Beautiful Trigonometry - Numberphile
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4 жыл бұрынFeaturing Ben Sparks.
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Catch a more in-depth interview with Ben on our Numberphile Podcast: • The Happy Twin (with B...
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Catch Ben on the latest Numberphile Podcast: • The Happy Twin (with B...
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@numberphile 4 жыл бұрын
Catch a more in-depth interview with Ben on our Numberphile Podcast: kzfaq.info/get/bejne/Y9p3ocxqtMiuh58.html
@JPEight 3 жыл бұрын
Numberphile Late to the party I know, but the final set of animations is how AC motors work, as well as field oriented control for brushless DC motors. With three intersecting lines it shows the relationship of three phase mains power. Most motors only use 3 phases, but multiphase motors do exist. Would have been cool to explore in further detail - maybe a future video?
@leovargas9480 2 жыл бұрын
captions in spanish please!
@spacemanspiff2137 4 жыл бұрын
This video needs to be shown in every high school trig class
@numberphile 4 жыл бұрын
Yes please. :)
4 жыл бұрын
I can still remember memorizing sin and cos values when I was in high school almost 30 years ago. It would have been so much easier to have been taught circle functions and tau. Why memorize when it's so easy to derive. So much time wasted 😢. At least younger learners will have an easier time. That said, I thought I would show these things to my kids and they will see the awesomeness, but I've had bad experiences so far with responses of "that's not what the teacher expects", and it makes me very sad 😞.
@VirtuelleWeltenMitKhan 4 жыл бұрын
@ "that's not what the teacher expects" that is the dark side about teaching
@TheEnderLeader1 4 жыл бұрын
@ it's a sad time we live in where surprising the "teacher" is seen as a bad thing. I never took Lockhart seriously until I tried to help my incredibly creative little brother with his homework, and saw all his mathematical imagination completely stamped out of him by modern maths education.
@chiiing8288 4 жыл бұрын
i wish my teacher showed me this. before this video i think of trigonometry as a formula that just works. Now i understand it a bit more.
@bgezal 4 жыл бұрын
"and I don't want to give too much away" Brady: So I'll just spoil it in the thumbnail and intro then.
@numberphile 4 жыл бұрын
Ben doesn't have access to the graphs which show KZfaq viewer attention span - Brady does!
@HasekuraIsuna 4 жыл бұрын
@@numberphile Oh, I'm sad to hear that. I thought Numberphile's views were 90% subscriber users who watches everything. : (
@bgezal 4 жыл бұрын
@@numberphile the Algorithm...
@badmanjones179 4 жыл бұрын
@@HasekuraIsuna were drawing in new fans, get them all addicted to math, then they become full length viewers
@ivanjones6957 4 жыл бұрын
to 10 anime betrayals
@wolfelkan8183 4 жыл бұрын
"I think [trigonometry] is the worst-named topic in mathematics" Imaginary numbers would like a word...
@francisluglio6611 4 жыл бұрын
Imaginary numbers don't have to be a topic. They just have to be numbers. It's up to the speaker to set it as a topic.
@danaclass 4 жыл бұрын
Aren't all numbers imaginary?!
@janschaffer5042 4 жыл бұрын
@@danaclass Aren't all imaginations numerical? :O xD
@joaoc6920 4 жыл бұрын
@@danaclass I mean vision is technically, an elaborate elusion. So sure why not.
@flexico64 4 жыл бұрын
My thoughts EXACTLY
@celewign 4 жыл бұрын
Something about the patient, thoughtful explanation combined with insightful interview questions combined with excellent, simple animations make this the best explanation of trig I’ve ever seen.
@numberphile 4 жыл бұрын
Wow, thanks.
@ivanjones6957 4 жыл бұрын
agreed
@arcanics1971 4 жыл бұрын
I couldn't agree more! 30 years after I leave school and suddenly it all makes sense!
@janderkran 4 жыл бұрын
So true!
@ThatOpalGuy 2 жыл бұрын
It's still beyond the understanding of a certain segment of our society though, and that's sad.
@JarHead54321 4 жыл бұрын
Those animations are mesmerizing
@phatkin 4 жыл бұрын
bruh when did I leave this comment
@warioseggs 4 жыл бұрын
@Multorum Unum fair
@alexcrespo3252 4 жыл бұрын
You could make one yourself, just go on desmos and the description for a point revolving around the surface of a circle is (sin a, cos a) With that info you can add them up in specific ways and have lots of fun. I hope you try it our
@davecrupel2817 4 жыл бұрын
@@phatkin 3 days ago
@puzzLEGO 4 жыл бұрын
I agree
@jgg75 4 жыл бұрын
I learned more trigonometry in this 12-minute video than I have in 40 years...
@arcanics1971 4 жыл бұрын
This just made some of the bits of trig I just didn't get fall into place. Ben Sparks needs to rewrite how schools teach trig! That's was brilliantly explained!
@kanishkachakraborty 4 жыл бұрын
Brought to you, by... Brilliant.
@lillie3029 4 жыл бұрын
arcanics1971 uhhh my last name is also sparks lol
@lillie3029 4 жыл бұрын
arcanics1971 and im also a yter
@amritanshurana4000 3 жыл бұрын
That's Class 11 physics its taught in schools
@dorothymiles7097 3 жыл бұрын
3:35 Complex/Imaginery numbers am I a joke to you?
@grizzlygamer8891 4 жыл бұрын
This annoys me quite a lot. I'm 36. I got great grades for Chemistry, Physics and Biology at GCSE but did abysmally in my maths exam and the best grade I ever achieved is a D. The exams at the time were full of trigonometry and I have NEVER been able to get my head around that one thing all my life. Seeing it applied to circles, rather than triangles has literally allowed me to understand the subject in the length of this video. I wish you were my GCSE maths teacher 😂
@stanstanstan 4 жыл бұрын
When it comes to school level mathematics, your success is mostly based on repetition of work, not understanding. But yes, this is a brilliant visualization of the trigonometric functions.
@evilotto9200 4 жыл бұрын
@@bregottmannen2706 "SohCahToa"- not all teachers teach some just need you to be able to pass a standardized test at semester's end
@scottriley5141 4 жыл бұрын
I am a maths teacher and hate that the curriculum focuses on triangles simply because that's what they are applied to in the syllabus. Circles are brought in when learning about the graphs but it's constantly compared to the triangles (because they've already studied them). It would be so much better (and elegant) the other way round but everyone learns about the triangles at GCSE and only students sitting the higher papers learn about the graphs.
@codyhannahmary83 4 жыл бұрын
I also wish my maths teacher had described things like this!! I failed Maths and stopped it after 5th form in NZ. But this is beautiful!!
@louisvictor3473 4 жыл бұрын
@@scottriley5141 Porque no los dos? The triangles and the circles in this case are inherently connected when you're using the cartesian plane or space (you can always draw the triangles for any point in a circle, you can always draw the full circle from a right triangle without further information, which is why they're equivalent). The problem is that the syllabus and education in general don't exist to teach people to understand what they're doing, just to be able to memorize how the tool operates. But when people understand the relationships, they understand where things come from and the line of reasoning that leads to it, you see the triangles on the circles, you see the circles around the triangles, you can see all the other forms you can derive from the same information because you understand. That is why no curriculum anywhere puts much attention in showing things like this, the beauty of pure mathematics because "it is not useful [to make a baseline employee, the curricula current purpose, sadly]".
@bharathir330 4 жыл бұрын
"It was a huge relief to me too that the word tangent wasn't a coincidence with the other definition of tangent, which touches the circle" 😇
@PaveDearce 4 жыл бұрын
4:50 In fact the name cosine comes from the fact that the **co**sine is the sine of the **co**mplement angle. Two angles are complementary when their sum is 90 degrees. So 30 degrees and 60 degrees are complementary angles. The cosine of 30 degrees is the sine of its complement angle. That is, the cosine of 30 degrees is the sine of 60 degrees.
@ivanjones6957 4 жыл бұрын
interesting
@angelmendez-rivera351 4 жыл бұрын
Yes. Hence the origin of the cofunction identities sin(π/2 - x) = cos(x), sec(π/2 - x) = csc(x), and tan(π/2 - x) = cot(x). π/2 = 90°. This also motivates the conjugate identities sin(x)·sec(x) = tan(x) and cos(x)·csc(x) = cot(x).
@orichalchromee88 3 жыл бұрын
Ah yes big brain you have
@keonscorner516 Жыл бұрын
_82_
@925NC 4 жыл бұрын
One of the best Numberphile videos I've ever seen. Coming from a middle/high school math teacher. Thank you! Keep up the great work!
@boRegah 4 жыл бұрын
My overall happiness with maths in school would have increased dramatically if this channel existed (and was in German) back then.
@user-fr2mw3sj2x 4 жыл бұрын
Deutschland oder österreich?
@the_venomous_viper1234 4 жыл бұрын
That 3D graph with the spiral changed my view of Trigonometry - truly beautiful. Love the work as always :)
@numberphile 4 жыл бұрын
Thanks - appreciate it.
@FYTClips. 4 жыл бұрын
Ikr, my jaw literally dropped to the floor when the changed the perspective
@elimelvin2988 4 жыл бұрын
I can finally see the dual particle/wave nature of light in this!
@Nyth63 4 жыл бұрын
Helix
@nielsen425 4 жыл бұрын
Numberphile If you replace the y-axis with the imaginary you’ll have Euler’s Identity. I know you know that. It would have been a great comment to make during the video. I also believe mentioning the deep connection to light propagation by allowing the x-axis to be a voltage field and the y-axis a magnetic field yields the way light works propagates would have been relevant. Oh, and when you showed the three axis’s with three dots rotating you had three phase power which is how the power grids around the world distribute electricity. Again, you showed the answer without mentioning the topic. Totally fun. Maybe I need to learn Visual Basic better to be able to reproduce your animation here. How many of the trig identities make more sense on this graph? I’m thinking they may all be here, but several of them seem to just fall out.
@sbmathsyt5306 4 жыл бұрын
wow! This is a great example of the beauty in maths. Great teaching with a great explanation of the animation. Loved it.
@numberphile 4 жыл бұрын
Thank you for watching it.
@seeseefok7659 4 жыл бұрын
@@numberphile I agree :D this is beautiful and well made, I love this channel!
@DaGizmoGuy 4 жыл бұрын
4:57 I *wish* I had seen this when I was still at school. Why was trigonometry never explained to me like this? It suddenly makes total sense now!
@jadenmolloy4830 4 жыл бұрын
Because at school you don't need to know it and it'll probably just confuse kids. The sad thing about school is you only learn the basic application of things, not the actual mechanics and processes behind them
@soupisfornoobs4081 3 жыл бұрын
@@jadenmolloy4830 yeah, it's *general* education, higher education is for the real learning and school's just the basics
@BrandonDoran00 4 жыл бұрын
I love how 10 minutes of video can give me a real understanding of what sin, cos, and tan *are* when none of my high school teaches ever thought to try. No wonder I hated trig...
@Jinsun202 Жыл бұрын
Yeah, because your teacher never had to spend any time/focus on behaviour management, admin, catering to different levels of understanding of students, time reatraints, did they? And you always paid attention 100% of the time, didn't you? Funny how commenters almost always take the opportunity to blame teachers, thus abdicating any responsibility themselves.
@BrandonDoran00 Жыл бұрын
@@Jinsun202 What is blud waffling about?
@arifahmad-7261 4 жыл бұрын
*the definition i like most is: oscillation is the projection of uniform circular motion on the diameter of circle*
@hoola_amigos 4 жыл бұрын
the simplicity is amazing!
@robinkovacic7961 4 жыл бұрын
@@hoola_amigos I agree, just realized what trigonometry is really about
@deactivated.1254 4 жыл бұрын
AWAZ2 I dont if what you say is true- for all I know is that you're saying big smart-sounding words
@mr.klunee4103 4 жыл бұрын
A lot of math concepts come to ife and thus make more since in physics. I.e. calculus made much more sense to me when I saw how it applied to kinematics
@arifahmad-7261 4 жыл бұрын
@@mr.klunee4103 yes✔
@jonopriestley9461 4 жыл бұрын
Ben: 'Nothing is moving in a circle' Me: 'Wait, so how does the earth spin? Ben: 'Each one of these dots is moving in a straight line.' Me: 'Oh, right. Context.'
@LeventK 4 жыл бұрын
😂♻️
@grizzlygamer8891 4 жыл бұрын
Careful there... We don't need to be spending the next year explaining to flat earthers how this is in fact NOT evidence that the world isn't a globe 😂
@GregorShapiro 4 жыл бұрын
The Earth is flat so there is no reason for anything other than straight lines!
@wavywomby263 4 жыл бұрын
The is only works if the radius of the moving "circle" is equal to the radius of its orbit so no
@CandidDate 4 жыл бұрын
I see a new understanding of General Relativity in the making. There is nothing that doesn't move in a straight line, relatively.
@greensponge6538 4 жыл бұрын
These animations are so spectacularly beautiful, all the jigsaw pieces just flitted right together 😭! Pretty exceptional stuff, wish school taught us this way. Never stop these videos coming, your work is amazing!!
@xaytana 4 жыл бұрын
6:37 "What's a tangent?" Perfect answer would've been, "What you're doing right now."
@randomjin9392 4 жыл бұрын
A straight line is just a circle with an infinite radius
@F1fan4eva 4 жыл бұрын
Random Jin a circle, in turn, is just an ellipse with 0 eccentricity
@harry_page 4 жыл бұрын
@@F1fan4eva An ellipse, in turn, is just a conic section with eccentricity between 0 and 1
@alaanasr7505 4 жыл бұрын
@@harry_page a conic section, in turn, is just a curve obtained as the intersection of the surface of a cone with a plane
@Killerthealmighty 4 жыл бұрын
What if a straight line is just a conic section with INFINITE ECCENTRICITY
@alaanasr7505 4 жыл бұрын
@@Killerthealmighty It is true. We just loop back to where we started. both eccentricity 0 and infinity gives us a line
@aldagle 3 жыл бұрын
0:13 to see straight lines concentrate on one ball moving up and down and then the other and look in the centre To see the circle concentrate on the invisible line between the circles
@bojandude 4 жыл бұрын
I've watched Numberphile for years, and although I've always enjoyed and learned something from the videos, it's never impacted me quite like this. The simple look behind what sine and cosine really are was a wonderful experience. Thank you.
@ThisNameWasTaken100 4 жыл бұрын
After twelve years of school, four years of university and eight as an engineer, I’ve not thought of the ‘trig’ functions like that. This is why I subscribed to Numberphile!
@sphakamisozondi 4 жыл бұрын
OMG!!! This video just blew my mind. The trig functions make sense in relation to a circle. Dude you just made me unlearn what have learned about these functions for real.
@ThatsGobbles 4 жыл бұрын
It’s amazing the amount of work and love that goes into these videos, these animations are beautiful!
@Yotanido 4 жыл бұрын
I actually never learnt trig in school. The first time I ever used trig functions was when I wanted to draw a circle on a screen. X axis is the cosine of t, Y axis is the sine if t. Now just take equidistant values of t between 0 and tau and you're golden. More values for higher resolution.
@numberphile 4 жыл бұрын
Some left over 'Pieces of Pi' are available if you'd like to support Numberphile (these are from the collection that was sent to Patreon supporters earlier this year): posh-as-cushions.myshopify.com/products/a-piece-of-pi Piece #1 is on ebay: www.ebay.co.uk/itm/203022020704
@informationparadox387 4 жыл бұрын
The animations were awesome!😍👌
@ivanjones6957 4 жыл бұрын
I understand 'trigonometry' better than ever before!
@Manoj_b 4 жыл бұрын
What is the relation between (ΠXi^xi(i,1,n)) to (ΠXi(i,1,n))^y ,where, n is Z+ ,and y =f(x).?
@TheDannyHamilton 4 жыл бұрын
What’s the missing sin()-like function called?? It’s clear when you overlay sin() and cos() that they are out of phase, but there’s space left over for one more phase to perfectly fit in between?!?!
@ankonpaul8991 4 жыл бұрын
May I ask what program Ben is using to create these animations
@atomiccompiler9495 4 жыл бұрын
In case anybody wants to read more about this, the yellow circle and the unit circle make what mathematicians call a “Tusi couple”, and in fact, it does have some applications, especially in astronomy.
@TheeDixieFlatline 2 жыл бұрын
Just what I signed in to say. I first ran across it in a book on Arabic astronomy.
@budzikt 4 жыл бұрын
Guys, your channel is gold. I'm repeating myself over and over again.
@shrutsilakari9711 4 жыл бұрын
I would love to see a follow up video on Trigonometry. It is one of my favourite fields of Mathematics at school. Maybe some beautiful proofs for the identities among other things would be wonderful. Mr. Ben Sparks is really talented and passionate and I love every Numberphile video which features him!
@brankooffice 4 жыл бұрын
This should be the first thing shown in school when trigonometry is mentioned.
@pendragon7600 4 жыл бұрын
No, it shouldn't.
@ivanjones6957 4 жыл бұрын
@@pendragon7600 yes, it should
@SSM24_ 4 жыл бұрын
Maybe not this _exact_ video, since it definitely assumes some prior understanding of trigonometry, but the visualizations definitely.
@ivanjones6957 4 жыл бұрын
@@SSM24_ true yes. but this animation is easy to grasp for visual learners with minimal equations to have to learn.
@B3Band 4 жыл бұрын
It's a great way to pretend you understand trig without actually learning anything. This is much better appreciated AFTER you actually learn the concept and use it properly.
@haydenperkes8974 4 жыл бұрын
This taught me more than 3 years of highschool. I want more. I think you healed my soul with those mathematical animations. I actually hate how much I liked that. This should be a series. Just mathematical animations and the proofs hidden within.
@enderwiggins8248 4 жыл бұрын
I loved hearing Ben on the numberphile podcast, he’s encouraged me to try for a PGCE after undergrad
@MysterX79 4 жыл бұрын
Every bit in this episode I knew already, but it was a wonderfull version to visualize it to my kids, when talking about it. Thanks for that.
@jochemdejong3406 4 жыл бұрын
That 3D animation really is beautiful
@rudranil-c 4 жыл бұрын
Of all the Numberphile's brilliant mathematician talks, I love Ben Sparks the most. Every single episode is fascinating.
@elizadawley6351 Жыл бұрын
Another comment to say the same thing as the rest: this video was so incredibly helpful and inspiring. Visualizing sin and cosine waves on 3 planes cleared up the entire concept of trigonometry very nicely. I wish this type of video could be shown more often in public schools. The in-depth (and fun) explanations that come from this channel could do so much to keep students interested and confident in mathematics. Thank you for the content, I will definitely be watching this video again.
@Raptiel 4 жыл бұрын
I seriously love your guys for making these videos. I literally watched all videos on this channel multiple times. My favourite ones are those about really large numbers, Surreal numbers and my most favourite topic of all INFINITY ❤❤❤. I cant thank you guys enough ❤
@therealcaldini 4 жыл бұрын
That IS beautiful. Simple yet brilliant video.
@bobjones5869 4 жыл бұрын
this guy is an amazing teacher please have more videos with him!!
@gabriellord9214 4 жыл бұрын
This makes so much more sense now!! Intuitive clarity, if that's a thing!! Excellent!
@WojtekCzaderna 4 жыл бұрын
I believe that this was the most useful videos I've seen. I literally got the shivers. I mean each Numberophile video is great but this one so nicely explains the things that we learn in school not even touching the point of the origin of SIN COS functions. Math is so beautiful if learned in this way!
@vikraal6974 4 жыл бұрын
The fact that ramanujan could see all possible combinations of these functions in his head still boggles me
@ZachGatesHere 4 жыл бұрын
I'm more than a little confident a lot of the Ramanujan stories are legends. This idea that he could just "see" everything is kinda silly. That he just knew strings of trivia for every single number, etc.
@MrHrman12 4 жыл бұрын
@@ZachGatesHere there are some really interesting video's on youtube about savant's who 'see' numbers and can do crazy sums in their head, maybe that is related, you should check it out if you haven't already.
@vikraal6974 4 жыл бұрын
@@ZachGatesHere when it comes to trigonometry he was a beast. Before he read Carr's book he had mastered Looney's trigonometry. He didn't steady Euclid's elements so I can't be sure of his mastery of geometry and in general but there is no doubt about his understanding of circular functions. Just look at his approximation of pi.
@jamirimaj6880 3 жыл бұрын
@@ZachGatesHere not "see", but "imagine". although Ram sadly is not that great at explaining the theories behind it. He's really just your more-than-average smart kid in class who understands stuff and can solve puzzles, but has a hard time in explaining the process behind. Don't get me wrong, Ramanujan is still a big part of why modern life in general exists, that's his legacy.
@koolguy728 4 жыл бұрын
"And nothing here is moving in a circle" ... I mean except for the invisible point that you're using to trace out the coordinates of the dots :P
@peterclancy3653 4 жыл бұрын
I saw a connecting rod on a piston driving a flywheel moving with the motion of one of these dots. A very elegant piece of engineering and now I know how the motion is constructed. Thank you. I wish my teaches at school had described the trig functions as you have.
@vijaysinghpatel-uy7je Жыл бұрын
Beautiful, both the mathematics and Ben's passion teaching it.
@FreshBeatles 4 жыл бұрын
this cleared up so much missing understanding
@idkusername2981 4 жыл бұрын
10:08 this tells me a lot of why my math teachers tend to make really hard tests...
@alexismandelias 4 жыл бұрын
They make hard tests so you have a reason to study. I'd bet you would open the book once if you didn't have to study for a test
@hybmnzz2658 3 жыл бұрын
You are the same type of person to get a bad grade in optimization problems in calculus then say "we did not learn this! You gotta spoon feed me!". And then you realize its useful, applied math.
@jeremyredd4232 4 жыл бұрын
Definitely recommending this video for my calculus based physics students. This is perfect for a review of vectors, this lends itself well to simple harmonic motion, great for polar coordinates, and eventually complex numbers. So dope!
@juliannicholls 4 жыл бұрын
I knew all of these things, and have seen a lot of the visualisations before, but seeing it all in one place and having it all synthesised together is awesome.
@geofftaylor8913 4 жыл бұрын
What a great way to explain it. If that had been presented to me in primary school I would have been light years ahead.
@adrianthegreat8190 4 жыл бұрын
“Oh yeah it’s useful, but I would have done it anyway” is the best quote to describe a mathematician
@slowburntm3584 4 жыл бұрын
Thank you for all you do! ❤️ Numberphile
@numberphile 4 жыл бұрын
You’re welcome.
@sahilislam6895 4 жыл бұрын
I haven' t seen such beautiful representation of these before. My life would have been incomplete without this. Thank you 😊
@1Osama9 4 жыл бұрын
““A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.” A mathematician apology Hardy
@srivatsajoshi4028 4 жыл бұрын
thats a beautiful quote
@diegonals 4 жыл бұрын
"Nothing is moving in a circle" *Sad carousel noises*
@ivanjones6957 4 жыл бұрын
nice
@0LoneTech 4 жыл бұрын
But it is moving in a circular reference frame cycloid, in the corner case where it became a straight line (rolling diameter equals enclosing radius). Another corner case is where it becomes immobile, because the rolling and enclosing circles are equal. All the other cases are actually useful in designing e.g. cycloidal or planetary gears!
@diegonals 4 жыл бұрын
@@0LoneTech Haha circles go woosh
@ivanjones6957 4 жыл бұрын
@@diegonals mega nice
@DqwertyC 4 жыл бұрын
But if you put a couple carousels on a larger carousel, then timed the speeds right, could you get all the seats to just be moving in straight lines?
@danielstephenson7558 4 жыл бұрын
Ben is one of my favorite Numberphilers. He's managed to explain 3 things I could not get my head around until now: the Mandelbrot set, the basics of trigonometry and The Golden Ratio to me using visual demonstration. I loves it. I had a good maths teacher at school, don't get me wrong, (Thanks Mr. Noble) but I'm still quite jealous of the tools kids have now to better understand these concepts.
@pkern161 3 жыл бұрын
I am taking finals this week at University and taking trigonometry. I have always been ok with math but this in depth trigonometry was tough. This video would have helped me so much this semester. It was so nice to see it visually. Wish I found you 12 weeks ago. Liked and subscribed now.
@IllidanS4 4 жыл бұрын
Considering the name "trigonometry", other languages use the term "goniometry" more commonly, moving from triangles to just angles.
@azureabyss538 4 жыл бұрын
Trigonometry originated at the Indian subcontinent receiving important influences from the Middle East and it picked it up various implants in its name meanwhile.
@silkwesir1444 4 жыл бұрын
@@azureabyss538 it may very well have originated on the Indian subcontinent, but the _name_ "Trigonometry" sure didn't. That word is as Greek as you can get.
@azureabyss538 4 жыл бұрын
@@silkwesir1444 I didn't mention that the name originated there, did I?
@ivanjones6957 4 жыл бұрын
one of my fave teachers!
@psyphy 4 жыл бұрын
Great stuff. Those visualizations are awesome. ❤️
@farhantajwarahmed3340 4 жыл бұрын
Just gave a new aspect to trigonometry. Thank @Numberphile ... LOVED IT!
@hichaeretaqua 4 жыл бұрын
1 year of geometry class in 10 minutes. Awesome
@naswinger 4 жыл бұрын
i think this is the most educational video i've ever seen. i never learned trigonometry in high school (not sure if it was skipped or not even in the syllabus) and i still don't know how i passed my calculus exams for computer science.
@402077662 4 жыл бұрын
Excellent visual representations and explanations!!
@tillybillyboyboy 4 жыл бұрын
This is absolutely one of the best KZfaq channels ever ❤❤❤ thank you so much for all this wonderful information!
@fractalnomics 4 жыл бұрын
This is very relevant to my current research into the (iterating) fractal, thank you.
@evanfortunato2382 3 жыл бұрын
My calculus teacher in highschool always said "everything you need to know about the trig functions can be found in their graphs." Guess he was right.
@kingdomadventures 3 жыл бұрын
Numberphile videos are always fun, and I always learn something, but in this video I was *taught* something, and it was, as the title says, beautiful. Thanks for this one.
@TheMuffinMan 3 жыл бұрын
I love this. It explains the underlying concept rather than just "How it works". I feel like understanding why something is the way it is will better help accept it and understand it.
@JM-sr6mj 4 жыл бұрын
Would be really cool to see these animations also with the hyperbolic functions!
@Veovisce 3 жыл бұрын
I know I'm late to this party, but yeah - that's exactly what I was hoping for after he covered secant, cosecant, etc. I don't think you can use a point moving around on a circle to reference the hyperbolic functions, the way everything was shown in this video though. The shape that the reference point would move along would have to be a hyperbola instead of a circle.
@technoultimategaming2999 4 жыл бұрын
3:35 Complex/Imaginery numbers *am I a joke to you?*
@hamiltonianpathondodecahed5236 4 жыл бұрын
More like "Understand my reality"
@AlisterCountel 4 жыл бұрын
I still debate if the name “lateral units” would have been any better. Read somewhere that was a debated name. That said, I can’t think of another possible name for complex analysis, or anything dealing with a name for the algebraic completion of the reals!
@samuelthecamel 4 жыл бұрын
I mean, they aren't wrong, complex numbers are pretty complex.
@angelmendez-rivera351 4 жыл бұрын
AlisterCountel The name lateral unit would apply to the imaginary unit, not the set of complex numbers in its entirety.
@ldonnell4437 3 жыл бұрын
I have tried to learn trig so many times and I can never seem to wrap my mind around the trig functions. But this video really cleared it up for me. Thanks you so much!
@joshbennettmusic 4 жыл бұрын
This is almost precisely the animation I had planned to create for my next music tutorial video (talking about harmonics and resonance). I need to get onto Geogebra by the looks! Thanks Ben and Brady (yet again) for a wonderful video.
@nerdomania24 4 жыл бұрын
strangly, but I have learned that all of these properties of sin/cos at my school in Russia and we had exactly that circle and even more advanced ones to help us in exams
@DeclanMBrennan 4 жыл бұрын
10:001"That's the bit that's got no use". How about for converting rotary to linear motion in Mechanics or visa versa ?
@hyfy-tr2jy 4 жыл бұрын
you are spot on...without this mechanic the piston driven internal combustion engine or steam engine would not be possible
@NisseVex 4 жыл бұрын
I don't think it would have been very fitting for him to say "and this is the bit that's useful for converting rotary to linear motion in Mechanics or visa versa" It's just his way of saying that it's the end of the trig lesson, you can't learn much from this any more, it just looks nice
@brianmathx201 11 ай бұрын
Amazing visual explaination video. Thank you so much.
@xwinglover 4 жыл бұрын
That was truly awesome and fascinating.
@erg0centric 4 жыл бұрын
"it's got no use" - creates ball bearing from first principles
@matthiasscherer9270 3 жыл бұрын
And other useful things like Wavepropagation, Gear(set)s... Ok, everything has additional details. And I am sure these principle ist used even in way more cases. Maybe it's got no use for Mathematicians ;-) :-D :-D
@AeroCraftAviation 4 жыл бұрын
0:19 Cool overtone background. Almost sounds like someone singing through the harmonic series or something. Nice maths too tho hehe. :)
@yvesnyfelerph.d.8297 4 жыл бұрын
Very valuable. The more you know, the more it all naturally falls together and forms different aspects of the same story. That to me defines understanding. To be able to communicate knowledge on this level is yet another thing altogether. Very few people ever get there but numberphile has a handful of these.
@benjaminpalmisano7046 4 жыл бұрын
I have been looking for a video like this forever
@omkargheware1450 4 жыл бұрын
If Ptolemy made trigonometry it would be like this.
@nickcarter4006 4 жыл бұрын
Keanu voice: "I know Trigonometry"
@scptime1188 4 жыл бұрын
The different interpretations of the basic version are so beautiful.
@nathanaelhahn4795 4 жыл бұрын
This is amazing. Best math video I've seen in a long time.
@dontsubscribe1954 4 жыл бұрын
You: gets 3.14 subs Me: Oh yeah, it's all coming together
@sunnyyt8778 4 жыл бұрын
Coincidentally my coaching also started trigonometry woooooooooooo!
@DaneliusUK 4 жыл бұрын
Fabulous. Enjoyed it, thank you.
@terrykosowick594 3 жыл бұрын
Excellent video. These animated graphs are extremely helpful.
@WillToWinvlog 4 жыл бұрын
The instant I saw that first animation I knew it was sin and cos!
@asusa555lfgaming9 4 жыл бұрын
"mitochondria is powerhouse of the cell."
@GenericInternetter 4 жыл бұрын
All these years and finally i understand the circular functions! Thank you!
@seanrutter3470 3 жыл бұрын
I could have used these vids WAY back when I was in highschool! I passed trig with a B if I remember rifht but I remembered. I didn't grasp. LOVE this channel!
@anshusingh1493 4 жыл бұрын
*I want the making of this animation*
@gauravjoshi6725 4 жыл бұрын
The video does justice to the title absolutely beautiful man❤️
@numberphile 4 жыл бұрын
Cheers
@marystone101010 4 жыл бұрын
Trip-pen-dicular! I had a trigonometry professor explain this quite well (sans three dimension and tangent) but I wish he had this. Awesome job illustrating this. Thank you for sharing.
@EmdrGreg 4 жыл бұрын
One of your best videos. Ben is a great teacher, and his obvious enthusiasm is no small part of it.
@numberphile 4 жыл бұрын
Cheers. Glad you liked it. Ben’s a top guy.
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