What your teachers (probably) never told you about the parabola, hyperbola, and ellipse
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- เผยแพร่เมื่อ 24 มิ.ย. 2024
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This video goes over the real world applications of parabolas, hyperbolas, ellipses, and circles.
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I wish our Mathematics teacher explained the use of Parabola, Hyperbola, Conics and other figures like this. I wouldn't have had any doubts.
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.
@@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)
I wish we had more teachers like @MajorPrep, I never knew that math was this useful until I met him
Yes our teachers are lodu
@@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.
If maths was taught this way in my school, everyone would have more interest to learn it
We only had "how to calculate", not math
every student will find math easy and pass with high grades if they were taught like these
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.
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.
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.
This channel deserves way more recognition and subscribers , excellently done
Agree, it's great !
yea...
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
@@SrmthfgRockLee wow that sounds great ; are you a student?
@@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) .
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.
Cool TIL. Thank you for your comment!
GPS also use the hyperbolar navigation... that way it can calculate position then calculate back to time.
Nice explanation, thank you.
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
in other words, it locates you in 4D spacetime
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.
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.
😃 😃
It's never too late
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.
Good catch
I had always heard GPS satellites use atomic clocks?
@@nawdawg4300 The satellites do have atomic clocks. But both the satellite and the receiver need to have super accurate time for it to work.
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
Thanks!
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.
Except for exanple imaginary numbers. If that topic comes up I don't even listen
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
@@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.
Martin S just think of imaginary numbers as a fancier way of saying the R^2 plane
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.
Your content are getting better and better in every video .
Awesome video; opening and closing it with the frog was pretty cool.
That ad is the only ad that genuinely interests me
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.
Well, he is an engineer not a mathematician lol
This video is fantastic in so many ways thank you for making these
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!
Could you please do a video on Computational mathematics?
Bump
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!
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.
Do applications of matrices next!(linear algebra and stuff)
There’s none
JOSEPH ASWATH yes with computer generations
Jumbo Bless CLEARLY you haven’t heard of arrays or tensors
Engineer 314 actually I have
@@jumbobless280 well there you have it. Arrays are just matrices in CS
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."
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.
I feel extremely fortunate to have "free" and open access to such quality content. Please keep doing what you're doing
"it doesn't matter what point you choose the third time, any point will do"
me: chooses the exact midpoint between the two locations
Laughed a bit too much at this comment
hell yeah XD!!
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
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!
This made me happy; I giggled at the end as everything connected at the end, the whole concept is so beautiful.
One of the best videos I've seen explaining math. You are amazing!
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😃
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.
I guess that's the best video u've done so far, one of the best I've watched tbh, Great work
This channel is so underrated!!... sharing your high quality videos right away!
Thank you!
MajorPrep U deserve it! Already subscribed
I'm so happy to be subscribed to you! You add so much value!
I just love how you bring back to earth the abstracts concepts
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!
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.
You never cease to fascinate me.
Video has been excellently made, you are doing a great work, really influental, well done
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.
yo i really got chills from this
Thank you! Nice explanations of the intuition behind conic sections.
Your work is amazing. You made me realise what they call madness in me is just one of the best traits.
Excellent my teacher never talks of origin and exploration of a science and math fields but only how to gain more marks
Cries in indian
@@vignesh.n7744 yooooo!!!! We have the same names
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.
And that's the hyperbola and ellipse I was so scared of in high school
this is the first video i saw on this channel and it is just amazingly explained!! loved it ❤
The application of long distance navigation is so amazing!!!
watching your videos just blows my mind
I really love your channel. this is exactly what i need 😭😍😍
One of the best explanations and demonstrations of conic sections i have ever seen.
Subscribed.
The visuals and animations you use in your videos are astounding, keep it up!
Just WOW... After this video I just have to subscribe.. great work of explaining practical usages of conic setcions ;-)
That first Brilliant segway was so smooth. You could say it was... brilliant.
Awesome video with a great explanation! I'm happy I found this channel.
I LOVE YOUR CHANNEL!
it's so helpful
You are doing an amazing job at making me fall in love with math even more than I already am
I am mind blown! Thank you so much for sharing this vital information!!
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.
I love this channel.....keep making such great videos .
Amazing video, deserves more recognition, clear and simple!
Wonderful. I just mesmerized
Ur my favorite channel! Thanks!
This is so smart Zack, ty
Thanks alot this was very educational I never knew this 🙏🏾🙏🏾🙏🏾
Fell in love with the content mate
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.
Well prepared. Very nicely done 👍
This was really very fascinating and very useful!
Amazing video! Brilliant way of explanation, thank you very much for making it.
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.
I was amazed when you showed the reason for the illusion at the end. Just giving the perfect ending to the video.
Laf, same. I let out a good ‘well, huh! How ‘bout that!’
Wowwww.....Like who knew to see hyperbola that way
Glad I watched it
Thank you so much Zach Star
You are AMAZING dude !
Keep up the good work!
all your works are amazing, god bless you
Elegant and Illuminating I love this
The demonstration and the use of the frog illusion then coming back to it is super creative and neat well done
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
Excellent video dude. Keep going!
Great Video......makes conic sections really interesting
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 :)
One of the best video I watched on real life applications of conic sections. Excellent Channel for amazing real life applications of theoretical concepts.👍👍👍
You give me a new eye to see the world, relate the world
This was such a useful video...thanks 😊🙏🏻
U really blew my mind.
Thank you!
Great channel i love your videos all of them are straight to the point and finely explained
Lovely smooth lesson . Thnx
incredibly awesome and clearly explained! I love this video!
This video changed my whole perspective on mathematics.
That was a really good explanation. You, sir are amazing!
The treasure definitely isn't in Ft Irwin. I've been there. It's not a pleasant place
That's some whole new level of intuition.
Thank you , great video !
Thank you very much 😊❤️
thank you so much for a very helpful topic on applications of conic. Hope you have more videos like this..
Amazing video!! Very detalied thank you for taking your time to share!!!!
Excellent work!
Awesome videos !!! Thank you.
Wow! Amazing! Thank you!
You are bringing revolution in the field of our so called education....need more thoughts and people like you in this world 💙
Wow this is really beautiful thanks
Edit: I just finished the video and wow you really blew my mind with that hologram stuff
yeah this is what scientists feel when they discover something
Thank you for this.
This video is amazing! These was just formulas for me in school time. Now I know they are much more than that,I know what they are... thanks
outstanding video. I was studying analytic geometry and this kind of pulls it all together.
This was a very good explanation of the concepts.