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
Produced by Emily Zhang, Han Evans, Gregor Čavlović, and Derek Muller
Thumbnail by Ren Hurley
Additional video/photos supplied by Getty Images and Pond5
Music from Epidemic Sound

[@duckyfam9012]

“I was amazed how badly it’s worded,” literally half of the SAT problems.

[@LJ3783]

Y’all are overcomplicating a simple problem as an excuse for flunking out of community college

[@NicholasAndre1]

@@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 😂

[@justarandomguy8694]

​@@LJ3783not really. The wording here is objectively bad, and dare I say, wrong.

[@LJ3783]

@@justarandomguy8694I'd say that's the real issue, it comes down to semantics.

[@cameronschyuder9034]

@@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

[@KevinJDildonik]

To all the 1st posters: KZbin 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.

[@savitatawade2403]

😂

[@kakyoindonut3213]

Nuh uh

[@Warr4real]

I’m 9 minutes in and I says 12k views and 150 comments

[@MrDJ2004]

haha

[@TeachAManToAngle]

Yeah but I was first before you even wrote this. . .

[@NoraOlson-ct7nr]

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

[@thatonecrossiant22]

It was the perfect explanation

[@anonymousguy5694]

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💀

[@juhaniu6371]

@@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.

[@EmmaSquire-ks9nu]

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.

[@yolanda6392]

@@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)

[@monopolyking879]

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.

[@magnuslarsson337]

Hear, hear!

[@Worms_Pro]

Keep It Simple Stupid KISS

[@The_E_Lord]

Damn I wish to do aerospace/astrophysics too

[@rose_allen]

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.

[@tmst2199]

@@rose_allen You're hilarious.

[@5MadMovieMakers]

This was a mentally challenging video to watch first thing in the morning. I'm awake now

[@nirbhaykumarchaubey8777]

Wait, it is night

[@krishmishra514]

It is 10 PM where I live and now I can't sleep😂

[@zayansaifullah2008]

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

[@willson8394]

You're mentally challenged

[@QuantyzIGuess]

@@zayansaifullah2008 same

[@felixp535]

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

[@Renegade605]

That was the "aha" moment for me too.

[@misterscottintheway]

This

[@argelovec6216]

There were 3 aha moments for me

[@Marco-xz7rf]

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 🤯

[@NickyG-NZ]

The earth around the sun was a fantastic example for why the frame of reference matters, especially with the graphic

[@BertonMylo]

It's all a matter of how you look at it, (perspective) as explained so well with the graphics at 5:51. Thank you for this video!

[@pommyknocker]

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

[@TupperWallace]

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.

[@LimeyLassen]

Fun!

[@davidklein1245]

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.

[@Mark73]

There's a recent TV version starring David Tennant that I remember that from.

[@wingracer1614]

@@Mark73 Really? I might have to check that out

[@BoneyMB]

Glad about him.

[@Shepard-Thomas]

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!

[@QYXP]

Did the professor change your grade?

[@Sciguy95]

​@@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.

[@VADemon]

literature tests: q.e.d.

[@pongmaster123]

@@Sciguy95 very cool, but also unprofessional

[@Derzull2468]

@@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.

[@aprskgp]

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.

[@Jazzerizer]

no wonder everyone got them wrong, there was no correct answer

[@tzadiko]

Why is everyone liking a comment that literally just repeats a sentence from the video

[@forkmonkey]

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.

[@davidbesant]

Brilliant. Wish I'd thought of that!

[@startibartfast42]

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

[@fra_dp]

That's actually a great example.

[@AsterothPrime]

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.

[@budle89]

this helps a lot!! thanks!

[@Darth_Insidious]

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.

[@willdurneybenson]

this comment helped me solidify ny understanding thank you

[@dr.albekhan8640]

Thanks. This is a great way to think about it! ❤❤

[@solimao1236]

Genius comment, thank you!

[@08-quocat6]

finally! i got it

[@Nowolf]

That idea helped me as well

[@fpgaguy]

I appreciate every one of your videos, they always make me think, and sometimes make my head hurt. Thank you.

[@_Euphorion_]

I've just found your channel and it is really brilliant. Keep up with the good work :)

[@Spondre]

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."

[@hieronymusbutts7349]

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.

[@zqzj]

​@@hieronymusbutts7349❤

[@glennpearson9348]

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).

[@CrosSeaX]

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.

[@myuzu_]

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.

[@Tim3.14]

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.)

[@niels6186]

You’re clever 👌

[@abhirammadhu2973]

That’s some pro level thinking🔥

[@munkhjinbuyandelger]

but why is it one? why cant it be anything else?

[@rambbler]

​@@munkhjinbuyandelger10:10

[@mmeettwwoo]

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??

[@sprockethead323]

Honestly one of the best random fact and knowledge shows I have seen in quite a while.

[@bytecode5834]

Fantastic video, thanks for sharing you knowledge

[@gregnixon1296]

It makes the story even better to know that one of the students who found the SAT error became a mathematician.

[@EagleOxford]

They should have offered him a job making the tests.

[@FlorenceSlugcat]

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

[@zzzzzzz1zzzzzzzzzz1z]

dude if he became a social worker i'd be more fascinated

[@jakemccoy]

@@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.

[@gregnixon1296]

@@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.

[@ZEROBRICKS]

I learned about this problem when calculating gear ratios of planetary gearboxes, using exactly same 1:3 ratios.

[@Dont_Read_My_Picture]

Don't read my nameDon't read my name

[@hexagonal7708]

The same thing happened to me

[@DrDipsh1t]

That was my exact thought was gear ratios lol.

[@venanziadorromatagni1641]

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.

[@dminsanebros]

I was just wondering this. It is only for planetary gears or all gears?

[@GodAesthetics]

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.

[@0biwan7]

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.

[@atticuscpchan]

4:20 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.

[@scramjet7466]

Thats convenient. In Jee they purposefully distort it

[@kernelsmith]

It didn't help you in the Writing and Language section...LOL, JK😂

[@techgeek2625]

​@@scramjet7466According to my experience most of them are close, if not to scale. Anyways scale doesn't really matter for the questions in JEE

[@attsealevel]

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

[@techgeek2625]

@@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.

[@user-rx4wo7il2g]

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.

[@korkow]

Imo this is a more immediately intuitive explanation than what was in the video!

[@kwimms]

This is a dumb fake question to convince you that the Earth is turning. These two clowns couldn't solve the time of day.

[@user-ow1ui5pw6z]

I also thought of this same explanation

[@brettgregory7799]

Excellent!

[@crussty]

Great visualisation. This should be pinned

[@martinfaust2783]

Love this video. Good explanation of this math magic. Great job.

[@josrthorst6316]

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!

[@tc6818]

10:44 The circle traveling on the outside of the triangle helped me visualize the solution best.

[@TinMan-kd2gv]

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.

[@JB-nf8nk]

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!"

[@stix562]

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.

[@anirbansingha6723]

Yeah

[@8Smoker8]

"I just put 3 down. I figured that's what they wanted". So depressing if you stop and think about it.

[@Magst3r1]

That's what the school system teaches you

[@p2imal]

​@@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.

[@jholsapple2918]

You (as I) initially analyzed from a gear-ratio perspective. The problem is more subtle. (see below addnl comments)

[@oching4]

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.

[@johneyon5257]

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

[@thibod07]

Very impressive video! I really enjoyed how the information was presented.

[@user-bt8mh1it2h]

What an awesome video,full of knowledge and images, lots of explanations,very good job😊

[@stevedietrich8936]

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!

[@888cromartie]

An actual honest response, lol at those who said they instantly concluded it was 4 rotations

[@enzolomongiello4497]

It is the kind of problems which when you see the solution you feel dumb because the solution is so obvious

[@clarkkent4665]

You weren't incorrect

[@jamiefa2000]

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

[@abinash446]

The answer is 3 only the video is useless

[@Cosmic9999]

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.

[@GameTimeWhy]

This is why common sense is not a thing

[@anteshell]

@@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.

[@wernerviehhauser94]

​@@anteshellTrue. The major problem with "common sense" is that too many people equate "I think that...." with "It is common sense that....".

[@sumermuktawat]

This channel information starts where common sense end. And there are many people who dont have common sense to start with

[@Mallchad]

​@@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.

[@alfreddaniels3817]

Fascinating. , thank you. Especially the circumference versus the linear pathway is something that keeps me wondering about our perception of reality 😮 What if I drive my car around the planet thinking I am on a flat road all the time ?

[@Neishy4AGTE]

I love these sorts of things where you can make it as complicated, or as simple as you like.

[@paparmar]

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?

[@johnwilson1094]

Yes! Sidereal time! Thanks

[@gabrielgonzalez1993]

Beautiful

[@ohyou_6599]

me, I've done that with timelapses over 24 hours. really cool stuff.

[@jaelwyn]

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).

[@xDXD-xo2qi]

wow ur ancient, did u shake hands with trexes back in the day?

[@adolforabasa]

Another way to see it is using curvature. The (exterior) integral curvature of along any closed curve in the plane is 2pi (thus adding one). Interior on the other hand is -2pi due to the change of sign in the curvature vector (thus removing one). This is one of the interpretations of curvature: it tells you how longer (or shorter) a curve gets by looking at the points sitting at distance one from it, provided the set of such points is well defined (always defined for the distance of any convex set for instance).

[@glennpearson9348]

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!

[@gruanger]

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

[@Redmenace96]

Thank you, for a great YT comment!

[@gruanger]

haha, good point@@Redmenace96

[@Alpha_Online]

​@@gruangerhave you watched it yet?

[@gruanger]

Watched it :) The video didn't annoy me but it is the problem I remember@@Alpha_Online

[@lexxynubbers]

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.

[@orangenostril]

Literally seeing it in front of her and _still_ insisting it's not true is wild

[@thehandleiwantedwasntavailable]

She sounds like a useless teacher.

[@erikthomsen4007]

@@orangenostril "Your coins must be faulty. The answer *is* 1. Now go and sit down!"

[@bunface]

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.

[@olivergottkehaskamp3369]

@@bunface 💖

[@johnnyshell2839]

The explanation you gave just showed your point. Pov determines internal and external proportion. +1 and -1

[@joeterp5615]

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.

[@jonathanbost8427]

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.

[@anainesgonzalez8868]

Literally same❤

[@vineethbharadwaj8187]

Exactly. Rotation and Revolution are pretty different imo. Pretty ambiguous

[@chrissherlock1748]

Revolutionary comment

[@wayneerichsen]

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.

[@vicpnut1]

Was mostly with ya till 10mins….then i felt like a toddler afterwards 🤦🏼‍♂️🤷🏼‍♂️😜

[@scottthacker9554]

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!

[@theswordofthespiritspeakstoyou]

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.

[@josephh891]

@@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".

[@theswordofthespiritspeakstoyou]

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

[@joelnilsson7129]

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"

[@joemarshall4226]

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.

[@annimon2814]

By far the coolest KZbin video I’ve see in a while

[@indigoriviera]

Fantastic explanation! You are one of the clearest and most creative instructors on KZbin. Thank you for your content.

[@ElectroBOOM]

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?! 😁😉

[@ThapeloMKT]

I was confident that I was right, but because of that, I was then confident I was wrong

[@iamdigory]

I'm just glad I got the correct wrong answer

[@ninthjeans3749]

same

[@michaelharrison1093]

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

[@stephensirait5146]

what was you trying to imply here bro 🤣

[@sarthak-ti]

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!

[@aleksitjvladica.]

Thou ne maketh a full point, anything of mathematics must be really interesting.

[@andrewrhsmith]

Agreed

[@bill5197]

@@aniketmeshram6598 reconstruct your sentence. Please.

[@aniketmeshram6598]

@@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"

[@humilulo]

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!!

[@HughEMC]

Amazing paradox😮 I mean the fact you can turn a straight line into a circle & observing the circles rotation from different perspectives changes the amount of rotations the outer circle makes in both cases. The reality of physics is awesome

[@Mr.MoonRabbit]

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

[@bvenable78]

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.

[@mleszzor6866]

Both of your stories are amazing!

[@raygordonteacheschess5501]

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.

[@kev4241]

can't get hung up on small quibbles, quickly scrawl the "F" and move on

[@josephkavanagh7815]

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!

[@R_gue]

I really liked the graphic when Jungreis was explaining his proof at 9:49. The additional +1 radius from the smaller circle added to the larger circle is super clever. Awesome video

[@M4TCH3SM4L0N3]

Geometry is the best mathematics, and I will never be convinced otherwise.

[@ADUAquascaping]

​@@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.

[@M4TCH3SM4L0N3]

@@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.

[@ahall9839]

@@RepentandbelieveinJesusChrist5 Sad how religion turns you into a mindless drone

[@MysticFiddler1]

I got this right at first glance by doing with visualization what you did with the cut-outs at 4:45. No math brain here, but a lot of practical application in life.

[@patrickbateman69420]

This really hurt my brain until the whiteboard explanation. Now it's so clear!

[@foxboy6662]

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.

[@basildraws]

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.

[@jeffmartin-g8r]

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).

[@dvelarde]

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.

[@hamasmillitant1]

@@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

[@basildraws]

@@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.

[@SLCCWebmaster]

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.

[@graup1309]

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.

[@rdizzy1]

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.

[@fragophilefiles9976]

But this time it's not about wording it's about a wild paradox!

[@Sandman382]

@@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.

[@lesliekerman4222]

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

[@stevenr5534]

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.

[@mikeroll8515]

Fantastic analysis...great video!

[@StefanNoack]

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.

[@MiauMichigan]

Great idea!

[@EduardoGarcia-eh6sh]

🤯

[@bobhuang94]

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.

[@EduardoGarcia-eh6sh]

Makes me want to research gears now

[@jamesonbornholdt7302]

We know...

[@PramodApte23]

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.

[@Leyrann]

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.

[@nameredacted1242]

Leave it to Veritasium to make a 45-minute fascinating video on a seemingly trivial topic!

[@louiejohncastillo9822]

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

[@theboxingbiker]

If you learn real math go to mathologer. Veritasium is rookie compared to him

[@kibnob]

I got the answer using the center-distance proof right off the bat!! Thanks for the self esteem boost, really needed that today

[@wonwoo0426]

This is such a delightful error! Gave me a good chuckle!

[@sudokode]

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 😂

[@jasonkilley]

Right?! As soon as I saw his title, I was like, ok that checks out lol

[@erikaz1590]

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

[@abrarhameem8424]

matched so perfectly, like a well written script from a movie😂

[@thegrizzly7402]

is it really a coincidence that the person who called out the test creators on a math problem is a mathematicion

[@MrPruske]

Always has been

[@LOCOBJORN]

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

[@Genesis-revelation70]

I did the same thing and guessed 9/2 since it was the closest answer haha

[@Mandragara]

I snipped the small circle into a string and draped it over the larger circle in my mind, giving me the answer of 3

[@oneilljames1]

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

[@Mandragara]

@@oneilljames1 The image is to scale

[@ADUAquascaping]

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.

[@hmpp7013]

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.

[@Drighiz]

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.

[@CF542]

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.

[@jaakkopontinen]

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.

[@silentdrew7636]

I don't think the question writer knows what a revolution is.

[@tristanpage9548]

Well I guess if anything it better prepares you for life

[@reefhog]

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.

[@bkucenski]

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.

[@Schweebcraft]

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.

[@mitchelljao]

Super interesting!

[@appa609]

Dude how fast are your feeds for this to matter?

[@fresheFresse]

@@appa609 On a production machine this matters. For one offs who cares.

[@devjk1]

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.

[@wingracer1614]

@@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

[@DeleteKernel]

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.

[@jessicapeyton5444]

If the big circle had paint on its perimeter and the rotating circle was getting painted as its edge touched the painted portion, there would be a blank space (with no paint) when the smaller circle is right side up (4:30). To paint the whole circumference of the small circle, you would need to go a little further which would reach 1/3 of the big circle. So even though the small circle has "rotated" 4 times, it has not matched up with the circumference of the big circle.

[@pradeepkrishnamurthy2557]

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!!

[@DavidEdwards9801]

Wait till they figure out how it ties in to space travel too =)

[@user-kb6mj7zq8t]

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.

[@curiaregis9479]

Veritasium is ridiculously talented at making videos.

[@tombiby5892]

How many sidereal minutes does KZbin take?

[@literallyjustgrass]

@@tombiby5892I have no idea but for a production like this it's not uncommon to have multiple hours of side reel just in case

[@dangerprobe1]

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…

[@thestranger1949]

Finally now i can relax. Huh this was satisfiying 😌. Thanks🎉🎉

[@lancedrath]

It’s cool how this problem has so many practical implications that most people wouldn’t even think about.

[@sinephase]

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

[@user-bm4ow6fh2x]

Yes; the entire industrial revolution relied on a precise understanding of gears.

[@berryl9653]

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!

[@temple69]

I still don’t understand exactly how the movement of the earth affects the rotation time.

[@patrickchang9135]

@@temple69 Watch a 3D demonstration of it

[@igarazha]

But why should we add 1 day for Sidereal year, if Earth may not "slipping"? But it was correct only for slipping case

[@duzyolek]

​@@igarazhaQuite the opposite. It works only if there is no slipping. Which is exactly the case with the Earth's movement around the Sun.

[@AwesomeHairo]

Thanks for not misusing any comma.

[@Nobody_Fn_Important]

I knew it was too simple. this was such a good video thanks for broadening my mind.

[@AndrewMoizer]

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 1:1 ratio, 3 for a 2:1 ratio, and 4 for 3:1. And then I watched the rest of the video and learned a few other things that made it all worth while. Thanks.

[@daleferrier3050]

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.

[@gardenjoy5223]

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.

[@MeMe-gm9di]

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.

[@the1doubledeuce]

@@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.

[@chronoreverse]

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.

[@Cotronixco]

No, not 1/3 at each corner. Less than that.

[@ebubegideon1060]

I love you and what you do Sir. Keep them coming. 🥳 You always blow my mind

[@peter9477]

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.

[@peter9477]

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.

[@x0rn312]

This is a good explanation.

[@marissabulso6439]

Thank you, that really helped put the broken pieces of my brain back together. 😂 Much appreciated. ❤

[@k.r.koushik9660]

Thank you so much. Was going mad

[@codyhall6802]

Great explanation thanks

[@justinjames3028]

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.

[@shubhamrkrock]

Man I live these videos so much! Brain food, love it!

[@HuntingSunder]

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.

[@BlueProphet7]

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.

[@SenneMeuleman]

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'

[@HHalcyon]

@@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.

[@RicardoLeonardoRamirezReyes]

@@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)

[@SenneMeuleman]

@@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

[@RocinanteGold]

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?"

[@kwimms]

This is a dumb fake question to convince you that the Earth is turning. These two clowns couldn't solve the time of day.

[@toriless]

They rotated the scores around themselves

[@suivzmoi]

they converted the score from solar to sidereal but all the good schools were only accepting solar scores. hang it up, son.

[@jakemccoy]

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.

[@John-qd5of]

😂 That is so funny. Where did the extra question go? Oh, no! Where did my application to Yale go?

[@Ran_ji]

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.

[@nightowlowo149]

this is one of my favorite videos on yt, ever

[@davidfehrle8561]

I had an error on my SAT too (in 2016). Half of the exams had a misprint that switched the time allowed for each section with another section. They ended up throwing away both entire sections of the exam, I was pretty mad since it was parts in my strongest subject getting tossed. Timing is a big part of the SAT and I feel bad for folks who may have spent longer on this problem since the real answer wasn’t listed which may have cost them more than just the one free point in the end.

[@samgray4]

This is why skipping questions you can’t immediately solve is such an important standardized test strategy

[@PANDEAD2]

If someone was dumb enough to continue wasting time on one question that was stumping them instead of moving on and finishing everything else and returning, I doubt it made much of a difference to their end score.

[@Boltclick]

@@PANDEAD2 That's not necessarily true. Some questions require more time, so a person might just assume this is a harder question. Thus, instead of spending their normal 1 min, they'll spend 3 minutes. Generally, the skipping questions when you're stumped is good if you don't know where to start or if you think the problem will take too long, but otherwise, spending an extra couple of minutes is usually worth it, as otherwise you'll just lose your train of thought if you skip the question. Since the question had a misprint, it's entirely possible that some people had the right idea, and were sure they knew how to solve the question, so they spent that extra bit of time to hopefully solve the question, instead of completely discarding their train of thought for that problem and moving on (since moving on effectively resets their progress on that question to 0).

[@Techburn997]

@@Boltclick Skipping then returning tends to be the better option as there may be later questions with similar reasoning that will simplify the harder question. It also allows you to divvy up your remaining time more equitably between any other questions skipped.

[@gabbleratchet1890]

It’s also a good strategy because you are penalized for wrong answers but not for blank answers.

[@jasonpatterson8091]

Watched this with a friend and they really struggled with the extra rotation per revolution until I showed them a coin rolling along the edge of a rectangle. It's getting around the corners that causes the additional rotation - angular movement is required without any linear movement. The circle is just the limit with an infinite number of infinitely small corners. On the inside of the circle (or any concave corner) that corner rotation is in the opposite direction, so in one loop of any size and shape it will result in -1 rotation.

[@MiauMichigan]

Thank you!!! I finally understand 😊

[@Warfred]

Actually get it now!

[@mk1cortinatony395]

that made it easier for me thanks. Pity the guy doing the vid couldnt explain as easily.

[@stephenwatkins7592]

@@mk1cortinatony395 He showed how the rounded path around the corners of the triangle could be pasted together to get a complete circle.

[@leif1075]

What dontou mean on inside lf circle the rotation is in the opposite dorection..the circle.rptsripnal.direction doesn't change so notnsure what you meant..and how does a circle have infinite number of corners..you mean because it has an infinite number pf tangent lines?

[@brahminverana667]

Loved this man! 🤯

[@johneyon5257]

3:27 i decided to watch the quarter being rotated around the fixed one again - this time i noticed something that i didn't notice before - instead of watching George's profile - i watched the point on the circumference of the rolling quarter that had touched at the start - that would be the "r" in "quarter" - the quarter had clearly only rolled halfway along the circumference when George's head was poised upright again at the bottom of the fixed coin try this - with the rolling quarter glued to the bottom of the fixed quarter - use you imagination and unroll the fixed quarter's outer edge into a straight line - see how the rolling quarter is now SITTING UPSIDE DOWN - it's correct to use the head's orientation when rolling on a flat surface - but roll on curved surfaces - and the upright orientation of the head becomes less accurate as an indication of a full rotation/revolution/roll thinking in terms of POV - is the question asking if the coin rotates from head upright-to-upright from the reader's POV - or has it rotated when it goes from touching "r" to touching "r" - ie from the fixed coin's POV too bad images or lettering is being used in the circles - instead remove them and leave the face blank - how are you going to tell when it has rotated/revolved/rolled 1 time - how about by placing a mark at the edge of the rolling coin where it first touches the fixed quarter - we would clearly see that the rolling quarter's circumference doesn't spool out until it is at the top again - that's 2 rotations of George's head - but 1 span of the circumference for the small and large circles - if you focused on a dot placed at the edge of the circle - that dot would touch the fixed circle 3 times - but the letter "A" would be pointing up 4 times - since i would have understood "revolution" to mean the playing out of the entire circumference of the rolling circle - therefore to me 1 revolution would mean when the dot has returned to touching the fixed circle - the answer "3 times: is natural the College Board had a dilemma - by invalidating the question due to the question's ambiguity - they probably invalidated students who got the correct answer because they had interpreted the question the way i described above - - a survey should have been done to find out if students were usually confused about the questions meaning - i suspect the 3 students who complained were overthinking the astronomical definition of "revolution" is not the only definition of the word - it is an absurd one in this instance since the astronomical revolution has nothing to do with the outer body's rotation - whereas the circles here are touching - and remain touching while the smaller coin is rotated - or revolved - or rolled using the wordage "how many rolls" would have been clearer - however i asked ChatGPT that - and it said one and a half rolls (?!) - - despite this - i asked ChatGPT "does a carousel rotate or revolve" - and it replied "A carousel typically revolves, meaning it rotates around a central axis or pole" (?!) the moral of my story - "everyone got wrong" is the wrong title - the other people probably interpreted the question in the way the author of the question intended - that "revolution" is defined in relation to the edge of the fixed circle - the students who interpreted the question as the rotation of the rolling circle relative to the page's fixed axis - came up with a different answer - not the one & only correct one --- there's a youtube channel called "MindYourDecisions" that tackled this topic too - since it's a math oriented channel - it has many math people viewing it - and they have deluged the comments section with assertions that the correct answer is 3 - some have added conditions - eg "in topology it is 3" - "depends on the POV" "tech-science" channel has animated the issue - and uses something called the "Willis Equation" - to explain the "Rotation Paradox" (the title of the video) - again - he distinguishes between the POV of the fixed circle - and what he calls the "outsider's POV" - which i consider the "page's or screen's axis or grid" - which is the one used when the edge of the circle is straightened out someone pointed out - using the astronomical definition of "revolution" - the moving circle revolves once around the fixed circle - so another possible answer is "1"

[@TimeBucks]

I can't believe how well the explanation is made.

[@user-om1tu8ur3m]

Good

[@BHUBANSINHA]

Fggg

[@user-vp9hk4jk3i]

Very good

[@batlrar]

I'm really glad you added in the part about the sidereal year - that's always bugged me! I always thought it was about how the solar system moves within space but couldn't find any satisfying answers about it when I first searched. The coin paradox actually unlocked the mystery of the SAT question for me early on in this one, since that example is so simple and yet counterintuitive. Seeing the quarter right side up on the bottom and wondering why made me think of things from George's perspective, and then I realized he was actually upside down!

[@TheMohawkManTV]

Woah that is a weird one, the center of circle A is moving along the radius of B plus the radius of A, which is the translation. On the Flat path the translation is only as far as it rolls in that direction. That's wild. Great video!! I liked the proof he gave with the slipping, really breaks it down!

[@eriquedobson7523]

2:32 This statement makes me feel better, because I TOO answered B, but I honestly couldn't tell you what the question was actually asking me to do. Atleast not at the pace the question would demand on the SAT/ACT

[@LackedMule1217]

Quite enlightening! To me, a more intuitive understanding of why the +1 rotation for Circle A rolling around Circle B is to imagine that Circle B has a radius of 0 (just a point). When this happens, Circle A will make a full rotation once to return to its original position. From there, you just expand Circle B and when its radius is r, matching that of Circle A, then you need 2 rotations and so on. Then the equation of (P + C) / C as in 11:04 makes more intuitive sense.

[@efstratiosanagnostopoulos6636]

I really like your idea. It is a common trick to get to extreme values (0 being the case here) in order to clarify things. The movement of the moon is another great example, as the rotation of the moon around the earth matches the rotation around itself. Thus, we always see one side of the moon, but still the moon rotates around itself.

[@mroldnewbie]

I really like you example, it actually makes it obvious!

[@therealBocaStudios]

He turned it into a rotation orbit thing but the practical application would be cogs in a gear like inside a clock or in a production line, the real answer would have to lie there, which suppose is 3. The quarter had made 1 rotation but the outside of the quarter had only managed half a rotation. I’m fascinated this had 3 possible answers.

[@p.l.3949]

This could made the video a 1 minute short! Great explanation!

[@werallgnnadieintheend]

Oh , that's a good explanation!

[@reidakted4416]

One of my SAT questions (on the verbal test) still bothers me. It was the analogy questions "A is to B as X is to . . . " and they were asking for the meaning of "sanction" and both "to approve" and "to punish" were options. I wonder who sanctioned that and if they were sanctioned. 😆

[@Dont_Read_My_Picture]

Don't read my name

[@fredrickcampbell8198]

My goodness.

[@lw8882]

or sectioned

[@MisterItchy]

This could be valid. I assume 'sanction' is the 'X' in the above. We would have to know what the A is to B part is.

[@ToaAsum]

Autoantonym

[@pikastudios2850]

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

[@mateofyt]

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.

[@sonnybowman]

For more clarity a line describing the circumference with a radius derived by subtracting point B from point A. If one were to move point A to the intersection of circle A and circle B the correct answer I suspect would be 3.

[@WobiKabobi]

“Mess up this test as a teenager and your entire adult life is screwed” is such a top notch system.

[@konstantinossarlis2214]

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...

[@415s30]

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.

[@phelan8385]

I didn't have to take the SAT so I didn't, still got into a really good California state university

[@MrTVx99]

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.

[@fatcatpatdat]

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