The SAT Question Everyone Got Wrong

Рет қаралды 12,290,968

8 ай бұрын

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.
Special thanks to our Patreon supporters! Join this list to help us keep our videos free, forever:
ve42.co/PatreonDEB
I invented Snatoms, a molecule modeling kit where the atoms snap together magnetically. Try it at ve42.co/SnatomsV
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
▀▀▀
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
▀▀▀
Special thanks to our Patreon supporters:
Adam Foreman, Anton Ragin, Balkrishna Heroor, Bernard McGee, Bill Linder, Burt Humburg, Chris Harper, Dave Kircher, Diffbot, Evgeny Skvortsov, Gnare, John H. Austin, Jr., john kiehl, Josh Hibschman, Juan Benet, KeyWestr, Lee Redden, Marinus Kuivenhoven, Max Paladino, Meekay, meg noah, Michael Krugman, Orlando Bassotto, Paul Peijzel, Richard Sundvall, Sam Lutfi, Stephen Wilcox, Tj Steyn, TTST, Ubiquity Ventures
▀▀▀
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

Пікірлер: 19 000

@duckyfam9012 4 ай бұрын

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

@LJ3783 4 ай бұрын

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

@NicholasAndre1 4 ай бұрын

@@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 4 ай бұрын

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

@LJ3783 4 ай бұрын

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

@cameronschyuder9034 4 ай бұрын

@@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

@NoraOlson-ct7nr 4 ай бұрын

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 4 ай бұрын

It was the perfect explanation

@anonymousguy5694 3 ай бұрын

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 3 ай бұрын

@@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 3 ай бұрын

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 2 ай бұрын

@@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)

@NCore_._ 2 ай бұрын

I don't like math, but any visual explanation like this makes me engross in it for hours, replaying multiple sections to fully understand it and appreciate the fact, that how amazing it is.

@anirudhkodial1977 Ай бұрын

Start learning Houdini. You'll be jumping down an endless rabbit-hole.

@DVnc_ Ай бұрын

Same bro

@prezentoappr1171 Ай бұрын

3blue1brown gang

@STWAREdits Ай бұрын

Idk why but my brain sucks at handling visual models

@swastikaxc7719 26 күн бұрын

Truly, that’s the case with me too!

@JClayJohnsonOfficial 2 ай бұрын

What makes it intuitively easiest for me to understand is to think about it this way: if the circumference of Circle B were 0 (i.e., a dot) then rotating Circle A around it would result in one revolution. So any addition to the circumference of Circle B would simply add on to the starting number of 1 rotation needed.

@jimwinchester339 Ай бұрын

I came up with a similar scenario: what if the outer wheel didn't rotate at all, or was a sqaure, but was rather DRAGGED around the inner circle. It would still complete one rotation on its own, right? That's the rotation of the reference frame itself. Incidentally, from the POV of any point on the "tread" of the outer circle, they do indeed make contact 3 times during the rotation around the inner circle.

@douggief1367 Ай бұрын

That's the kind of simplified thinking that gets to a good solution with minimal fuss. Well done.

@velvetbees 23 күн бұрын

So, is it safe to say that B could be as small as one atom and this is still true? And that it stops being true only if B gets larger than it is? I'm from the visual learner, math challenged peanut gallery.

@palmerquiver 22 күн бұрын

@@velvetbees hold a quarter in your hand and keep it facing you. Turn yourself in a circle and note how (from an aerial view) the quarter would have rotated 1 time. But relative to you, it wouldn't have rotated at all. This experiment simulates how a circle with a radius of 1 to ∞ would orbit (without slipping) a circle with a radius of 0. I may not understand this well enough to explain it clearly, but that's my best attempt.

@5MadMovieMakers 7 ай бұрын

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

@nirbhaykumarchaubey8777 7 ай бұрын

Wait, it is night

@krishmishra514 7 ай бұрын

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

@zayansaifullah2008 7 ай бұрын

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 7 ай бұрын

You're mentally challenged

@QuantyzIGuess 7 ай бұрын

@@zayansaifullah2008 same

@felixp535 7 ай бұрын

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 7 ай бұрын

That was the "aha" moment for me too.

@misterscottintheway 7 ай бұрын

This

@argelovec6216 7 ай бұрын

There were 3 aha moments for me

@Marco-xz7rf 7 ай бұрын

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 7 ай бұрын

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

@-ADOI- 3 ай бұрын

I was so confused because of the word "revolution," "1" is what I thought the answer was because of that

@engrpas 2 ай бұрын

Yes, there's a distinction between "rotation" and .revolution" The outer coin makes one revolution but several rotations.

@tomsawyer283 Ай бұрын

Same, I felt dumb when 1 wasn’t listed at first then thought about it again and thought 3 was the next “logical”…ist. Because the original wording is legit asking after how many revolutions…will a revolution be completed lol

@JustNuggie Ай бұрын

same

@God.is.Human.19 Ай бұрын

4 toppers meet

@God.is.Human.19 Ай бұрын

@@JustNuggie4 toppers meet

@SuperJm1200 2 ай бұрын

Good job, very clear. My professor in computer science used to say that if you are a good programmer and you have an error in your code chances are you are usually off by 1 somewhere.

@gregnixon1296 Ай бұрын

I have found that in confusing situations in math the key error, or answer, is -1, 0, or 1.

@Shepard-Thomas 7 ай бұрын

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 7 ай бұрын

Did the professor change your grade?

@Sciguy95 7 ай бұрын

@@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 7 ай бұрын

literature tests: q.e.d.

@pongmaster123 7 ай бұрын

@@Sciguy95 very cool, but also unprofessional

@Derzull2468 7 ай бұрын

@@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.

@Spondre 7 ай бұрын

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 7 ай бұрын

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 7 ай бұрын

@@hieronymusbutts7349❤

@glennpearson9348 7 ай бұрын

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).

@Xingchen_Yan 7 ай бұрын

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_ 7 ай бұрын

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.

@LGTVQHD Ай бұрын

as soon as Dr. Doug drew it on the white board with dots, it instantly clicked that the point touching the circles is moving 3r but the center of smaller circle moves 4r wow such simple yet mindblowing question.

@brucelade8551 Ай бұрын

Excellent video. Thank you !!! This is possibly the best STEM video I have seen. The link to sidereal time etc is brilliant! To see practical application of "tricky maths" is how people learn. Well done! And thank you again

@KevinJDildonik 7 ай бұрын

To all the 1st posters: KZfaq 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 7 ай бұрын

😂

@kakyoindonut3213 7 ай бұрын

Nuh uh

@Warr4real 7 ай бұрын

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

@MrDJ2004 7 ай бұрын

haha

@TeachAManToAngle 7 ай бұрын

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

@forkmonkey 7 ай бұрын

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 7 ай бұрын

Brilliant. Wish I'd thought of that!

@startibartfast42 7 ай бұрын

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 7 ай бұрын

That's actually a great example.

@AsterothPrime 7 ай бұрын

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 7 ай бұрын

this helps a lot!! thanks!

@markrittman2437 Ай бұрын

I took the SAT in 1982 and scored a 780 in the math section, indicating that I likely missed just one math question. When faced with this question, I initially thought that it needed to roll around three times and then once more, leading me to select 4 as my answer. However, upon realizing that 4 was not provided as an option, I doubted myself and ultimately chose 9/2. As I doubt that I would have chosen 3, this is probably the question I missed.

@sj-237 Ай бұрын

But SAT authority discounted the problem. Was your score corrected?

@jimwinchester339 Ай бұрын

That makes you a very sharp cookie.

@JayJay-ye7ic Ай бұрын

Did this question stand out, or do you remember all the questions from 40+ years ago

@markrittman2437 Ай бұрын

@@JayJay-ye7ic No. I don't remember anything about the test in 1982. I'm just guessing.

@douggief1367 Ай бұрын

Congratulations Mark. I was very smart like that too (but not exceptional). I value it, but not too highly.

@proteusnz99 Ай бұрын

Fascinating, excellent explanations and graphics. Thank you.

@tc6818 5 ай бұрын

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

@TinMan-kd2gv 4 ай бұрын

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 4 ай бұрын

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 4 ай бұрын

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 4 ай бұрын

Yeah

@TupperWallace 7 ай бұрын

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 7 ай бұрын

Fun!

@davidklein1245 7 ай бұрын

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 7 ай бұрын

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

@wingracer1614 7 ай бұрын

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

@BoneyMB 7 ай бұрын

Glad about him.

@bengarrett4984 2 ай бұрын

Thank you for including the practical application of this math problem. One of the most frustrating part of my education was asking the teacher why I needed to know something and getting the answer "because I said so".

@Burnoff_ 2 ай бұрын

That's why you don't study in American schools lol

@JackDespero 2 ай бұрын

I needed to watch the video twice for the intuition to settle, but I think I finally got it. It is one of those paradoxes that is hard to understand even when you know the answer. Then it does click and it makes total sense. It is so obvious that you are confused as to why you were wrong the first time. The world is fascinating.

@stevedietrich8936 7 ай бұрын

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 7 ай бұрын

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

@enzolomongiello4497 7 ай бұрын

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

@clarkkent4665 7 ай бұрын

You weren't incorrect

@jamiefa2000 7 ай бұрын

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 7 ай бұрын

The answer is 3 only the video is useless

@user-rx4wo7il2g 7 ай бұрын

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 7 ай бұрын

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

@kwimms 7 ай бұрын

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 7 ай бұрын

I also thought of this same explanation

@brettgregory7799 7 ай бұрын

Excellent!

@crussty 7 ай бұрын

Great visualisation. This should be pinned

@bytecode5834 2 ай бұрын

Fantastic video, thanks for sharing you knowledge

@littlezombie9621 2 ай бұрын

Mathematically it‘s actually really easy to calculate. 1) Calculate the distance d that point A has to travel. If you think about it, that‘s not the circumference of circle B, but the circumference of the radius B plus the radius of A, creating a third circle C around point B with point A now on it‘s outline. The circumference of this new circle C is now the distance d that point A has to travel to get back to its starting position. Formula for circle circumference: 2 * r * PI Now we know that r = rB + rA and rB = 3 * rA -> d = 2 * (4 * rA) * PI = 8 * rA * PI 2) Calculate the distance dRev that circle A covers with one revolution, which is equals the circumference of circle A. Again we use the formula for circumference, this time on circle A. -> dRev = 2 * rA * PI 3) Lastly, calculating the number of revolutions needed, we divide the total distance point A has to travel on d ( = circumference of circle C) by dRev (the circumference of A). -> R = d / dRev = (8 * rA * PI) / ( 2 * rA * PI) rA and PI cancel each other out. -> R = 8 / 2 = 4

@blinkers88 2 ай бұрын

"easy"

@tanez778 2 ай бұрын

@@blinkers88 I mean it's pretty easy if you understood the video, it's more or less exactly this part 9:45

@varjain 2 ай бұрын

Yeah "easy" SATs dont have enough time to calculate that you know

@abrokeprogrammer 2 ай бұрын

Ikr Also... U didn't really need to write the whole second half The answer is simple The R is 4r then it's 4 times

@abrokeprogrammer 2 ай бұрын

@@tanez778the video is a waste of time for such a simple answer

@glennpearson9348 7 ай бұрын

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 7 ай бұрын

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 7 ай бұрын

Thank you, for a great YT comment!

@gruanger 7 ай бұрын

haha, good point@@Redmenace96

@Alpha_Online 7 ай бұрын

@@gruangerhave you watched it yet?

@gruanger 7 ай бұрын

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

@Cosmic9999 7 ай бұрын

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 7 ай бұрын

This is why common sense is not a thing

@anteshell 7 ай бұрын

@@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 7 ай бұрын

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

@sumermuktawat 7 ай бұрын

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

@Mallchad 7 ай бұрын

@@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.

@annimon2814 3 ай бұрын

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

@parv09955 2 ай бұрын

It's revolutions, not rotation. So the logical answer is 1.😁

@Honeysaini9050 2 ай бұрын

😂😂

@Tim3.14 7 ай бұрын

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 7 ай бұрын

You’re clever 👌

@abhirammadhu2973 7 ай бұрын

That’s some pro level thinking🔥

@munkhjinbuyandelger 7 ай бұрын

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

@rambbler 7 ай бұрын

@@munkhjinbuyandelger10:10

@mmeettwwoo 7 ай бұрын

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??

@monopolyking879 4 ай бұрын

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 4 ай бұрын

Hear, hear!

@Worms_Pro 4 ай бұрын

Keep It Simple Stupid KISS

@The_E_Lord 4 ай бұрын

Damn I wish to do aerospace/astrophysics too

@rosly_yt 4 ай бұрын

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 3 ай бұрын

@@rosly_yt You're hilarious.

@Affalterbach1967 2 ай бұрын

There is a special glee where a defective exam question is dissected by a former teacher.

@SeanMilligan-kj5ok 2 ай бұрын

This was amazing. Thank you.

@jonathanbost8427 7 ай бұрын

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 6 ай бұрын

Literally same❤

@vineethbharadwaj8187 6 ай бұрын

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

@chrissherlock1748 5 ай бұрын

Revolutionary comment

@wayneerichsen 5 ай бұрын

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 5 ай бұрын

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

@scottthacker9554 7 ай бұрын

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 7 ай бұрын

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 7 ай бұрын

@@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 7 ай бұрын

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 7 ай бұрын

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 7 ай бұрын

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.

@pikastudios2850 3 ай бұрын

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 3 ай бұрын

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.

@anujbansal11 2 ай бұрын

Well this was so simple, got it right in the 1st attempt. The center of circle A is 4 units away from center of circle B. Hence the centre of circle A (treat it as centre of mass) must travel the circumference of this fictitious circle (4 units) to reach to its original position. Hence 4 is the answer.

@gregnixon1296 7 ай бұрын

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

@EagleOxford 7 ай бұрын

They should have offered him a job making the tests.

@FlorenceSlugcat 7 ай бұрын

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 7 ай бұрын

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

@jakemccoy 7 ай бұрын

@@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 7 ай бұрын

@@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.

@sarthak-ti 7 ай бұрын

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. 7 ай бұрын

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

@andrewrhsmith 7 ай бұрын

Agreed

@bill5197 7 ай бұрын

@@aniketmeshram6598 reconstruct your sentence. Please.

@aniketmeshram6598 7 ай бұрын

@@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"

@Knocklehead 21 күн бұрын

This was very head-melty and satisfying! Thank you!

@MissVL487 Ай бұрын

So many of your videos have blown my mind but this one... explosion!!!! Woah

@ZEROBRICKS 7 ай бұрын

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

@Dont_Read_My_Picture 7 ай бұрын

Don't read my nameDon't read my name

@hexagonal7708 7 ай бұрын

The same thing happened to me

@DrDipsh1t 7 ай бұрын

That was my exact thought was gear ratios lol.

@venanziadorromatagni1641 7 ай бұрын

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 7 ай бұрын

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

@PramodApte23 7 ай бұрын

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 7 ай бұрын

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 7 ай бұрын

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

@louiejohncastillo9822 7 ай бұрын

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 7 ай бұрын

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

@N65-sim 3 ай бұрын

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 😆

@nico2006t 2 ай бұрын

Excatly

@neilmckie2768 3 ай бұрын

I now need to wrap my head in cold towels, lol. Really interesting - especially the various ways in which you demonstrated the various outcomes. Thankyou

@Darth_Insidious 7 ай бұрын

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 7 ай бұрын

this comment helped me solidify ny understanding thank you

@dr.albekhan8640 7 ай бұрын

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

@solimao1236 7 ай бұрын

Genius comment, thank you!

@08-quocat6 7 ай бұрын

finally! i got it

@Nowolf 7 ай бұрын

That idea helped me as well

@R_gue 7 ай бұрын

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 7 ай бұрын

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

@ADUAquascaping 7 ай бұрын

@@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 7 ай бұрын

@@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 7 ай бұрын

@RepentandbelieveinJesusChrist5 Sad how religion turns you into a mindless drone

@facundomartinify 2 ай бұрын

This has to be the best channel on KZfaq

@user-hd4nu8zd2q Ай бұрын

FRFR

@vollabgedreht0036 18 күн бұрын

Thank you very much for this wonderful video and thank you very much for improving my knowledge 🙏

@berryl9653 7 ай бұрын

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 7 ай бұрын

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

@patrickchang9135 7 ай бұрын

@@temple69 Watch a 3D demonstration of it

@igarazha 7 ай бұрын

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

@duzyolek 7 ай бұрын

@@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 7 ай бұрын

Thanks for not misusing any comma.

@tadessebekeshie7231 3 ай бұрын

It is amazing. Thumbs up for the three students.

@bhuvansoc9432 10 күн бұрын

Dude I’m bowled ! I got my answer as 3, but when that was wrong, I was just checking up my basic maths ! The catch here is the number rotations by the other circle, while the length should always tally to 3 times the smaller

@foxboy6662 6 ай бұрын

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 6 ай бұрын

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 5 ай бұрын

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 5 ай бұрын

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 5 ай бұрын

@@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 5 ай бұрын

@@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.

@pradeepkrishnamurthy2557 7 ай бұрын

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 6 ай бұрын

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

@nanofoods Ай бұрын

If math was taught like this in school, I wouldn't suck so badly at it now. Loved this episode. Thank you.

@cbwavy 2 ай бұрын

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

@atticuscpchan 7 ай бұрын

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 7 ай бұрын

Thats convenient. In Jee they purposefully distort it

@kernelsmith 7 ай бұрын

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

@techgeek2625 7 ай бұрын

@@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 7 ай бұрын

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 7 ай бұрын

@@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.

@ElectroBOOM 7 ай бұрын

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 7 ай бұрын

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

@iamdigory 7 ай бұрын

I'm just glad I got the correct wrong answer

@ninthjeans3749 7 ай бұрын

same

@michaelharrison1093 7 ай бұрын

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 7 ай бұрын

what was you trying to imply here bro 🤣

@tomoakhill8825 3 ай бұрын

Starting in 1967 and continuing through 1974 I took the SAT 4 times: "practice", "merit scholarship", college entrance exam, and, 5-years-later, another college entrance exam when I finally went to college. My low score on the math section was 792 out of 800, I got an 800 twice. Every single SAT TEST I had to figure out what _wrong_ answer (2:35) the test writers wanted on multiple questions. Obviously I was good at deducing the "correct" wrong answer. Remember they are testing people like Dr. Doug Jungreis, and me (I have a physics Ph.D. from Harvard). But no one with our skill set works for the College Board writing tests, and only 1 in 1000 students scores as high as we did.

@plektosgaming 2 ай бұрын

Praxis tests are like this as well. Multiple wrong answers and having to figure out what they thought was "correct". It looks like they have lifted old SAT questions and dropped them in. Really sad when you consider that this is the exam that is required of K-12 teachers in many states.

@gokselaras9002 15 күн бұрын

You count everytime it faces upward but if you look at the little circle, at every time it faces upwards, the point of contact on the smaller coin only change 270 degrees

@paparmar 7 ай бұрын

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 7 ай бұрын

Yes! Sidereal time! Thanks

@gabrielgonzalez1993 7 ай бұрын

Beautiful

@ohyou_6599 7 ай бұрын

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

@jaelwyn 7 ай бұрын

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 6 ай бұрын

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

@TimeBucks 7 ай бұрын

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

@user-om1tu8ur3m 7 ай бұрын

Good

@BHUBANSINHA 7 ай бұрын

Fggg

@user-vp9hk4jk3i 7 ай бұрын

Very good

@johnnyshell2839 3 ай бұрын

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

@SpongeDavid1145 Ай бұрын

Highly educational and challenging video!!

@lancedrath 7 ай бұрын

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

@sinephase 7 ай бұрын

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 7 ай бұрын

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

@allanmiller4967 7 ай бұрын

What a cool proof. I am so glad that Dr. Jungreis went on to become a mathematician and is doing well. Excellent video!!!

@Arob4343 Ай бұрын

When I saw the coin example, my thought was basically “but the coin only did half a rotation…clearly they want the coin to do a full rotation”. Then you essentially covered that difference, I’m glad

@davidcolombier5673 3 ай бұрын

very good explanations. Thank you.

@StefanNoack 7 ай бұрын

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 7 ай бұрын

Great idea!

@EduardoGarcia-eh6sh 7 ай бұрын

🤯

@bobhuang94 7 ай бұрын

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 7 ай бұрын

Makes me want to research gears now

@jamesonbornholdt7302 7 ай бұрын

We know...

@Mr.MoonRabbit 7 ай бұрын

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 7 ай бұрын

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 7 ай бұрын

Both of your stories are amazing!

@raygordonteacheschess5501 7 ай бұрын

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 7 ай бұрын

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

@josephkavanagh7815 7 ай бұрын

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!

@cykopat 21 күн бұрын

When Doug first appeared, I thought, “wow that’s the Doug from the Doug cartoon”.

@mattc2626 2 ай бұрын

10:49 This image really helped everything click for me. When the circle goes around a corner it rotates but doesn’t cover any linear distance on the surface of the triangle.

@daleferrier3050 7 ай бұрын

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 7 ай бұрын

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 7 ай бұрын

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 7 ай бұрын

@@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 7 ай бұрын

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 7 ай бұрын

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

@user-kb6mj7zq8t 5 ай бұрын

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 4 ай бұрын

Veritasium is ridiculously talented at making videos.

@tombiby5892 4 ай бұрын

How many sidereal minutes does KZfaq take?

@literallyjustgrass 4 ай бұрын

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

@ivandetoledo 2 ай бұрын

Thank you for giving my brain the cramps 😂😂😂 It was great! 👏🏼👏🏼👏🏼

@lflmura Ай бұрын

I love this channel!

@4RILDIGITAL 7 ай бұрын

Three of them got it right by saying that the question was wrong.

@wqters5772 7 ай бұрын

likebot more

@prashantmishra9985 7 ай бұрын

1k likes within 5 minutes? Wow!

@EzraHaviland 7 ай бұрын

Also 3 is still a correct answer to the problem it’s just badly worded. So everyone who answered 3 still got it right.

@stevejones1318 7 ай бұрын

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.

@rfvtgbzhn 7 ай бұрын

@@stevejones1318they forget an A. If there was one more A in the question, it would be correct.

@Schweebcraft 7 ай бұрын

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 7 ай бұрын

Super interesting!

@appa609 7 ай бұрын

Dude how fast are your feeds for this to matter?

@fresheFresse 7 ай бұрын

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

@devjk1 7 ай бұрын

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 7 ай бұрын

@@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

@mariusherghelegiu6241 14 күн бұрын

absolutely ingenious, and even if I heard about the "sidereal time" 45 years ago through one of the Jules Verne books, I never got into this insight.

@thestranger1949 3 ай бұрын

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

@RocinanteGold 7 ай бұрын

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 7 ай бұрын

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 7 ай бұрын

They rotated the scores around themselves

@suivzmoi 7 ай бұрын

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

@jakemccoy 7 ай бұрын

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 7 ай бұрын

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

@AndrewPang-if3wu 5 ай бұрын

7:44 whoever came up with that headline deserved a raise.

@jhbhbhbkjb 4 күн бұрын

I looked at it and thought the answer would be 4, but then thought I was wrong because it wasn't an option.

@douggief1367 Ай бұрын

Dear Seekers, I have an interesting story to tell. I'm nearly 70 now. As a boy, I was a total math nerd. After school I dropped math altogether (except for practical daily needs). Surprisingly, I got the answer 4 (before watching the presentation). I don't regret working with my hands for most of my working life. I've kept math as an interest but not an obsession. I have learned to often do "thought experiments" rather than using formulae. It works for most needs. Have a good life. --Doug.

@donaldsearing 7 ай бұрын

This is one of the most interesting "simple" math problem videos on KZfaq. Amazing job!

@lexxynubbers 7 ай бұрын

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 7 ай бұрын

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

@thehandleiwantedwasntavailable 7 ай бұрын

She sounds like a useless teacher.

@erikthomsen4007 7 ай бұрын

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

@bunface 7 ай бұрын

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 7 ай бұрын

@@bunface 💖

@brycehins206 4 күн бұрын

This effect is most visible by letting the larger circle's circumference be a straight line, then let the small circle roll along that line from bottom to top. When finished, move the top of the line and the circle in an arc to the side, making the line form the original larger circle. As the smaller circle moves with line during this, you can see it rotate an additional time. Basically, break the move into two phases.

@MRLOL5233 Ай бұрын

Veritasium’s videos always keep me awake at night 😂

@graham1034 7 ай бұрын

This was a lot more interesting than I initially expected. Great explanation and visuals that made it easy to understand all of the facets of the paradox. Kudos!

@ADUAquascaping 7 ай бұрын

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.

@SLCCWebmaster 7 ай бұрын

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 7 ай бұрын

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 7 ай бұрын

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 7 ай бұрын

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

@Sandman382 7 ай бұрын

@@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 7 ай бұрын

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

@adolforabasa 3 ай бұрын

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).

@sebastiangundolf6740 Ай бұрын

Adolfs really know how to suck everyones fun out of any activity 😅

@TurnStyle72 Ай бұрын

Omg... I'd legitimately scrape into MENSA, and my head hurts! 🤣 Fantastic video - thank you so much. 😊

@Barrickade89 7 ай бұрын

This blew my mind. Even incorporating sidereal time into this just topped it over the awesome scale. Glad I clicked it. Thank you for the explanation.

@MyFiddlePlayer 7 ай бұрын

Here's the thing...I understand sidereal time, and I still got the problem wrong the first time I thought about it! (Whoops. Of course, TBF, it doesn't help that the correct answer was not one of the options.)

@theplacebeyondthelies2429 7 ай бұрын

it‘s still wrong, earth is not a rotating ball revolving around the sun, the constant speed theory of the rotation of earth contradicts this whole video. Since constant speed theory of earth is essential to justify „we don‘t feel any consequences of such a rotation“ this house of cards folds in. There is so much evidence out there outside of the realms of astronomy that prove the earth is flat and not a ball. As Jesus says blessed are the eyes of those who see. What He means is that it‘s God‘s creation (flat), not a people’s creation (ball) and truth is with God in Heaven! Friendship with the world means enmity with God. It‘s the blind leading the blind in this world.

@batlrar 7 ай бұрын

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!

@SchawjibbWanders 3 ай бұрын

I am 40 now. My father told me about sidereal year concept when I was 9 or 10. I just didn't believe him then; I thought he might have made that up to add another day in a year! This video made me nostalgic and, as by product, helped me understand the concept.

@abenzer3033 2 ай бұрын

Love this channel

@ItsYoji 7 ай бұрын

The Eureka moment for me to get the problem was when you showed the rotation from the viewpoint of the larger circle. That was brilliant, well done!

@Hendrik_F 7 ай бұрын

@@seekerofthemutablebalance5228 It makes sense because the number of rotations depends on your frame od refrence. From the viewpoint of the larger circle the small circle rotates 3 times, but from the viewpoint of an external observer the small circle rotates 4 times. The difference comes from the "camera" from the viewpoint of the larger circle rotating too. The "camera" has to rotate so it always sees the small circle.

@Parhaimmisto 7 ай бұрын

Poe content creator in the wild.

@testest12344 7 ай бұрын

@@seekerofthemutablebalance5228 The center of the circle rotates 4 times because, if you draw a line from the center of the larger circle to the center of the smaller circle, it forms a radius of 4 (1+3) but the outer portion of the circle rotates three times, that's why his demonstration at 6:15 has the blue arrow.

@peter9477 5 ай бұрын

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 5 ай бұрын

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 5 ай бұрын

This is a good explanation.

@marissabulso6439 5 ай бұрын

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

@k.r.koushik9660 5 ай бұрын

Thank you so much. Was going mad

@codyhall6802 5 ай бұрын

Great explanation thanks

@PB-sk9jn 3 ай бұрын

I got it right, and thought 4. Because if you rotate around a zero radius toothpick it rotates once.

@mitchb311 3 ай бұрын

I loved the chalkboard explanation because it highlights how I saw it all along, which means the answer really is B(3).

@mateofyt 3 ай бұрын

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.

@HIVELY26 7 ай бұрын

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.

@Yosetime 7 ай бұрын

Well said!

@oahuhawaii2141 7 ай бұрын

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.

@kirbya9545 7 ай бұрын

@@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 😂

@Stevelemontrudy 7 ай бұрын

@@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?!

@kirbya9545 7 ай бұрын

@@Stevelemontrudy and unlike a bag of chips 40% of this video isn’t air 😂