What your teachers (probably) never told you about the parabola, hyperbola, and ellipse

[@krishnasahu6824]

I wish our Mathematics teacher explained the use of Parabola, Hyperbola, Conics and other figures like this. I wouldn't have had any doubts.

[@jimmysboringplace8502]

I haven't learnt those properties until I had Technical Drawing (I'm from Spain if you want to make an idea). There, I learnt some properties and uses and some tangencies. It's quite boring but it's worth and useful for other topics.

[@krishnasahu6824]

@@jimmysboringplace8502 We Indians read that when we are in 11th and 12th grade without even knowing what is the practical use of these. That may be one of the reasons why Indians are known to be good in Maths.(Though I don't consider Conics, Parabola, Hyperbola as part of Maths)

[@sebastianfeuerstein9306]

I wish we had more teachers like @MajorPrep, I never knew that math was this useful until I met him

[@vikraal6974]

Yes our teachers are lodu

[@lonestarr1490]

@@sebastianfeuerstein9306 Well, usefulness is not inherent to math. Math doesn't care if it is useful or not, and therefore, many mathmaticians won't either. By I admit that's advanced math perception. School teachers should indeed focus more on real world applications, because you cannot expect school kids to comprehend the joy and satisfaction of pure thinking.

[@Aman-jl7kp]

This channel deserves way more recognition and subscribers , excellently done

[@rique3012]

Agree, it's great !

[@SrmthfgRockLee]

yea...

[@SrmthfgRockLee]

i totally do these things on my own and wanted to do videos about em n theres..this channel which alrdy has my ideas as videos o_O.. the format i do is totally like the same.. its so fun to numerate things n think about things in life.. have numerations/priorities-all the dependencies

[@Aman-jl7kp]

@@SrmthfgRockLee wow that sounds great ; are you a student?

[@SrmthfgRockLee]

​@@Aman-jl7kp yeh fourth course for coach as well as 2nd specialty physical teacher in school. age 26 soon. Ultramarathonner & i've gone into super microdetails about 100% motivation how music effects our brains.. the best music for the certain kind of activity, especially motivation is the most complex.. the opposite of relax.. and like the best videos-colours/structures, what motivates us.. Biorhytmicality/optimalness - what is good for us, worth to do something intensively or not.. why i believe running is better than pushups..it requires less will power and can be much more fun - u use imagination meanwhile, high speed..the faster u run the happier u are in a way(metaphor). i have many facebook groups and im re-organising my thoughts often - going to re-type them again goodly/shortened in better format through pictures on album with different colours on some letters as i am above much of the facebook/other designers, but other ppl who dont type as often like me wouldnt find a use in such a thing. even twitter/youtube went black, but facebook still has no black option=bad for the eyes, even if u have it minimized there's still a bit of white no matter how u use it..black screens are better..black colour, for the eyes. going to have blogs on blogspot com as well, and start making motivational youtube videos - sports being one topic, other..education-brain, easiest ways to remember, what to focus in life. Though Im wondering if i should use my real name in utube like id o in facebook.. i'll definitely have a seperate account for utube videos of course, i already have one for motivational videos by songs/videos, though due to copy rights i cant post many of my famous mixes(mixes of famous musics, i like to listen 5-15musicssametime) .

[@ShantanuBaviskar]

If maths was taught this way in my school, everyone would have more interest to learn it

[@tiktokclipsgermany2793]

We only had "how to calculate", not math

[@ramkumars2329]

every student will find math easy and pass with high grades if they were taught like these

[@krazyk5993]

As a high-school student I can confirm that most pepile still would not give a dame if math was taught like this. There are many variables that go into why pepole enjoy or pay attention to certain things. The problem with education has a lot to do with the school sure and also has something to do with the students and mentality. No one is blame free. So comments luke this kinda annoy me ngl.

[@War-Daddy]

It’s partially true. The main problem is disrespectful students and the instructor has to spend half the time dealing with them. You usually see more passion in college instructors than elementary, middle, and high school because if someone is taking a college math class then it typically means they want to be there which means they will pay closer attention.

[@davidb5205]

Self-selection bias. Why did you click on a video titled "What your teachers (probably) never told you about the parabola, hyperbola, and ellipse" in the first place? Initial interest in the subject is necessary; many students don't even have that. You can teach 1001 ways, but you can't teach someone who feels forced to go to school and learn. This is why honors and elective classes, magnet schools and colleges, have students who are more engaged. Because they are self-selected students who _choose_ to be there.

[@tiemen596]

2:10 This statement is not entirely correct. Knowing the distance to 3 satellites is enough to pin-point where you are on Earth, including altitude, even in 3D. We draw spheres rather than circles, which will have 2 intersection points. One of those points will be on Earth, the other one will be in Space, some 20.000 km above the satellites. Take your guess. It is, however, correct that we need a 4th satellite, but the reason is more complicated. Let me try to explain: The way we determine the distance to each satellite is as follows: - Each satellite sends a signal that includes the time and location of transmission. - The GPS receiver compares the time of transmission to the time of receiving the signal. Multiplying by the speed of light (and correcting for atmospheric delay) tells us the distance to each satellite. This would work perfectly well if all the clocks are exactly on the same time. Those on the satellites will be maintained accurately, but your GPS receiver clock is not that accurate - it would be way too expensive! So, instead, we use a 4th satellite's signal, giving us a fourth equation, allowing to solve for all four unknowns of our receiver: x,y,z and t. x,y,z being its coordinates, and t being its clock-offset.

[@Guztav1337]

Cool TIL. Thank you for your comment!

[@kaweewattt]

GPS also use the hyperbolar navigation... that way it can calculate position then calculate back to time.

[@bip901]

Nice explanation, thank you.

[@raffaelepiccini3405]

The thing is that the example he does a few minutes later where you don't know the distance but only the difference between distances is exactly the situation we have for GPS. We only know the starting time of the signal so we know what difference in distance is between the satellites , which forms parabolas instead of single points

[@Double-Negative]

in other words, it locates you in 4D spacetime

[@jorgechidote]

I was a bit unmotivated when I first watched the video and then bam! You hooked me, this is amazing, great video!! I wish you could go into detail into the acoustical engineering, i never was able to take that elective at my school.

[@anishnehete]

😃 😃

[@Guztav1337]

It's never too late

[@sethsims7414]

The fourth satellite is for solving for time. You could get position and altitude from three satellites if the receiver had a atomic clock also. But they have cheap crystal oscillators which aren't nearly as accurate. So the receiver is also solving for the current time. That's why cellphones have really accurate clocks, the cell towers have GPS in them and since they are not moving they can solve for the time very accurately by averaging over several GPS fixes using something like a Kalman filter. The cell phone gets it's time from the cellular network. I mean they could do the solving themselves if they wanted, but GPS processing is pretty power hungry so they usually don't.

[@anuartogaibekov2493]

Good catch

[@nawdawg4300]

I had always heard GPS satellites use atomic clocks?

[@reaganharder1480]

@@nawdawg4300 The satellites do have atomic clocks. But both the satellite and the receiver need to have super accurate time for it to work.

[@Papucho257]

THANK YOU! I literally got anxiety over his statement. As a Surveyor I use VRS a lot and its well known you only need 3 satellites for location

[@prapanthebachelorette6803]

Thanks!

[@vemo2474]

I always say to myself after a math lecture: is this gonna benefit me in real life or have any impact on us as humans. And I always find the answer in your channel.

[@forloop7713]

Except for exanple imaginary numbers. If that topic comes up I don't even listen

[@Alex-02]

Martin S Not yet, you never know what might happen in the future. For example, what if it’s necessary to calculate stuff dark matter

[@nagarmalsharma9992]

@@forloop7713 bro what are you even saying? Imaginary numbers pop up in most of the AC circuits, signals, frequencies and everything to make everything much much much simpler. Even in Euler's formula, i pops up, which you already may know is used in Fourier transform(one of the most important and practical applications of mathematics) And maths need not even have a practical use for that time, maths in itself is such a beautiful entity. If you hate imaginary number, you'll have a really tough time in advance physics and advance mathematics.

[@LCCD1143]

Martin S just think of imaginary numbers as a fancier way of saying the R^2 plane

[@Guztav1337]

School isn't really there to learn what you need for your job, or how to even get a job, not explaining money and loans. A bunch of other important stuff is not thaught. School is not there to aid that. School is simply there to make you a normal human being. That is: Able to read/write, basics of all subjects (math/physics/history/other langauges/...), and of course make friends... and many more included in basic citizen. One of the most important things is just keeping your brain active. Instead of speding your time runing around with your friends, or read reddit all day. They force you to actually use parts you normaly don't use. Keep the brain activated. *Being able to learn whatever is the most important skill you will ever learn in school.* It's so important to be able to learn when you get a job. School is not to make you able to do all work, it's enabling you to learn the future work you will do.

[@shoaibsh2872]

Your content are getting better and better in every video .

[@littlenarwhal3914]

Conic sections is one of those topics that isnt properly discussed in high school even though it's very accessible and has many beautiful properties... instead of spending time and time again on just parabolas, conic sections as a whole should be given more focus because they are just so incredibly important and fundamental to simple algebra.

[@david0aloha]

That's because conics is included in precalculus because of its relevance for orbital mechanics, which was relevant when many math curriculums were being designed in the 50s, and a lot of teachers have no connection to the "why" of conics.

[@JoystickStereo]

Awesome video; opening and closing it with the frog was pretty cool.

[@vintyprod]

This video is fantastic in so many ways thank you for making these

[@doodelay]

holy shit this is gold, I love how your channel is mostly APPLIED math and not just pure maths like numberphile. You really go out of your way to highlight applications, which stays true to your channel's original theme. Awesome job man, only suggestion at this point would be to keep your videos around this minute range and to try not go over 15 minutes, otherwise, for your channel specifically, it tends to ramble and seems sort of endless. But buddy, this is pure gold.

[@katphisH11]

Well, he is an engineer not a mathematician lol

[@AnindyaMahajan]

Remember learning about the ellipse reflection fact back in my conic sections class in school, but my teacher never gave a real-life application of it (nor did we, as students, thought of one at that moment) so no one paid much attention to it. After watching this video, it just makes so much more sense why such a special property would be so desirable in actual real-life situations. Very interesting and well-researched video. Keep it up!

[@moonchild.7645]

I feel extremely fortunate to have "free" and open access to such quality content. Please keep doing what you're doing

[@rrbar14]

This was so interesting. I did know about the ellipse sound/light wave phenomenon but never would have expected the parabola illusion or especially the GPS map application of hyperbolas! Very cool.

[@Calm_unbothered_af]

This video changed my whole perspective on mathematics.

[@taniamanik2012]

That ad is the only ad that genuinely interests me

[@withjoe1880]

I can assure you that most of what you learn in school can be meaningful if you use it correctly. While the applications might not be obvious at first, finding them out on your own can be a powerful and motivating experience. Creativity in mathematics is something that you can't teach. Showing applications before learning the fundamentals could help motivate students, but it might also give them a stronger sense of "I am not doing that, why do I need to learn this?" If the applications are presented, I believe that they should be presented after the fundamentals and/or with caution and assurances that the applications presented are not the only ones. Adding applications to a course tends to limit one's ideas of a topic, as many applications are very niche. That's why people tend to think that school doesn't teach them the skills to live in the "real world". I appreciate this video for pointing out the "interesting" applications of conic sections, but what they teach you in school is the formulas and how to analyze the actual shape of the functions. Sometimes showing the application first makes some things look easier, but the fundamentals are equally, if not more important if you are going to be performing calculations or analyses. My advice to anyone reading, put in the effort to learn everything you can because knowing more can't hurt you; it will be useful down the road (if you try to use it). "Ignorance may be bliss, but knowledge is power."

[@Tommy_007]

I agree with you that the fundmentals must be taught from the beginning. Most students don't have any patience or persistence, or they just ask: "Is this going to be on the exam?". They want to be entertained right from the start and lack the intellectual curiosity (or ability) needed to study math. I have tried many times to indicate the (beautiful) applications before teaching the fundamentals. Usually it is a waste of time because the students don't listen.

[@jaspaw.5473]

Could you please do a video on Computational mathematics?

[@williamsprout925]

Bump

[@tp7886]

As a Modal Accoustic Emission engineer I use accoustic and plate wave (seismic) theory every day in testing composite materials. I wish my math professors had highlighted more of the real world applications. Luckily there are videos like this one. Very well done!

[@raghavkamath]

This channel is so underrated!!... sharing your high quality videos right away!

[@zachstar]

Thank you!

[@raghavkamath]

MajorPrep U deserve it! Already subscribed

[@PaulJohnBalderston]

Been loving these new videos. I'd love to see the next major video be about engineering physics as there isn't much information out there. I know the curriculum is a little more variable but you're videos are such an amazing resource that it would be great to see this covered. Thanks!

[@TVbr7]

I guess that's the best video u've done so far, one of the best I've watched tbh, Great work

[@Cyanrobin123]

For a rectangular map, you would only need 2. Let me explain, if you put one at the top right corner and the bottom right corner. You can triangulate where where it is because you know what side the treasure is on because you said that it is on the map

[@DavidAndrewsPEC]

I loved this.The perfect introduction to conic sections in applied settings! Stary with a riddle. Basic principles ... then return to the riddle, using those principles to solve it! Ed-psych me gets emotional when I see videos like this.

[@swaniketchowdhury]

This parabolic reflection technique is also used in antennas, to be specific Parabolic Reflector Antennas. Where instead of focusing the light, we focus EM waves. Which gives the antennas a very strong directivity.

[@28mmforge22]

I always hated math in school, but loved physics..if they explained the practical uses like this I would have been way more into it

[@iZeroPvP]

One of the best videos I've seen explaining math. You are amazing!

[@sayanak9929]

Thanks to you, I still aspire to learn new topics in mathematics and physics! Great Job 👍🏼 Thank you for widening my spectrum of knowledge! Keep up the great work😃

[@mikey10006]

Do applications of matrices next!(linear algebra and stuff)

[@jumbobless280]

There’s none

[@jumbobless280]

JOSEPH ASWATH yes with computer generations

[@projectjt3149]

Jumbo Bless CLEARLY you haven’t heard of arrays or tensors

[@jumbobless280]

Engineer 314 actually I have

[@projectjt3149]

@@jumbobless280 well there you have it. Arrays are just matrices in CS

[@BangMaster96]

One of the best explanations and demonstrations of conic sections i have ever seen. Subscribed.

[@vandanamarchande3387]

Thank you very much 😊❤️

[@bendavis2234]

The visuals and animations you use in your videos are astounding, keep it up!

[@manishvyas7089]

Excellent my teacher never talks of origin and exploration of a science and math fields but only how to gain more marks

[@vignesh.n7744]

Cries in indian

[@vigneshv3846]

@@vignesh.n7744 yooooo!!!! We have the same names

[@ff-ti7nj]

they don't understand it either, besides, explainung a stuff over avd over again for different students, gets boring, eventually you give up on being a good teacher.

[@yousifkhalil9655]

"it doesn't matter what point you choose the third time, any point will do" me: chooses the exact midpoint between the two locations

[@the_flying_airplane5335]

Laughed a bit too much at this comment

[@mysticdragonex815]

hell yeah XD!!

[@bas3995]

Very excellent presentation sir,. All classes must have a presentation like this, which will provoke the eagerness within students and once learnt will never be forgotten. I will definitely recommend this to all of my friends and relatives

[@ezra2370]

yo i really got chills from this

[@DavidPysnik]

Thank you for putting "probably" in your title, as I do teach most of these uses to my students when I teach conic sections. Your animations are very good, though, and I plan to show your video next time I teach the topic. One good application you didn't mention, though, was that the back of car headlights are parabolic so that the light that would shine back toward the car, and otherwise be "wasted", is instead reflected out in parallel beams that help better light the road in front of you. The headlight bulb is placed at the focus point of that parabolic mirror to accomplish this.

[@seayellow5834]

The application of long distance navigation is so amazing!!!

[@itsshopboy]

You never cease to fascinate me.

[@shanebrady9606]

Hi Zach, I have been watching a tonne of your videos and love them. Lots of things you talk about is way over my head but I love listening about it from over here in Australia. Have been really inspired and have signed up to your sponsor brilliant to improve my knowledge. Thanks for the inspiration mate!

[@jel4133]

I really love your channel. this is exactly what i need 😭😍😍

[@prateekgupta5945]

One important detail that you missed is that the GPS satellites only emit the signals. The device which has the GPS antenna receives these signals and performs the actual calculations of the position and altitude.

[@schenzur]

This made me happy; I giggled at the end as everything connected at the end, the whole concept is so beautiful.

[@meganp6387]

Really enjoyed this video!! It’s not every day you see mathematical concepts being put to use, and you’re right, these concepts aren’t taught in school. I feel like they should be; it’d make math class much more fun.

[@abhinavchauhangujjar6456]

Your videos raised my interest in mathematics because now i know real world use of mathematics, previously i was thinking that mathematics is about learning formals and formals are random things like someone just said this equall that. Teachers is my college and school never made sense of mathematics they were just like these are steps of solve it and put that formula in that situation and another formula in some other situation. And i think that is why most students don't like maths because they can't relate it to their life, they think their are plenty of formula and step and they can't learn all of them, they don't know that technology they are using isn't possible without mathematics. Now i want to become a mathematics teacher who can make sense of mathematics. *Thankyou* Please More videos on real world use of mathematics likes series, diffential equation, integration, fourier series etc

[@TheMursk]

Go ahead. You will realise that those few hours a week any teacher has to work with isn't enough to cover all possible applications.

[@abhinavchauhangujjar6456]

@@TheMursk that may be true, but it implies that all maths teachers are the same

[@malachibre2198]

I appreciate this video a whole lot! I remember learning conic sections in pre-calculus and being so disinterested because we never got a good reason of their usefulness (other than of course circles), especially hypberolas.

[@puppergump4117]

That first Brilliant segway was so smooth. You could say it was... brilliant.

[@xlfc]

Just WOW... After this video I just have to subscribe.. great work of explaining practical usages of conic setcions ;-)

[@FrankieStankie17]

Question: What is the formula of the focus of a parabola? Great vid btw, I absolutely love this kind of content!

[@GIboy1990]

The treasure definitely isn't in Ft Irwin. I've been there. It's not a pleasant place

[@tasninnewaz6790]

I think that It's not an engineering channel. It's an applied math channel and It's says Whatever is beautiful is math. As a math student, I want videos on every math topic to be uploaded. Thank you Zach Star for introducing us to the practical world of mathematics. Love from the core of my heart. From Bangladesh.

[@fernando2011]

I'm so happy to be subscribed to you! You add so much value!

[@DylanMaddocks]

This video is a wonderful use of sponsorship, there were many times where I thought "oh wow he's using brilliant to teach" I've seen so many sponsorships by brilliant, but none made me want to join them like this video did by actually showing the content on their site, they need to encourage this type of promotion more. Btw I subbed and clicked the bell :)

[@manleunglam1263]

watching your videos just blows my mind

[@idrisShiningTimes]

I am mind blown! Thank you so much for sharing this vital information!!

[@nightrous3026]

I was actually interested in conics because of orbital mechanics. A flyby of a space craft past a body traces a hyperbola, and orbital/suborbital trajectories are traced by an ellipse. They can be circular as well. Edit: im still pretty interested in conics because theres actually alot to conics, like the focus of a parabola, and parabolic lenses/satelitedishes

[@priyanshumandhata4064]

Video has been excellently made, you are doing a great work, really influental, well done

[@kehindeadebisi7318]

Your work is amazing. You made me realise what they call madness in me is just one of the best traits.

[@RohitKumar-lw1mt]

I love this channel.....keep making such great videos .

[@ariannasuen4061]

Automatic subscribe. One of the best ways to learn is to make your brain establish relevancy, and that comes through wonderful videos of applied math like yours. Beautiful illustrations, concise explanations. Well done!

[@safihalim_1]

This was really very fascinating and very useful!

[@ankity951]

You are great teacher. Im also an electrical engineer , by getting inspired by you i also left my job and i choose teaching physics as my profession. You are very great teacher sir.

[@lilshake139]

Great Video......makes conic sections really interesting

[@aryansingh7209]

I was amazed when you showed the reason for the illusion at the end. Just giving the perfect ending to the video.

[@ronjon7942]

Laf, same. I let out a good ‘well, huh! How ‘bout that!’

[@tanmoydutta5846]

And that's the hyperbola and ellipse I was so scared of in high school

[@mo-issa]

The demonstration and the use of the frog illusion then coming back to it is super creative and neat well done

[@daviddafitt]

You are doing an amazing job at making me fall in love with math even more than I already am

[@noobie8488]

you have shown me how it is fun to study conic section . So a very much thankyou

[@fakebobbyhill296]

Yup this is exactly the one thing my teacher never mentioned about partabola, hyperbole, and elipsauce. I remember everything else about those things like it was yesterday when we learned that in biology.

[@imankhalili7629]

You are AMAZING dude ! Keep up the good work!

[@philamras3732]

Just got to say this is one of the best videos on maths I have ever seen. Thank you so much for making these videos.

[@profjoaoluizpacheco2471]

I just love how you bring back to earth the abstracts concepts

[@VanshSharma-vp5tn]

Wowwww.....Like who knew to see hyperbola that way Glad I watched it Thank you so much Zach Star

[@steelshade]

Math tutor here. Flashlights and car headlights also have parabolic mirrors behind them to direct more light forward, with the bulb at the focus. If you have a lamp with a circular opening in the lampshade above covering it, the shadow cast on the wall behind the lamp will be a hyperbola.

[@rook839]

amazing job. would have never thought that they had such crucial and ubiquitous applications.

[@shay3355]

I'm so proud that i subscribed to this channel way earlier... Also , I am from India and our class just started conic sections...And I'm sure your video is going to help me understand them a lot... thnx

[@z50king29]

Thanks, Zach. I'm going to play this for my Math 3 kids during our conics unit. Maybe twice. Once at the beginning and once at the end. Thanks

[@shashankkatiyar31]

Came to learn A, learnt A to Z. Great, thanks

[@alirizaburki123]

This guy feels me the essence of mathematics.

[@mahdinoroozi1614]

all your works are amazing, god bless you

[@soumyajitroy4385]

this is the first video i saw on this channel and it is just amazingly explained!! loved it ❤

[@GhostPants0.2]

Great channel i love your videos all of them are straight to the point and finely explained

[@nivesh3555]

NCERT class 11th mathematics book has defined conic sections in the same way although my teacher never told me I was familiar with these definitions. Thank you for this nice video.

[@gajrajsingh51]

This is very good , keep it up :) . I love conic sections so this made me very happy. :)

[@ankitaaarya]

Me too

[@mounirbaroudi5890]

Elegant and Illuminating I love this

[@antonaparin]

Ur my favorite channel! Thanks!

[@Alhamdullilah101]

This rlly is the most intelligent way of developing a beginners interest into this fascinating subject. I'm beginning to love maths now😊

[@jinkyninasogo-an7647]

thank you so much for a very helpful topic on applications of conic. Hope you have more videos like this..

[@phenomenalphysics3548]

I LOVE YOUR CHANNEL! it's so helpful

[@abhigyanpandeyavinashi0390]

You give me a new eye to see the world, relate the world

[@masterbunny1307]

Wow this is really beautiful thanks Edit: I just finished the video and wow you really blew my mind with that hologram stuff

[@oussamanhairech5178]

yeah this is what scientists feel when they discover something

[@bigmackdombles6348]

Excellent video dude. Keep going!

[@shubham-sc3jn]

In the map problem, we can do it in 2 guesses. We can guess the corner point of the map at first. This would lead to a circular arc of some radius as the possible locations. This circular arc would intersect the boundaries of the map at two points. We can then pick one of the two intersection points as our second guess. This would then lead to another circular arc which would intersect the previous arc at precisely one point (the treasure location)

[@wazowski5296]

The most useful 13min of my day.

[@abhigyanpandeyavinashi0390]

Wonderful. I just mesmerized

[@acherongoon]

Parabola's, nearly every description misses a key for radio transmissions, yes they come to a focus, but also the distance travelled from a very distant point is the same because it also has a directix, a straight line perpendicular to the direction of the line of symmetry, so a signal running parallel also CONSTRUCTIVELY INTERFERES at the focus to ensure that the signal is boosted.

[@juliasmith1182]

Well prepared. Very nicely done 👍

[@broken_radar]

incredibly awesome and clearly explained! I love this video!

[@pravatyadav3623]

Finally i understand conic section application in real world.. till now i used to mug up the formula of conic section and move along... so thanks