That weird light at the bottom of a mug - ENVELOPES
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- Опубліковано 21 сер 2021
- Envelopes are cool.
Interactive Demos on Desmos:
www.desmos.com/calculator/ihm...
www.desmos.com/calculator/tho...
Did I get anything wrong? Let me know! I swept over a lot of interesting things here to keep it short!
This was made as part of 3Blue1Brown's Summer of Math Exposition: www.3blue1brown.com/blog/some1
#SoME1
I'm not saying I'll be disappointed if your future videos DIDN'T illustrate concepts with line rider, but I would be thrilled if they DID.
Agreed
I want cosmic inflation theory.
You’ll be disappointed to know Line Rider wasn’t used, but pleased to know it was just as incredible.
@@CALIGS Exactly. i may not have my little beanie hat, but I am waiting in LINE to go along on this RIDE.
im not saying im a DUMBASS, but i literally understood NOTHING in this video (this is a joke)
I think the beauty of this video is that when you got into the numbers, I had no idea what you were talking about, but I could still fully understand the actual meat of the puzzle. You told two stories at once, one for the average viewer and one for those interested in the technical part. Even with intuition alone, you managed to beautifully demonstrate the math to someone who doesn't really know much about the numbers.
its not about the numbers, but rather about notation and operations
Math is beauty. I'm sorry you weren't blessed with teachers that were able to demonstrate it to you.
@@tongpoo8985 I'm fully aware of the beauty of math, I just appreciated the way this video presented it. I don't remember writing this comment but I'm sure I understood the technical part as I have always been a nerd.
@@kiranaun9593 oh ok no offense meant, I figured since you said you didn't get the mathy parts you may have been one of the unfortunate victims of the education system who didn't learn math because they had bad teachers, whether they weren't good at teaching it so you thought you were bad at it or they didn't demonstrate the beauty and perfection of it so you didn't have an interest. Many such cases
@@kiranaun9593 At 6:22 why is the numerator 0 but not the denominator?
This was such a joy to watch! I loved the humour, that you tackled an everyday mystery and the intuitive way you explained it. I hope you’ll make many more!
e
Thanks I was thinking of commenting this
absolutely astonished by how you were able to PROVE that the shape at the bottom of the cup is a cardioid. limaçons just flew over my head when i was learning precalculus, but this finally convinced me that they are not made-up shapes! i am deeply inspired by your lucid presentation and visualization, it really helped visualize the math. thank you for this video!
BRO, you have no idea how exited i am by this video, ive been thinking about those shapes for YEARS now ever since i figured out how to make them in notebooks in school, ive been so curious, wondering if anyone ever described them but i never had any clue what to call them and thus i had no way of searching for information on them, i could only keep making them in my notebooks. Thank you so much for this enlightenment you have brought me!!!!!1!
Heart shaped limicon
try putting in r= 1- cos theta or r= 1- sin theta and other variations of these equations in demos. you will get similar shapes!
Expected to look down and see a few hundred thousand subs - you’re going somewhere, keep it up :)
meanwhile only at 300ish! wow! this is the first time ive stumbled across such a small channel and it feels magical! The quality of content was soo high. This guy is going places! cant wait him to go from 300 to 300k to 3M!
@@sdrawkcabmiay Wow, in 16 hours it went from 900 to 1150? That's crazy, right? I only gain like 5 in a whole week.
Congratulations on "winning" the contest. I can absolutely see why you did.
When you mentioned bezier curves at 7:30 I thought "now I have to watch the bezier video"
I was so proud of myself back when I discovered that same technique for smooth lines in lone rider. Knowing there's a connection to an underlooked everyday phenomenon is so cool
I used to doodle what you drew in line rider all the time when I was a kid! I never knew they were called envelope curves or thought about how they relate to the mug shadow. Definitely a highly underrated facet of reality
As a person who suck at anything related to math, you've made this video wonderfully easy to understand and made me understand the basic concept of the question I have always asked myself while enjoying a cup of tea. Thank you 💜
This guy is about to be blessed by the UA-cam algorithm
Excelent video
thats what i was thinking! Such high quality content and only at 300 subs? nah, we gonna get him to 3 mil!
@@pvic6959 yah this guy have high potential to serve our curious mind.
And then he doesn't upload anything else for 2 years.
indeed
I have question: does the "envelope" shape change depending on the shape of the cup?
What if it was a square cup with perpendicular and flat surfaces instead of a curved surface?
This explains such a simple mystery from my childhood ❤ very cool. Thank you!
This was a great video. I certainly didn't understand the bits of maths briefly explained over here but I went right to the wiki pages and learned the whole origin of bezier curves and how to calculate them. I never had a good relationship with mathematics ever since I was a kid but these types of videos help a LOT. I'm still a teenager so I have a lot of time to establish a healthy curiosity in my studies and through these, I'm glad to say that I'm getting way better not only in factual subjects such as maths and science but also in artistic philosophies. Im glad Im in this side of youtube now and saved my future self from possible bad outcomes.All thanks to channels like yours. Thank you.
I realized right away that this was going to relate to Bézier curves, but I did not understand how those work. Now I understand exactly what is happening, which makes using them in graphics tools so much easier. Thanks for the cool video!
Thank you dude, seriously mind blowing video.
I found this by googling "light at the bottom of mug". I remember trying to google this like a year or two ago and not being able to find it, and I googled it again on a whim today. The Line Rider comparison was a stroke of genius. Haven't heard about that game in years, used to LOVE Line Rider. It felt like one of the first real creative games before that Minecraft stuff. It's great that you have the laymen explanation as well as the nerd stuff. Maybe someday I'll understand stuff like partial derivatives but the best teachers put accessibility first.
Paralogical, your style is so nice to watch and your humor is refreshing.
There’s just something so satisfying about how light can be calculated
-I call it "Butt light", because to me heart-shapes are just butt-shapes.- ...Anyway, thank you! I hadn't come across this channel before and I love getting answers to questions like these! :D
💡+ ☕️=🍑
Wait, are you saying that you drink Butt light? I'm not sure if that's better or worse than the beer....
_"heart shapes are just butt shapes"_
glad i aint alone. and thats precise reason why i dont use heart symbol as reaction wherever i have choice.
Okay you say this but the heart symbol is actually based on a woman's butt
@@yash1152 Funnily enough, I use butts as reactions instead of hearts
This was fun, funny, engaging and informative. The video is also really well paced and edited. You have a real talent for this! I hope you make more videos in the future!
I had watched Freya's videos on bezier curves earlier and used these envelopes to write some rudimentary code to generate bezier curves, I wasn't sure if I was right, but yeee. Also, I remember drawing curved lines with the envelope things in my school notebooks, never knew they were this cool.
I've always seen this and kinda suspected it had something to do with lines intersecting like that. I've had that image of the intersecting lines in my head for years (literally) trying to figure out precisely how it works. Now, I finally understand, and my brain has been set free (for now at least). Awesome video, I'm waiting for the next one.
My prediction: this is going to get really big really fast. This will be one of those videos that will randomly appear in your UA-cam Recommended’s along side History of Japan and Vsauce. Commenting now when the views are in the thousands and your subs are in the hundreds, not hundreds of thousands.
This was an amazing video. I'm astounded at how much style and humour it had. As well as a detailed and decently in depth explanation of this concept which yet wasn't too detailed that it became confusing. Keep up the good work!
Absolutely brilliant. The way you speak is really soothing and reminiscent of Grant Sanderson. I particularly liked the envelope tangent (and the humour).
Subscribed just in case you intend to make more of these.
So cool! Love the explanation and humor.
Imagine being bad at eyeballing stuff, but using math to be super accurate
Fantastic illustrations! Hope to see more from you.
Love your videos. Hope to see more. Never settle for speed over quality, these videos are masterpieces.
I have played around with envelopes many times, and noted the envelope is the limit of the intersection of nearby curves, but I never used something like the F(x,y,t) notation. Very cool and enlightening to see it from that perspective.
Thorough and efficient explanation. I enjoyed this a lot.
I was looking for someone to explain it logically and Im fascinated by the way you represented it. Best explanation on envelope Ive ever seen. Im looking forward for your next videos :)
Incredible. The video quality, the editing, and the near flawless marriage between nerdy math and intuition. You deserved my subscription, I wouldn't want to miss more of those that are (perhaps) to come.
This video gave me the 'excited grin' that's been missing for a while now. Please upload more such videos. Thank you for reminding me how much I love Maths 🥺
i like how you brought us from simpler concepts to harder ones
the journey was good
I love coming across videos like this. These little gems make wading through the cesspool of the internet less insufferable. Bless you.
I too have participated in SoME1 and found this absolutely fantastic video on UA-cam while scrolling my recommendation. The way you have presented the complete video with every single point is phenomenal! Keep it up!
Interesting to see the results of the light in the mug is the same pattern as an FFT graph in audio! There must be some form of wavelength component.
Kinda! Because the shape of the mug is circular, it can be expressed with sinusoidal functions just like the wave motion of sound :)
They are related actually. The cardioid curve can be plotted in polar coordinates using a simple sinusoidal function
r=1-cos(θ)
I already knew about the quadratic-bezier-curve-like shape and cardioid but I never quite understood how to formalize these concepts. Your video is amazing at explaining the connections to envelopes and has some cool visuals! Keep it up!
massive W
indeed, this W appears to be one of of such great massiveness that it creates an easily detectable curvature in space-time
i liked this video a lot! i’ve always wondered what that reflection was, and tying it together with calculus and limacons really was the cherry on top for me. bravo!
Very well done. Lots of enthusiasm.
Thanks for this, it took me back to a time in high school when I learned about radial coordinates (r, theta instead of x, y) and wrote a program (in Turbo Pascal - there, that dates me) to tick along 360 degrees of theta and calculate r based on whatever formula the user put in and then plot the resulting points. Most of the results were boring, but with some sines and cosines in there, we got nice cardioid and limaçon shapes. Your image of the lights in the bottom of a mug reminded of that time and gave me a sweet nostalgia hit. Thanks!
Dude this video is so good, wish get a lot more visibility because you definitively deserve, keep going with the content
I've always wondered about the "cup bum" since I was a child. Thanks for the video.
I would love to see a more detailed breakdown of the derivation of the formulas you have presented. Not all of us can read those mathematical scribbles so easily as others! Excellent video.
It's kind of peculiar to me that even when the opposite side of the thorn is shrouded in shadow, it's still a strong enough effect to produce those rays of light.
I used to marvel at these 'mug butts' as a kid! Cool to know I'm not the only one to wonder how they happen.
This is such a great educational video, I was shocked to find it's your first one. Thank you and please keep on making videos like this one!
Very nice job!!! Loved the explaination and the math behind this natural phenomena
I figured it would be a cardioid, but I didn't know a cardioid could be represented as an envelope like that, that's cool!
Even though i understood almost none of the maths, your voice was soothing enough to listen to to enjoy the video. Not to mention I've seen lots of art made with these curves, so knowing they're called envelopes is cool. Not to mention the cardioid is a really cool shape in general
I have always wondered about it, thank you so much for explaining it. I didn't understand it completely but now I know where to look to learn more.
Very cool concept. Never learned this specifically in calc 3, but recognized that shape. Keep making new videos, i came from your new one
Based on the quality of this video, I was actually surprised to see your subscribers were only in the hundreds. I guess this is just how it is since your channel is still young and this is the only video so far.
I am really looking forward for the future of your channel. This comment shall serve as my time capsule. I hope when I run across this again, your channel will have the views and subscribers it deserves.
1.6k subs now😄
@@jasboi8642 3.25k subs now
4.22k subs
5.84K subscribers now
16k
Great video! I used to draw envelopes all the time and now I have a piece of art of some lines forming a complicated envelope that I found at a thrift store!
This is very informative and interesting, I had to draw "those cool math lines" in an art class some years ago but they didn't explained what they were so your video opened my eyes, thank you
"I have bad eyeballs" really got me for some reason. 🤣
Okay I looked at this channel after watching the video to watch some more videos like this. But there aren't any other videos posted. This was such a good video! Please, if you see this, continue your UA-cam channel!
Light absolutely fascinates me, thank you so much!
ur quality, amount of knowledge and insight is out of the world man, keep going ..............
Simply delightful! What a succinct and intuitive explanation!
Great explanation and style! I hope you create more videos like this :D
One of the mysteries connecting all kids with mugs: The mug heart-butt, examined, mulled over, wondered about, appreciated (especially on particularly sunny days or right under the "good light").
Clicked on this ImMeDiAtEly
then got distracted with Line Rider.
I had an intuitive understanding of what was going on, but I had no idea there were such elegant formulas to describe it. Beautiful and clear illustrations!
This is a phenomenon that I've just barely noticed on the side of things, and I never bothered to find out why it happens. Thanks for showing me!
I love it, the math, the jokes, the animation. Please, make more videos.
I haven’t even watched the video and I’m fascinated that you found a cardioid of light.
we need more of this type of stuff!!
First year engineering at the university in Ghent, Belgium. The prof called it a kidney line. Don’t remember how he did it but this explanation of yours is real elegant.
I had to do a double take when I saw you only have 550 subscribers. This was a beautifully constructed and explained video, well done. Hope you continue to make more of these.
Thank you very much and you have just solved my mystery rested in my mind for two decades!
One of the most pleasing videos I have ever seen!
very beautiful demonstration.
Dude I love this! Make more videos!
Immediatley subscribed. High quality content at it's finest. Keep it up! 💪🏻💪🏻👏🏻👏🏻
omg love your video, not only show formula, it let me know math is in our real life in the cup but no much people notice, hope you keep doing it
Actually amazing video bro, im glad to say i was here before it blows up. Good luck with SoME1, great video!
This was so cool! I really like your style of explaining things
I've been wondering about this for a long time. Great video! :D
Please, may we have some more! Thank you for a really nice explanation!
That was brilliantly explained ! 👏🏻
Ah yes of course. Heart shaped, yes.
I can really see the efforts you put in this video, no one can stop this channel from going viral now, good luck dear
I love this video so much, I learnt so much and paralogical's explanation is so engaging
Thank you for sharing this! I have worked with convex envelop of functions before, but never did I understand what only does the points on the contact set matter. This video gives me some insight of it.
Delightful. Congrats on being a big winner.
You are a freaking rockstar educator. A league of your own. Keep making these.
Awesome vidéo ! Each of the aspects fit perfectly to create some enjoyable, understandable and detailed content !
I love when we can get cool math examples out of something I used to doodle in the corner of my school notebooks!
Reached here from 3B1B
I have always wondered about this exact topic. I even sent images to my friends as a fun question.
So delighted to see this video
Thanks a lot!!
I was wondering about this too, thankfully, you made a video about it.
Same , i was too fascinated by this reflecting designs
the lines making a curve thing blew my mind in middle school math i would do exactly what ur doing in line rider all the time
Interesting! I just learned about Nuquist curves in control theory and they look just like this!
I was thinking about that cardioid the other day, good thing I found this!
What a professional video! I loved the end, this is a million-sub worthy channel.
I love it. I love every bit of this
Great explanation
Back in the 70's, string art used the idea of envelopes, e.g., to form a ship's sail. I've wondered about the mathematics for quite a long time. Thanks for this very fine answer.