The SAT Question Everyone Got WRONG - An Alternative Proof

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Let's look at the viral SAT problem that everyone got wrong! Showing you the basics of the problem as well as an alternative proof!
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For those of you that are new here, hi there 🌞 my name is Ellie and I'm a Part III Mathematics Graduate from the University of Cambridge and current Astrodynamics Software Engineer! This channel is where I nerd out about maths, physics, space and coding so if that sounds like something you're interested in, click the subscribe button to follow along ☺️
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[@EllieSleightholm]

To try everything Brilliant has to offer-free-for a full 30 days, visit brilliant.org/EllieSleightholm 🚀 The first 200 of you will get 20% off Brilliant’s annual premium subscription!

[@leif1075]

Thanks for sharing Ellie. Don't mean to bug you but I reslly hope you can respond to my other question when you can. And by the way , for this question from.the center circles POV, 3 OS a correct answer. Wouldn't you agree with that because it is valid? Hope to hear from you.

[@thevivekkuma]

​@@leif1075hello Ellie I know India toughest exam is iit jee advance But also upsc is tougher than jee advance because jee advance students came for upsc and upsc selected students never go for jee advance 😊😊😊

[@maisonbishop4582]

As someone who just graduated with a math degree, I felt like an idiot for not getting this right at first😂

[@superball2452]

great question! Thanks for covering. My initial intuition was: 3 would be how many rotations we get if we spin the big coin under the small coin once. But relative to each other, we're seeing an additional rotation of the big coin in opposite direction. great to see how geometry touches into algebraic topology

[@mharouny1]

Brilliant explanation! As an extension to what you were saying, you can say that you have to take a larger "step" to meet each point on the circle than you would need to meet on the flat line.

[@natsleightholm1048]

Love this!

[@armanavagyan1876]

PROF i pray God every day that THIS CHANNEL continue to exist😘

[@silver6054]

Becoming a Patreon might be even more effective!

[@ypbj]

Yes we need it! Amen 🙏 God bless all

[@tomasgarza6090]

Circle A is subject to both a rotation motion (about its center) and a translation motion (around the circumference of Circle B). In order to prevent slippage, the rotation motion must conveniently adjust its speed to the translation speed, depending on the relative sizes of the two circles. Now, suppose we stop the rotation and let Circle A simply glide around Circle B., glueing, as it were, the point of tangency. This means that the relative positions of the point of tangency and the center of Circle A change in such a way that, at the end of the process, they are back at its original state. Thus, Circle A will have given one whole turn, due only to the translation motion. This, I hope, explains why there is one more turn in the end. The rotation motion contributes whatever number of revolutions result from the ratio between the radii of the circles, and the translation motion contributes one additional turn.

[@DownhillAllTheWay]

The example with the triangle makes it immediately intuitive, but like most people, I got it wrong in the first instance - however, when I say "like most people", that includes the examiner who set the question, who also got it wrong - and we know this because the correct answer did not figure among the multi-choice answers.

[@jim2376]

Number of small coin rotations around large coin. Formula: (R + r)/r, where R = large coin radius, r = small coin radius. For example: R = 3 and r = 1. (3 + 1)/1 = 4. Muy facil.

[@VarunAstro]

Wow you actually full-filled my wish ❤❤

[@IsaacNewton-ed4oj]

If the inner circle was a dot then then the number of revolutions would be 1 . And if the outer circle was a dot then it would be rb/ra (just removing the +1 from your formula as the radius of the smaller circle would become 0)

[@MATHSNISHANTVERMA]

@EllieSleightholm which site or app are you using for the platform where you are solving it 8:41

[@isobar5857]

Clear as mud for me! Still can't explain it when you substitute the circles for gears that can't slip. i'm so confused...oh well, go to the back of the class!

[@zarraz756]

in the last demonstration, something comes out of the blue: line between Oa center and green point Ab. It helps for alternate angles calculation, but what is its justification, construction and angle value (parallelism and same theta angle?) ?

[@lousleightholm]

Great question & answer! I was lost initially but you explain everything so well! Thank you

[@elyaelovenom]

the art of mathematics !!!!!! ellie I appreciate this channel and tricking math questions that u post here 10Q a lot

[@jimf2525]

I like ur proof. Very smart. I think you may have slipped up near the end. At 15 minutes and 40 seconds where you say 2 pi = N x theta hat. If theta hat = 4 pi, then doesn’t N = 1/2? I’d think 2 pi N = theta hat. I’ve made some videos and it’s extremely hard to get everything right in one take. It gave me newfound respect for politicians who have to answer questions on the fly. My respect for them went from zero to epsilon. 😂 Anyway, good luck with your channel.❤🌈🤓💃🥳🥁

[@jimf2525]

And in 3 years buy my future book Endo’s Deity.

[@J7m7s]

How we would solve it if the center of the smaller circle would be at the top?

[@larryallen1093]

Also, how about if the small circle was inside the large circle rather than outside the small circle. I suppose engineers who deal with gears know all about this stuff.

[@AbdelkaderDjebbouri-s5k]

Thanks you vert much

[@marshian__mallow2624]

Would you be able to make a video talking about your job position more? I can’t find much information about what exactly an Astrodynamics software engineer does and how much it pays. Also to get a job like that would you have to specialise in applied maths as opposed to pure maths?

[@josephbenson606]

Aerospace engineering, applied maths, pure maths, physics - you can pretty much specialise in anything that deals with numbers, mathematical models and dynamic systems. If by specialised, you mean a postgraduate degree, you would probably want to specialise in something related to spacecraft and satellites, or orbital mechanics. As for what an astrodynamicist does, they study orbital mechanics and travelling in space, but in the context of mission planning, orbit transfers and trajectory efficiency and lots more in space

[@marshian__mallow2624]

@@josephbenson606what I mean is if I do an undergraduate in mathematics that is mostly pure maths with some physics modules. If I do a masters should I do a masters in applied maths, mathematical physics or can I do a masters that mostly focuses on pure maths?

[@gavintillman1884]

Nice proofs. SATs didn’t exist in 1982 though. Either the year is wrong or it isn’t a SAT. 1982 predates SATs, GCSE and the National Curriculum. It was my O Level year.

[@josephbenson606]

American SATs lol

[@gamingzeraora443]

I did this proof with just rolling motion by myself

[@virais4605]

You are brilliant! Your resolutions are incredible, I found your channel by chance and I'm grateful to God for that, I barely started exploring the enormous amount of content you have available on the platform, but I'm already impressed with the amount of skills you bring together. So is this what Cambridge graduates are capable of doing?

[@DalyHenry-n1q]

I think that's sure ,best intervalle geometric🤝

[@bigheart99]

I have the feeling that if the fixed circle was a dot the coin would just do one rotation, because the dot has no radius, so in your final formula the radius of B would be 0, so the solution would be 1. I'm not very confident about my reasoning though, it just makes sense to me 😂

[@Anordinaryguy-ke7oq]

Interesting

[@GauravSingh-wf4kc]

1 and undefined

[@imeprezime1285]

Now add third small circle rolling inside small cirlcle as it is rolling on big circle 😄

[@eartphoze]

Thanks mum dad 🙏 I love mum dad

[@luisakehau1398]

Geometry ❤ ...

[@jamesjohn2537]

Hi, Ellie, I recommend you to take a look at the Big Bang Theory series comedy, there is a lot of applied maths going on there!! And have a great day

[@jamesjohn2537]

Am trying to guess here, numerical answer would be 3 since the radius of small circle is 1/3. Isn't?

[@angel-meta]

I love u so much 🥹🥹 u have no idea, thank you ellieee! 🥰🥰

[@MandipChhetri]

Here after veritasium sat video...

[@crazyabtu1]

I am the 100th who liked your video so much , great work , love from India 🇮🇳

[@armanavagyan1876]

I first like then watch UR VIDEOS 😊

[@milanvadoliya3376]

U calculated rotation to the centre but we need rotation at surface.u did nothing if u can imagine u just increased diameter of bigger circle,so extra rotation of small circle is come from increased dia of bigger circle.

[@tech_path_]

First

[@larrywimberly4930]

your sliding the coin

[@HBV-um1lq]

why you change intro music every time