The hardest problem on the hardest test
Вставка
- Опубліковано 7 гру 2017
- A difficult Putnam question with an elegant solution.
This video was sponsored by Brilliant: brilliant.org/3b1b
Help fund future projects: / 3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: 3b1b.co/putnam-thanks
Home page: www.3blue1brown.com/
Solution to the puzzle mentioned at the end: brilliant.org/3b1bindicator/
These videos exist thanks to Patreon:
/ 3blue1brown
A different write-up of this solution:
lsusmath.rickmabry.org/psisson...
1992 Putnam with this problem:
kskedlaya.org/putnam-archive/1...
A problem with a similar flavor came up on the 2005 Putnam A6. Give it a try! The solution for that problem, by the way, was written by Calvin Lin, a friend of mine who works at Brilliant. Small world!
kskedlaya.org/putnam-archive/2...
kskedlaya.org/putnam-archive/2...
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
Korean: tebaioioo
------------------
Animations largely made using manim, a scrappy open source python library. github.com/3b1b/manim
If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and has many other quirks you might expect in a library someone wrote with only their own use in mind.
Music by Vincent Rubinetti.
Download the music on Bandcamp:
vincerubinetti.bandcamp.com/a...
Stream the music on Spotify:
open.spotify.com/album/1dVyjw...
If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with UA-cam, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that).
If you are new to this channel and want to see more, a good place to start is this playlist: 3b1b.co/recommended
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The video: "The hardest problem on the hardest test"
Me who barely passed math classes: “Hmm, lets see.”
hahahaha same here. Barely passed math but tought: well maybe i can solve it
Even if you ace your Maths quizzes and exams, I don't think that you can completely understand what he's saying
@@lukeskywalker691 i had descriptive geometry in my architecture studies and was later a tutor for it, and as architects we are generally pretty good in spatial thinking and i understood the problem and even his solution almost fully, but i would never thought of it myself ofc haha
Same
@@krewpi it is just about finding things you love to do. i was very average to under average in math, but when i started studying architecture it really began to make fun and i ended up being tutor.
You know it’s getting lit when the smart kid brags about getting 3/120 points
Hello 👋
@@Umar-yi2ot excuse me, mr vertical version of my logo
@@Kali-bs7oj you mean horizontal? You're the vertical one lol
@@melviness4769 I saw it as vertical since the colors are stacked vertically but yeah I see now how I kinda am the vertical one haha
Because hes only smart not genius xd
what i find even more amazing is that someone had to come up with all of these problems and solve all of them
ikr
EXACTLY, I hold respect for professors that are able to make great problems like these , not too easy to spoil the fun, yet not impossible for the students to solve by themselves.
@@quantumgaming9180maybe they just put something rly random that looks hard and then someone solved it and after the solution looks right they jusf accspged it
I remember watching this back in 2017, my freshman year of high school, and then falling in love with this channel and math itself. Here I am in 2022, a freshman math undergraduate, still knowing damn well that I could never solve this by myself lmao
Lmfao
hahahahhaha@@mgara514
Imagine taking this test only to see some kid start flipping a coin
😂😂😂😂
I'd defo start laughing at him and myself
Gotta be creative to figure it out
Whenever you realize it’s not multiple choice😰
@@kellycong8388 i think he understands the joke mate.
"If you choose 4 random points on a sphere...."
I think I changed my mind can I go home now?
My math prof, first lecture in first course: “Let’s take a simple example. Let E be a Banach space with norm M…”
Exactly. That line itself made me lose my hope.
Is it okay if anyone here didn’t mind if I only just asked if anyone ever wanted to ever watch my videos that I made? I hope that’s okay if I just asked. I don’t mean to bother anyone.
Why u are asking this answer your personal questions by yourself
Exactly😂 a rational mind would give up in that point😂
You can further extrapolate the simplification to a one dimensional problem: given the space between two random points on a bounded line, how many solutions will contain the center? Given a first random point, there is always a 1/2 chance that the other random point is on the other side of the midpoint. You can then extrapolate from one to three dimensions by cubing the solution. (1/2)^3 = 1/8
Works in the 0th dimension as well. Given a random point on a point, what's the probability that they'll be the same point? (1/2)^0=1 😅 crazy how math works.
you're just taking the assumption that it can be cubed. there needs to be serious proof behind it.
@@shubhamtokas5995 but that might be easier than the original question
that's really actually cool, idk if it's just a coincidence or if that's actually how it works cause you'd need to continue testing that in 4+ dimensions unless you could come up with a rigorous proof like in this video
@@kennethluo4934 1/2^n It's correct in every dimension. It's the proof that's the hard part though
About 5 years ago, I watched this video and got inspired to study maths in college and take this test. This Saturday, I took the Putnam and solved 1 question!!!!
that is so cool! great job :D
I'm thinking of taking maths in college too but I'm worried it'll put a burden on me as I'll be taking the maximum of 5 subjects. But this is so interesting :(
Teacher: "The test won't be that hard."
*The test:*
Bratans Bratuchas 1.7k likes but no comments?
@@bluegamer07 yes, whats up with that?
Bratans Bratuchas strange.... well whatever I am glad to be the first one I guess lmao.
@@bluegamer07 it isnt strange at all I bought 2500 likes first then the other 200 came by themselves
Bratans Bratuchas why would u buy likes though?
This guy: explain all the math
Me: still trying to figure out what a tetrahedron is
Oh
oh me too
I’m gonna okay myself but a tetrahedron is a 4 sided 3D shape if I’m not wring
@@somerandomdudewhodoesstuff3107 like the Egyptian pyramids?
@@asaniwasabi no i think the pyramids are square based 3d triangles (pyramids)
Your teaching abilities are phenominal, you have explained this in a way that makes perfect sense to me without simply removing relevant details to avoid simplifying them, which is what most 'teachers' would do and consider it a job done.
I’m in high school and I’m about average in math, I was so close to seeing this video as a write off and leaving. I’m so glad I decided to stick around, you explained this in a way that even the average can understand, you are an amazing teacher and this video was extremely entertaining!
What do you mean seeing this video as a write-off?
It's a way of saying "math is too difficult and I'm not interested in learning this because I'm not going to use it in my real life anyway".
This is not for average university students
High school teachers be pulling this out then saying “This is a college level class, it only gets harder from here”
TRUEEEEE
💀
That's actually a great idea. April fools will be brutal next year.
@@thegrim418 oh no
My math teacher did a huge ass equation and said "Its primary school knowledge" I don't even know how to deal with fractions
*In class:* The solar system has 8 planets
*In tests:* exactly how many stars are there in the universe
you have spoken the truth
Probably 24 stars
I actually don’t know lol. Something like 2,000,000,000,000 x 100,000,000,000
Nova nah maybe like 17 24 seems like too much
But why are we here just to suffer? Hm i guess 17 is more scientifically possible than 24... Thanks
Wow, the animation, and music, the way you explained all of this. This is a work of art. Well done.
I really love how you break it down ...it makes so much sense and you are super understandable! Thanks for what you're doing to teach these concepts. And breaking it down beyond the answer to this question to what you can apply to all other situations is GOLD! 🥰
teacher: cmon guys i taught u this
Haha yes fucking teachers be like
"Common peeps i just literally taught you THIS exact problem yesterday"
us: Noo, you taught the nerds that. The rest of us were busy raising our hands, waiting for our turn to ask for help..
You had this 3 years ago...
Me at school: "ugh maths is boring"
What I watch when I go home:
it boring cuz u too slow git gud noob B)
my PB: 7 minutes 38 seconds 12 milliseconds
git gud
Awesome 🤣🤣
@@deleted-user-82u3ht92 Sad but true..
@@beangobernador tf is you talking bout
@@butcherpete9252 LMAOO
My brother recommended this channel, and this is a great introductory video to your content. The math is above my head, but the discussion about the process of problem solving is relevant to anyone. Cool!
I love this way of visualization 3Blue1Brown as well as other Math related UA-camrs use. It really helps to understand these kinds of problems on a deeper level. For example, I doubt I would‘ve gained the same key insights from just reading through the listed write-up in comparison to your great video. I wish this method would be used in actual classrooms, however, with the dawning age of smart boards and such we might get tho this at some point ^^.
teacher: im just gonna skip this question, u guys should have learned this last year
teacher last year: im just gonna skip this question, u guys should learn this next year
@@atikshsingh1598 😂
Why is this situation so damn relatable...
teacher who taught us the previous year : I'm just gonna skip this question, u guys should have learnt this last year
@@rithanipriyanka2393 teacher: this ones self explanatory
Girl: I don’t get why he doesn’t get my signals
Her signals:
lolllllllll
AHAHAHAHAHHAHAA
damn I didnt think id find something this accurate out here
Lololol
G: he is cheating
His boyfriend:
I’ve watched this video every year since I was a freshman in high-school and now I just finished my freshman year of college and I finally understand every part of this proof and wow is it elegant
Watching it again 4 years later and I can see the Alice-Bob problem solving applied here too. Subtle shift of perspective from numbers to concept is all it takes from solving one particular question to solving an array of similarly framed questions
This is hard enough to understand with diagrams and a helpful teacher, but imagine how smart you have to be to solve this with just pen and paper...
And limited time
Some people even solve these things mentally 💀
@@slatined4576 i did bro. When he said it was 0,25 chance of the point cirkle to be in the area of the triangle i immidiantly knew it was 1/16 for the sphere
@@slatined4576 naw im kidding i dont know the answer lmao
Its not about being smart, math revolves about knowing concepts, and recognising where you can use them. You might as well make an analogy to your native language, you know what words to use and when - thats math, but its a foreign language.
You know shit is real when the kid with photographic memory starts re-reading his notes
*god help us*
@Lil Quack Satan has left the chat
Wait.. then whos left?
@@jasongrenbox6997 Zeus?
@@mynameisjeff5397 Zeus has left the chat
I took this exact test in college. I remember this question and it's great to finally see the solution.
And what was your score? Has anyone scored 100 percentage?
@@KejriwalBhakt haha, 0
Every now and then I come back here and always end up amazed. Love this video, I'm in med school, but I participated in math olympics through out all my highschool, love maths
Him: Explains hardcore math
What I learned: ah yes moving lines inside circle very nice
LOL😭
Youre not alone Sir. Still I wish I could have had a math teacher like him
Same
It’s not hardcore math lol..there’s just too much of it and you gotta have great intuition of the different patterns in your mind..so basically you need to be very creative and imaginative to solve these..
Damn. I remember when 3blue had fewer than 200k. Wasn't too long ago, either.
How it's all grown.
Me: Watching cute cat videos
UA-cam: So I have heard you like tetrahedrons
Your cat watched this video about tetrahedrons.
Andreas F they’re only one step closer to world domination
CreamHeroes?
I know it's cringe, but I'm just curious
Same HHAAHAH
I am c a c k l i n g
This video was very insightful, always love your videos. Thank you!
This is really good. Too many people tend to think the math is just memorizing a bunch of formulas, when in reality, they are like logic puzzles, almost like sudokus. So for all the people who say that math isn't your thing, maybe memorizing isn't your thing. This is way beyond my league, and yet you explained it so that I don't need any prior knowledge and equations.
But you need to know the rules before you can play.
teacher: “no calculators for question 5!”
the question:
He did all of this without a calculator...
@@Ryan-wp6vr Yeah he did, if you exclude the graphing software
@@parallelogrum7967 that was for the video not for the answer
i dont think a calculator would help you with this question
even with calculator i wouldn't even know how to use against this question
“Take a moment to digest the question”
Me : *What is a tetrahedron?*
So true
And now Im dead thanks hahahaha
If you're actually wondering it's a triangular pyramid with 4 faces lol
Ari Wang Thank you kind stranger!
U shouldn't be here .... 😀😀
Thank you for explaining this in a way i can understand my man. Keep doing your amazing work as you deffo got my sub
I have just realised that math is fragmented. It doesn't matter how much of it a person may get wrong, what's important is that one experiences each of the questions within their own categories, gaining wider experience of each category respectively, and then having all the tools combined to connect all the pieces of the puzzle. That's what I just realised anyway thanks to this video👍🏼
Me only a few minutes into the video:
“What’s a tetrahedron?”
Not related but go pack go
@@casperthegamer7176 hell yeah GPG!
Alright, real answer here
*Tetrahedron is like pyramid but all the edges are parallel.* Think of it like cube and cuboid. All 12 edges of cube is the same length , meanwhile there's 2 different pair of different edges of cuboid with different length. In this case, *tetrahedron is a prism with 4 triangular faces, 6 straight edges, and 4 vertices (aka corners).* Hope this helps you
I am so not understand any of this... But I still watched
Build more pylons
Teacher: there will only be 3 questions
Me: thank god
Test: 1,1A,1B,1C, 2, 2A, 2B, 2C, 3, 3A, 3B, 3C
@Angel Buceta this isn't Instagram
More like 1, 1A, 1Ai, 1Aii, 1Aiii, 1Aiv, 1B, 1C, 2A, 2B, 2Bi, 2Bii, 2C, 2D, 3, 3A, 3Ai, 3Aii, 3Aiii, 3Aiv, 3B, 3Bi, 3C, 3D, 3E
@@Anthony-tp1md more like 1 a b c d e f etc. 2 a b c etc. 3 a b etc
Test B-Sides
bottom text
Basically physics tho...
My teacher: this worksheet is due tomorrow. Don’t worry, it has only 3 problems
Worksheet: 1a, 1b, 1c, 1d, 1e, 1f, 1g, 1h, 1i, 1j, 2.....
Every single video without fail manages to blow my mind
I'm still in highschool and understood the way you approached this question,my mind hurts but at the same time feels relieved and proud.
Me after 3 mins: I understand
Me after 6 mins: I understandn't
Me: after 2 seconds i understand
Me: after 1 min. Im'nt understand
Damn this is underrated
It’s actually simple. You just have to break it down into simpler forms and use your understanding of formulas and equations to prove and solve it
Did you understand ??
*Yesn't*
Ye
After watching this I had a great discovery. Big enlightment. I can safely say, that i've come to the genius conclusion that I understood nothing.
Ahh i too was enlightened to the fact that my noggin containing cerebrum was able to decifer nullity to what the pictorial visual was about.
😂
@@daveasence8948 😂
this is 100% me 😂, i never felt so relate in my life
What? That was super well explained, came on
In 1D it would be 2 points "randomly" selected out of 2 points on a line, probability of 1/2 that it is the different point and the connecting line goes through the center. For 4D and above I think it's quite helpful to move away from the visual intuition and describe it formally, but it is still the visual intuition that was the key to the solution.
Yes good point and the 1D case would be very easy too, the probability that two random points on a line when connected contain the centre. Doesn’t matter which side of the centre the first point is on, the 2nd point just needs to be on the other, which is of course a 1/2 chance as you said!
Before coming across 3Blue1Brown, I never knew just how much simple intuition could be transmitted by one man to an incredibly large audience.
Imagine coming home tired from learning math at school, only to find this in your recommended.
Why can’t i see your sub count?
@@kingdinodragonite3470 cause ur bad
Everywhere I go I see your face 😂
Heyy
This is the first time I see you without 100 likes
Professor's: Put's effort making a hard question
Me: **Leaves it blank**
He'll be sad
Oh I see what you did... your pfp
Profesor: (ur profile Pic)
My monography be like
Put is
You made a _greeeeat_ mistake
A good teacher is very important in every student's life,you are absolute good teacher 👍
I lovveee these sort of math questions,,, and I love them even more when someone just explains this well how they can be solved so that I don't have to think much :D ( because usually I cant solve them alone, but no doubt if by chance i do solve something this hard its the best feeling in the world)
Me watching this: *"Hmm yes, tetrahedron."*
Hahaha
Bro that was the moment when i realized "yea i shouldnt be here"
exactly my reaction lmfao, this comment made my day
hmm yes, 10 times 12 is 120
Bruh exactly lmao
During a math test I get so anxious and scared of making arithmetic mistakes that when I have to do 6 divided by 2 I use the calculator
I swear i do 1 plus 1 and things like that on calculator
me.
That’s just sad 😦
6 divided by 2?
It's so easy lol, It's 12
*Checks in calculator*
Oh...
I once got 9,90 points out of 10 on a test just because I wrote 6/3=3 😂😂
I did the problem with a square and it made it way simpler to do it with the circle! It’s really interesting because framing the question in a certain way makes it so that the shape of the object is almost arbitrary!
I inscribed the circle in a square. I then divided it into 4 parts by the diagonals.
Take an edge. That edge is 2 of the 3 points of your triangle. Now move the last point and note the area under which the middle is covered. That area should be only one of the 4 parts of the square that you cut using the diagonals. Using the same diagonals, you get 4 of these situations because there are 4 edges and each of them gives you 1/4.
If you take a fresh square now and make 2 cuts that serve the same purpose as the diagonals in the other case, you’ll find that you have another set of 4 configurations that give you an average area of 1/4 because each set of 2 is mirrored.
Since the circle is inscribed and we used areas we can use the same cuts for the circle and it still holds.
If you do the same thing with a cube and make 4 cuts. You can do the same thing but you get 1/8.
This shit is so cool
i may be years behind on anything like this but you explained it in a way that makes sense
what a beautiful mindfuck
xD
I changed this so you will never now why those people are crying
@@Malik-im8zgchill brub
@@Malik-im8zg you do realize that "useless comments" make up 99% of youtube right?
The Number Four too true
As a wise turtle once said.....
“I don’t know”
Nem eu.
If a turtle said that to you, it's time to check your meds.
I love these videos, they very interesting and really well done
Amazing explanation man totally loved it
When I'm studying maths for exams, it's a nightmare but when I'm casually trying to comprehend it through videos like this, it's so fascinating.
I feel this so much, just having a maths exam a few days ago..
@@dangomangothe1941 I hope that it went well xD
@@sahazmarkk5624 oh god as an atheist I hope as well
@@dangomangothe1941 lmao, good luck for results
@@dangomangothe1941 cringe
Me: Watching Minecraft
UA-cam: So i herd u leik polygons
This is at the same level of some minecraft redstone.
I was just watching minecraft then saw this
I've just watched a minecraft vid, wtf.
Timothy Moore same
Same dude.
I love how it's emphasis on the key being in how we think not the solution itself.
very interesting
Being brilliant at maths is one thing. Being brilliant at perception/framing is a completely different skill. Good video!
It's all cool in the exam until the atheist kid starts praying
asian atheist kid*
@@ten1162 uhmm that might mean the apocalypse is coming
That’s me lmao
@@user-dk3et3hw9t what’s wrong with believing or not believing in god? Can people just get over it?
@@user-dk3et3hw9t whether god is real or not no one knows! Doesn’t matter to much, just live a live after your own morals
Imagine solving questions like this with just pen and paper.
You write and scribble.
@@z.e....3175 and flip a coin
This is Mathematical Olympiad
For eg.. JEE
@@pin2398 I'm preparing for the same ; )
It's the 7th time I'm watching this and still amazed how great this problem and the solution is
In class: 2+3=5
Homework: 2x3=6
Test: 4 points are randomly chosen on a sphere, what is the probability that the tetrahedron formed by connecting the points also contains the center of the sphere?
Illuminati final test “If I have 8 oranges in my right hand and 7 apples in my left hand how many bananas I ate in lunch “
There are 69 likes should I like it?
@@user-vn1zi9mx3z Me: Can I go home?
Just Like The Old One no until you get the correct answer
EricYyt
Zero bananas because you only have oranges and apples in your hands.. I am thinking to take this Putnam test
Me at 10PM: ok let’s get some sleep tonight
Me at 3AM:
Double Yell me rn
Double Yell me rn
3:43am rn
3
What should I say?
I live in Germany and its 4:56 am
I think it often really helps with 3D problems to simplify to 2D, and 1D and see if you can find a pattern. That gives you an idea about what the answer might be; trying to proof or disproof your idea often gives you new ideas about how to approach the problem. This is especially powerful when you try to solve problems in 4+-dimensional systems.
this video made me hooked to your account and made me love mathematics, thankyou
It is quite interesting how it can be simplified by just visual representation, doing it by formulas on the other hand is probably pretty confusing though.
Having eyes is a blessing.
@@attempt58 True
@@attempt58 And a brain to visualize with
@@beybrain7896 nothing really matters without the brain
@@evilhutdug4665 well yes, as without a brain you have no conscious
I swear every elegant solution of a math problem is basically a big bruh moment
so true doe
*when you get your test back*
yeah i always think for so long only to find out the solution could be found out by a third grader
Maths is really beautiful tough problems have simple solutions but complex understandings
Under what circumstance would anyone be able to find this.
I was never good in math, but is so cool when someone presents something that you would never think about it specially when you get a visual representation, great vid thank you youtube algorithm.
Wow, nicely visualised!!!
All the jokes in the comments aside, you've just explained something to me, a person who is terrible at math, in a way that actually makes sense. I think that says something about your teaching ability
truly. where was this guy in 6th grade?
@@kukokeko Where was this guy during my entire schooling career (so far)
facts bro why can’t teachers be like this
Exactly. Teachers should be taught how to teach first
@@valediction9174 ;( we getting there, but teachers still payed like shit and not actually taught how to teach, just to show
Class: Solid, liquid, and gas
Homework: Plasma
Test: Fabricate anti-matter then harness the energy and relay it to energy required to the construction of several dyson spheres spanning the M31 group[5 marks]
Me: The mitochondria is the powerhouse of the cell
This comment is underrated
Answer (D): None of the above
@@saaramb3452 you can prepare anti matter using particle accelerator.. but you need at least a gram of that antimatter to harness the energy for building the Dyson sphere around a star...let us a assuming that you want to build one of those several Dyson spheres around our very own sun... Then you need start recruiting at least half of our current world population as the labor force required for this project. Assuming that you are a very good public relations company and have recruited half of the world population for this horundus task, still you need atleast a gram of anti matter to use it as start off to provide you energy for this start up job, but our current particle accelerators at CERN can produce about 100,000 anti protons per day and each of these last an average of 10 seconds.. So a gram means ahh... Let's assume it to be hydrogen's anti protons for calculation purposes 1 mole of anti-Hydrogen is 2 grams that (because hydrogen exists as H2) which means 1 moles of anti-Hydrogen contains (6.023*10^23) anti hydrogens so 1 gram is (3.0115 *10^23) which requires you to prepare a particle accelerator that is as efficient as that it need to create 3.0115 *10^23 anti-protons( I m using the word proton instead of hydrogen because it doesn't matter hydrogen can be called a proton as it has has only one proton and we count the proton and neutron for mass number) so the particle accelerator should work at an efficient 3.0115 *10^17 times the one currently being available.
So in plain word's if we have the materials we would have done that long ago, unfortunately we don't have the materials we require. A gram of anti matter costs around 62 trillion dollars which means you need to sell your country for that!
@@ganeshprasad9851 ok thanks, i'll consider invading another planet
haha get it it’s funny because school is bad please give me likes
Problems like this is so amazing they teach you so much , about your approach to problem and hoe you see a problem,
Many People will find math difficult due to complexity of the given circumstances in a problem but it can be broken into smaller less complex parts ,,,,,every fking problem
Thats The Beauty of math
one of my favourite videos on the internet
I never thought I would be able to understand how to solve a putnam problem... i am completely overwhelmed with joy... your style of explaining the problem just blew my mind.... i have been a subscriber since last year or so, thank you for making me realise the elegance in math
Wow! Your 'simple' presentation makes one wonder why so many billions of us can't even begin to grapple with the problem. It takes special talent for making the nearly impossible accessible. As a teacher, you must be unforgettable and irreplaceable. As a student, your teachers must have felt humbled to have met you.
Fr1nc3sc41 I had one and only one teacher like this in math who was almost this good at explaining difficult problems, and even he doesnt hold much of a candle to this guy
The thing is:
this doesn't actually help you solve those problems.
They are designed in such a way that you have to have the right understanding and intuition to solve them.
Anybody can solve them if they know the correct method - but nearly nobody does and there are so many problems and variations that can be given that no person can ever hope to come even close to remembering them all.
hat is needed is the ability to come up with the solution on your own - and that is hard.
Not surprising you're an Indian (its a compliment, no negativity intended)
@@z_vizo4594 Smart Bois
Dawg why did the UA-cam algorithm send me here I’m dumb asf
Literally was watching highlights of football and the next vid was this
Felt this😭
fax im only tryna listen to Carti snippets
@@ez-boys4268 i was watching highlights of football to
They know that, so they're recommending you videos to make you smart, or at least pretend that you are to a group of nerds.
this is probably the best problem explaination thankyou
Great explanation and easy to understand 👍 🙌💯
He’s literally solving the meaning of life and I’m trying to make sure that 3+4 is 7 just in case
Using two calculators because you don't trust the first one
@@ea8455 😂
@@ea8455 was looking for this comment, and was not disappointed. 😆. A man of culture indeed.
Enes Akbulut you cracked me up HAHAHHAHAHAHAHAH
Same.
I probably watched this 100 times Now i have started to understand what an tetrahedron is
😂😂😂😂
a 3d triangle
Ahhhh!This was suppose to be a joke
HAHAHAHAHA
I still wonder. what is it actually? :|
I don’t even understand basic algebra but I still watch videos like this. Haven’t got a scoob as to what you’re doing.
Awesome. Always try to find a clever way to re-frame the question.
"Some of you with some multi-variable calculus under your belt..."
"...uh....yeah, I got tons of that. Need a bigger belt even."
Yeah same i need a huge belt for all of the multivariable calculus
😭😭😭😭
um
me : * barely scraping maths*
also me: i bet i could do this
haven't done maths in 10 years
also me: i bet i can do this with my pure primary school mathematics
Tamanna Kareem lol same
OnO
@@adriannanad4675 A thing i like abaut this probelm is that you can "oraly" solve it with just almost no understanding in mathematics.
Thank you, this video gave me an extended essay topic
I watched this video a while ago and now when I was preparing for jee advanced I saw the 2d version of this problem and suddenly remembered your video
I must be doing something right to have gotten this on my reccomended.
Nope you have anime pfp
For sure it ain't spelling 😏
@@jesse406 ok.. you’re subscribed to “dloow”
@@OKayD3N wtf do u have against people who put anime pics as their pfp? they just like anime
@@jesse406 What’s the issue with me being subbed to Carson?
Math questions be like:
Jimmy has 21 oranges
He is 2 hours late for school
Solve for the mass of the sun
Not really
@@kkaaii177 it be like that
okay but we can actually calculate the mass of the sun despite the unrelated information given
@@dingyworm I mean, with the information we've been given? No, but if they've given us the uniform density and radius of the sun, it should be a piece of cake, even that's not necessary, if we're given the gravitational force between earth and sun, with the distance between then and earth's mass, we can easily find the sun's mass
@@dingyworm yes of course
That way of thinking will help you in life too. When you get an insight there’s a temptation to rest on the solution, but using your new understanding of the overall pattern if you then try to use that insight to recontextualize the problem thru its lens, you can simplify your approach instead of ending up with a complicated solution. Often it can shift your perspective from seeing many problems with many different solutions that are hard to manage all at once, to seeing that they were all a connected problem with a simpler overall solution, because you stop needing to bandaid symptoms when you can work on the root cause
Why is it so interesting and soothing listening to people explain complex math questions when you don’t have any idea what’s going on. “How do you like them apples”
50% chance. It either does or it doesn’t. Problem solved.
That's not how this works, that's not how any of this works!
Possibility. Not probability. Possibility of you finding a 100 dollar build the next time you go for a walk? 50/50. Probability of you finding one? Probably near 0. (including the probability that you ever go for a walk in the first place lmao)
Let's imagine a world where everybody gets the irony
Krakatoa Dude congrats on taking a post too serious. You win.
@@krakatoadude4231 And then we have that one guy...
Bruh why am I so addicted to videos that I can't understand???
And what part didn't you understand on this video? I mean the math wasn't that complicated at all.
Because you have an anime profile pic
@@disadadi8958 stfu
Because people have always had an interest in understanding things they can't, that's why we're where we are today
@@disadadi8958 😳 you good bro
Just took the Putnam last Saturday, I probably wouldn't have even know it existed without this video
Love your work.
When you explained the 2d case, I guessed the 3d case would be 1/2^3.
I assume, (rather than prove), the 1/2^d pattern continues into higher dimentions.
eg: 4d case would be 1/2^4 = 1/16
Interestingly if you take the limit of the 1/2^d series (sum the probabilities 1/4,1/8,1/16,...), you get p=0.5
So if you genralise and make d a random integer >1. the odds of the center point of an n-dimentional circle being enclosed by a n-dimentions triangle is 50/50.
I'm sure others have noticed that and stated it more formerly, but it gave me a buzz to find it myself :)
This guy is amazing at explanations. If he can teach the hardest problem this well, imagine what he would be like as a high school teacher.
Yeah
Hed probbaly be a better professor, most hs students disrespect or ignore the teacher then ask for them to re explain it or to have special tutoring over subjects they didnt listen to
@@alycias7345 yes it does, atleast for me.
@@connorschultz9022 I know it's really sad to see, and to top it all off the teachers most of the time do.
Why teach one class, When he can teach the world with his UA-cam channel.
Fastest 3 things in the universe:
1- light
2- universe expansion
3-me clicking on a 3blue1brown notification
the universe expansion between two points is faster than the speed of light provided the two points are far enough apart. The chance two random points in spacetime are not far enough apart to outpace the speed of causality is infinitesimal, assuming an infinite universe, therefore your list should be
1-universe expansion
2-light
3-the joke flying over my head
· 0xFFF1 I was going to make a similar, but less considered point.
· 0xFFF1 why does it depend on how far apart two points are? And what is the semantics of your hexadecimal username?
Kyle Horne
pick two points within your eyesight, the expansion of the space between those points is not the speed of light or anywhere close to it
However the further apart the points are the faster they move apart up to (and at a great enough distance) exceeding the speed of light
This here is a little strange to imagine but arises because the universe is expanding from every point including points between points which brings us this acceleration
Alex Nope yeah the universe is expanding faster than the speed of light, pretty much
Thanks to you sir for your amazing 3D visualisation
Loved it ❤❤
The way that is described for the imagination part it is the most fundamental thing for solving any problem
And remember: This was just ONE QUESTION. FROM A WHOLE TEST
in germany we are getting kind of used to this kind of questions. often the solutions are even longer
@@M3rcuryMan Only if you're doing a masters/phd in math in Germany.
@@M3rcuryMan Bist du sicher!? haha
@@M3rcuryMan I don't belive you.
@@whateveryh2119 actually we do, this test is hard but not extreme, our education system is hard