diameter caused by the size of the tool instead, since everything is based on the center of a circular tool.
Super interesting!
Dude how fast are your feeds for this to matter?
@@appa609 On a production machine this matters. For one offs who cares.
As a CNC programmer, that's not really true. I just asked a couple other programmers/machinists at my shop this question and nobody got it right. The thing you have to deal with is varying chip load, which isn't the same at all.
@@fresheFresse Yeah doesn't matter at all for one offs and low volume stuff. When you need a machine running 24/7 for years to make 12 million of something, a fraction of a second quicker could save days
Ironically, the problem identified by the three students, was essentially the same problem that ETS faced when it had to account for converting scores based on 79 questions, to the 80 question scale. "Where did the extra question go?" is a lot like "where did the extra day go?"
This is a dumb fake question to convince you that the Earth is turning. These two clowns couldn't solve the time of day.
They rotated the scores around themselves
they converted the score from solar to sidereal but all the good schools were only accepting solar scores. hang it up, son.
Pretending the question was never there is improper and creates more inaccuracy in the scores. The question was part of the test and consumed time that could have been used on other problems. At least some students failed to answer some other questions correctly because they wasted time on this question. So, any student who answered 3 should have been given full credit. The test makers who allowed this faulty question also administered a faulty correction.
😂 That is so funny. Where did the extra question go? Oh, no! Where did my application to Yale go?
I got this right at first glance by doing with visualization what you did with the cut-outs at <a href="#" class="seekto" data-time="285">4:45</a>. No math brain here, but a lot of practical application in life.
To me it was actually intuitive that it should be 4. Think about it, the circumference of the smaller circle travels as much as ITS CENTER around the larger one. The distance the center of the smaller circle travels is really a circumference of radius (1 + 1/3) times the larger one: 4/3 the radius of the larger circle. Divide this 4/3 by 1/3 to get how many times the smaller circle’s circumference wraps around THIS “true travel circumference”, and this is 4. (Edit: I watched the rest of the video, turns out my intuition was exactly what was explained in the video haha)
I can say from experience, pointing out flaws in a test is such a double edged sword. I pointed out 3 bad questions on a science test in 7th grade, and the entire class hated me because "I" messed up their scores.
A good teacher will give everyone credit for a bad question, right or wrong. Or AT LEAST nullify it, which could hurt a score if you were 'right' I suppose.
bro why do you even do that in 7th grade... of course people are gonna hate you when you pull such nerd behaviour... What makes it worse is that even though the questions were bad you could probably answer them 'correctly'
@@SenneMeuleman What "nerd behaviour" are you talking about? You can't have errors like that when it comes to numbers. It is correct to point out such errors because it could be a life or death sentence in a world of numbers. These things must be correct. The teacher messed up there and it's nothing to do with "nerd behaviour". At least that mistake was in a classroom.
@@BlueProphet7 Yes, otherwise, it is unfair. The goal of a test is to measure learning, but some students think the test is the goal by itself. (I am a teacher)
@@HHalcyon mannn, in 2 years i'm done studying and can become a math teacher, do you think i will always make correct questions? Naaaaah impossible, but if its just a stupid test and the desired answer is pretty clear, even though wrong... then what is the problem? And if it really is a problem i would just give everyone a point for that question so no one can complain
It’s cool how this problem has so many practical implications that most people wouldn’t even think about.
what amazed me is it's as simple as putting the smaller circle on the inside of the larger one and seeing it makes less rotations
Yes; the entire industrial revolution relied on a precise understanding of gears.
The main idea is the "center" of the small circle, not any point on its circumference has to return to the starting point. It has to travel a longer path.
Fantastic video, thanks for sharing you knowledge
I’m glad you chose 3 at first. I didn’t feel so stupid because of it. 😂 The triangle shape was what helped it click with me. When the circle is going around one of the corners, the point it touches the triangle doesn’t move, but the circle rotates by a third before carrying on. Third multiplied by 3 corners equals 1 extra rotation.
Did you even watch the video? Did you miss, that it is always just +1? So 365,24 days of rotation about the sun becomes 366,24 from a different view point? +1 exactly even there.
Yeah, that makes it a lot more intuitive for me as well. Especially since you can easily in your head generalise it to rectangles, pentagons, hexagons, … So the circle intuitively follows.
@@gardenjoy5223 I mean, he saw the whole triangle part, didn't he? The concept is not the easiest to fully grasp, and I also agree that the triangle part helped to make it make sense to me, a simpleton.
I thought 3 immediately, backtracked because it had to be a tricky question if it were on Veritasium, recalculated 4, didn't see it on the list and decided to just watch the rest of the video.
No, not 1/3 at each corner. Less than that.
“Mess up this test as a teenager and your entire adult life is screwed” is such a top notch system.
As a EU ex-student in some backwater country, we always loved to quarrel and argue about our SAT equivalent/university entry exams. Meanwhile in a supposedly model country, poor students are basically sitting trivial pursuit style pop quizzes that determine their academic future. It's basically the concept of just testing your ability to take tests, cranked to 11. Just because a system is horizontal/standardized, should not excuse it for being extremely poor at measuring anything with actual substance or biased. Thankfully more and more universities are moving away from such evaluation models...
I enjoyed not being able to major in things due to crazy math that you wouldn't even use in that field, and if you did you could figure it out because it isn't a test.
I didn't have to take the SAT so I didn't, still got into a really good California state university
It’s funny how people are scared that AI will take over their jobs and they will. Because the education system is training people to be like robots. How useful it would have been to have deep discussions about a controversial topic with the rest of the class or you discuss morals in details. You’d learn to speak, listen, think on the spot, look at different perspectives. But no, the system just overly emphasises teaching outdated subjects to an irrelevant degree and determines your life by a test you cram for and forget everything you learnt in the past 10 years after you finish. The system is designed to keep you a failure. Also my high school and university tests and exams were all cheated on. The high school exams were leaked and sold on social media. I know that because I saw the diagram on social media in the question (obviously they hid all the numbers), and I thought it was just a scam and no way the exam board is this incompetent. Turns out they were, I was in the exam and I saw that question and my blood was boiling. Obviously most cheaters didn’t get caught. Then in University we had lockdowns. No in person exams so you had 24 hour open book exams that they made impossible in difficulty. Wouldn’t be a problem if they also made grades to reflect that, except for the fact that people were literally working together because it’s open book. You had entire groups of people working on the paper together and obviously no way to catch them either. The only thing the education system taught me is cheaters always win.
When they said to "hang it up" if you mess up, I almost thought they were telling you to go hang yourself if you fail
This means that one confusing question can become a paradox that can't be easily solved.
I got it right :). I thought I was wrong at first because my answer wasn't listed in the test's list of answers. My hypothesis through observation and thinking about the equal diameter case and the case where the stationary circle has zero radius (is just the point at the origin) was that for 1 revolution of the moving circle, its center will move 1 perimeter (the moving circle's) distance. With that hypothesis (I did not rigorously prove it), with the moving circle having radius a and the stationary circle having radius b, I set (a+b)*2*pi*r = X*a*2*pi*r, and get the answer X = (a+b)/a. The left hand side of the initial equation is the distance the center of the moving circle travels, and X is "how many moving circle's perimeters".
That actually blew my mind. It was so great to see how a simple math question with two circles can be related to space observation. Thank you for such a great content!!
Wait till they figure out how it ties in to space travel too =)
What is so interesting about your videos is that almost 100% of the I couldn't care less about the topic. Yet, I'm still enthralled through the whole thing. That is most definitely a compliment just to be clear. I love that you love to teach. That's all that matters.
Veritasium is ridiculously talented at making videos.
How many sidereal minutes does KZhead take?
@@tombiby5892I have no idea but for a production like this it's not uncommon to have multiple hours of side reel just in case
Simply while the small circle is moving, keep the camera rotating counter-clockwise for a total of 360 degrees, so it will look like 2 hooked gears with the big one taking one full turn and the small one three. After that, make one 360 degree rotation clockwise of the camera, during which the small circle will make the 4rd rotation.
Spirograph flashbacks. One observation. When the coin rotates outside the circle, the additional rotation is in the same direction as the other rotations, hence N+1. When inside the circle, the additional rotation is in the other direction, hence N-1.
This is an excellent observation by me.
YOU SUCK!
No, you do.
are you fighting yourself?
lmao
The fact that he noticed this on this test as a kid is pretty incredible.This would have driven me mad when my numbers didn't make sense.
True. There's a huge difference between understanding the entirety of a problem and understanding the problem from the perspective of memorized steps to follow in order to reach the right answer. If you throw a ball around the world without rotational energy, how many times does it rotate? Well, if you visualize it along its entire path from the perspective of the ball with no senses, zero. From the perspective of the ball looking at Earth, 1. That's not going to be covered in a textbook and that's not going to enter the minds of almost any stressed kid who hadn't considered it within a single minute's timeframe.
We once had to work out down to which depth someone could breathe through a garden hose under water. With the parameters given the result turned out to be merely a meter-and-a-half. When the calculation was done correctly, the result seemed so absurdly close to the surface that everyone thought their answer was wrong and consequently spent far too much time checking and rechecking... 😅
Do you remember the limiting factor? Is it the force of the vacuum that we can generate with the diaphragm or something to do with the hose diameter and pressure losses?@@FLScrabbler
It's the difference between being upright and facing your target. Notice how on the two identical coin experiment, after the first rotation of the turning coin when it's at 6 o'clock; it's upright but not facing it's target(it's north side is now touching the target coin where previously it was the south side that was touching). In order to make one complete move you need to make one rotation for the target and additionally make one rotation for yourself to get upright again).
I think it has to be more about critical thinking ability and not taking the words as written at face value. I admit the term revolution had me making the assumption that got to the "wrong" answer because of my perspective. Also it proves the fallibility of being human, which is in all of us. And that isn't a bad thing. The test makers had the intension to be correct, from a certain point of view. I see this whole case not just as a mathematical one but a sociological and phycological one. In the end, everyone learned something.
I think the most intuitive way to understand this is to imagine the inner circle is just a point. Even though there is no circumference, the outer circle would still have to rotate once to go around it.
👌
bro. this is amazing,thank you
That's one way to see it. Another is to try it with two equal rolls of ducttape. As you unwind the outer one around the inner, you will notice that the point of contact only travels at half the speed of the center of the outer roll. If you start from 12 o'clock and roll it clockwise down to 6 o'clock, the outer roll has done a full revolution around its own center. But it has only unwinded half of its circumference, because the point of contact has rotated _in the opposite direction_ at half of the speed - it went from 6 o'clock over 9 o'clock to 12 o'clock of the moving roll of tape. So the actual length of unwinded tape at this point is 1x the circumference (for the whole rotation of the outer tape) minus 1/2x the circumference, for the counter-rotation of the point of contact. So 1/2 the circumference for 1/2 revolution, even though the outer tape has spun a whole 1x around its own axis. But if you imagined the outer roll of tape to be made out of super-thin tape and be infinitenessimally small, then this counter-rotation would make up practically 0 distance. Like if it only has 1/100 the circumference of the inner one, then it only needs 101 revolutions, so only 1% more than if the counter-rotation was no factor at all.
Yeah, I was surprised they didn't include that example.
Yeah good way to visualize it
The reason the head turns more times is because it doesn't reach the edge of the coin. The head is rotating from it's own circumference inside of the coin, which also makes the circumference of the static coin larger to meet the Uber circumference of the head.
To count the revolution of smaller coin we should put a mark on circumference of it. At touching point of 2 coins. It gives us simplest way of understanding the revolution.
My brain didn't fully accept this until I pictured a circle going "around" a straight line segment in the same manner. Picture a horizontal line segment, circle positioned above it at the left end, bottom (not right or left side) of circle touching the end of the line segment. The circle travels to the right along the length of the line. Then to flip itself around the right tip of the line to the bottom side it has to undergo a 180 degree turn, but while doing so it travels no additional distance along the line. (Its centre travels a distance along a semicircle, but the part touching the tip of the line does not.) Then back along the bottom of the line to the left, then another 180 degree rotation back around the left tip, to the top again. Total distance traveled is just twice the length of the line. Number of rotations is some amount to accomplish that traveling, PLUS one additional complete rotation. Same thing for any convex shape that it travels completely around.
I hadn't watched this far when I wrote that, but he almost describes this at @11:15, though for some reason he stops after only one side of the line.
This is a good explanation.
Thank you, that really helped put the broken pieces of my brain back together. 😂 Much appreciated. ❤
Thank you so much. Was going mad
Great explanation thanks
I love how science channels, this one especially, can take you from what you think is a pretty clickbaity title, into a deeper appreciation for the sciences. These videos are just the right amount of learning to interest ratio for me. I feel like I'm just enjoying any old video, but at the same time learning *how* to think, and not just *what* to think.
Well said!
The thumbnail is clickbait because it shows the wrong question -- it pared down the original SAT question to be very incomplete. Note how different the actual question is with more details.
@@oahuhawaii2141lol he had a whole video about this. It’s called “clickbait is highly effective.” Idc if he wants to do clickbait as long as the content is actually good 😂
@@kirbya9545 I agree. Flashy thumbnails is the game you have to play. It's like a really flashy bag of chips...If you open it and it's full of delicious chips, then who cares?!
@@Stevelemontrudy and unlike a bag of chips 40% of this video isn’t air 😂
Before I clicked I thought 4 and was confused cause the option wasnt there
Fantastic analysis...great video!
I’m a retired Judge and when starting my career as a Prosecutor, first I had to take the Bar exam. I prepared very hard as I knew three smart fellows who each had failed the Bar three times and finally gave up on practicing law. I remember an ethics question that had no fully correct answer. It had the two parts of the answer listed separately with no choice answer that combined them. So one had to figure which part of the answer was more important to whom ever was grading the test. Apparently I guessed correctly more often than not.
Same. I was raised by a father who was an attorney. He taught us to think very critically and to try to consider all possibilities before drawing conclusions. Word problems on tests were very difficult for me because of my inability to begin from a point of a blank slate. Before I had even finished reading most questions I would recognize the answer will depend on one or more unstated assumptions. Most of the time the question would not include all the necessary information to eliminate enough assumptions to be sure of the answer, unless only one answer choice was even reasonable. The worst were problems that seemed to be designed to lead you to two possibilities. Not knowing the assumptions the test author was making, you just had to guess between them. I don't fault my father though; critical thought is the foundation of healthy skepticism. Today I am astounded at the inability of people to parse information logically, failing to recognize when relevant facts are being omitted
The LSAT had an entire section that was subjective back when I took it. Not long after, they quietly eliminated that section.
I'm sorry but nobody has pointed out the joke in the comment? Ethic question on an exam for lawyers? Before you string me up and then nail me to cross, I know not all lawyers are bad, just the bad ones give everyone a bad reputation.
@@daviddrake5991 "Ethics" has a different meaning in a corporate context. Ethics means playing by the rules some governing body has set, at the cost of losing one's license or facing severe penalties. Not so much about doing the morally correct thing. One does their business ethically, or they lose their livelihood.
@@daviddrake5991 I get it. My dad used to say (tongue in cheek) most of the lawyer jokes must have been made up by dead-beat dads who were paying alimony and child support. He, having grown up on a farm and the son of a sharecropper, had a special place in his heart for poor people. He used to take homegrown veggies to various poor folks in his home town. I know because I was the bond servant in his gardens, lol On the other hand when he served in the state Senate he spoke of a senator who had a postmaster in his district intercept social security checks in the mail so he or his staff could personally deliver them to well-placed locals. Big ethics problem there IMO