The hardest problem on the hardest test

[@calebsherrock8749]

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...

[@bombfire8280]

And limited time

[@slatined4576]

Some people even solve these things mentally 💀

[@renedan7247]

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.

[@IGTKYIYKSM]

@@renedan7247 true, but it is about how smart you are. Albert Einstein had an sort of special form on his brain wich scientists suspect made him better at logic thinking and therefor math

[@scptime1188]

@@IGTKYIYKSM He did have an IQ of 160 after all.

[@Hamentsios10]

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.

[@daveasence8948]

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.

[@Hammy_tch]

😂

[@Hammy_tch]

@@daveasence8948 😂

[@guesswho9541]

this is 100% me 😂, i never felt so relate in my life

[@Hansulf]

What? That was super well explained, came on

[@Kali-bs7oj]

You know it’s getting lit when the smart kid brags about getting 3/120 points

[@Umar-yi2ot]

Hello 👋

[@Kali-bs7oj]

@@Umar-yi2ot excuse me, mr vertical version of my logo

[@melviness4769]

@@Kali-bs7oj you mean horizontal? You're the vertical one lol

[@Kali-bs7oj]

@@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

[@jamesleodelacruz]

In that case I would have at least negative 1004 points

[@isaacmalik3714]

what i find even more amazing is that someone had to come up with all of these problems and solve all of them

[@drawwithme4964]

ikr

[@quantumgaming9180]

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.

[@kinghosty]

​@@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

[@enjoipls.]

"If you choose 4 random points on a sphere...." I think I changed my mind can I go home now?

[@magicmulder]

My math prof, first lecture in first course: “Let’s take a simple example. Let E be a Banach space with norm M…”

[@azysgaming8410]

Exactly. That line itself made me lose my hope.

[@lordartoriuscollbrande7434]

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.

[@man-vd4zx]

Exactly😂 a rational mind would give up in that point😂

[@SkullKingize]

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

[@saaramb3452]

This comment is underrated

[@Aakash_Goswami1]

Answer (D): None of the above

[@ganeshprasad9851]

@@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!

[@saaramb3452]

@@ganeshprasad9851 ok thanks, i'll consider invading another planet

[@grieferjones2237]

haha get it it’s funny because school is bad please give me likes

[@knownbynone558]

The video: "The hardest problem on the hardest test" Me who barely passed math classes: “Hmm, lets see.”

[@kaydasilva595]

hahahaha same here. Barely passed math but tought: well maybe i can solve it

[@lukeskywalker691]

Even if you ace your Maths quizzes and exams, I don't think that you can completely understand what he's saying

[@pianoingels7128]

@@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

[@netaropati7738]

Same

[@pianoingels7128]

@@noiseofthedead 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.

[@matthewgeary1811]

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

[@mgara514]

Lmfao

[@gazingstar-zz9gf]

hahahahhaha@@mgara514

[@nujak3271]

This guy: explain all the math Me: still trying to figure out what a tetrahedron is

[@Artist_of_Imagination]

Oh

[@akdarklight156]

oh me too

[@luckymario8910]

I’m gonna okay myself but a tetrahedron is a 4 sided 3D shape if I’m not wring

[@wesburrows3733]

@Asani Wasabi no i think the pyramids are square based 3d triangles (pyramids)

[@wesburrows3733]

@Asani Wasabi i think the tetrahedron is a triangular pyramid so the bottom is triangular. sry for the confusion

[@wisechimp6159]

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?

[@user-vn1zi9mx3z]

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 “

[@justliketheoldone4767]

There are 69 likes should I like it?

[@justliketheoldone4767]

@@user-vn1zi9mx3z Me: Can I go home?

[@user-vn1zi9mx3z]

Just Like The Old One no until you get the correct answer

[@xOxAdnanxOx]

EricYyt Zero bananas because you only have oranges and apples in your hands.. I am thinking to take this Putnam test

[@sahazmarkk5624]

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.

[@dangomangothe1941]

I feel this so much, just having a maths exam a few days ago..

[@sahazmarkk5624]

@@dangomangothe1941 I hope that it went well xD

[@dangomangothe1941]

@@sahazmarkk5624 oh god as an atheist I hope as well

[@sahazmarkk5624]

@@dangomangothe1941 lmao, good luck for results

[@Arcessitor]

@@dangomangothe1941 cringe

[@clone2255]

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!!!!

[@kuolich287]

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 :(

[@alejrandom6592]

Nice

[@JUSTREGULARSCREAMINGAAHH]

Same with me and I'm 11!!

[@jan-pi-ala-suli]

👏👏👏👏

[@dolichakraborty6020]

Bt Putnam p1 is easy af

[@Josealock]

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.

[@attempt58]

Having eyes is a blessing.

[@Josealock]

@@attempt58 True

[@beybrain7896]

@@attempt58 And a brain to visualize with

[@evilhutdug4665]

@@beybrain7896 nothing really matters without the brain

[@coconuutz1892]

@@evilhutdug4665 well yes, as without a brain you have no conscious

[@rushilkumar5258]

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

[@Fr1nc3sc41]

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.

[@coolnoah8183]

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

[@ABaumstumpf]

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.

[@z_vizo4594]

Not surprising you're an Indian (its a compliment, no negativity intended)

[@stevanhaire5300]

@@z_vizo4594 Smart Bois

[@husseinmohammed1431]

Teacher: there will only be 3 questions Me: thank god Test: 1,1A,1B,1C, 2, 2A, 2B, 2C, 3, 3A, 3B, 3C

[@Anikinoro]

@Angel Buceta this isn't Instagram

[@Anthony-tp1md]

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

[@grada.r5049]

@@Anthony-tp1md more like 1 a b c d e f etc. 2 a b c etc. 3 a b etc

[@somewhat_human]

Test B-Sides bottom text

[@kd204]

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.....

[@caitlinphillips8243]

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.

[@TheRealGuywithoutaMustache]

Imagine coming home tired from learning math at school, only to find this in your recommended.

[@kingdinodragonite3470]

Why can’t i see your sub count?

[@EAOO]

@@kingdinodragonite3470 cause ur bad

[@mrgoose3453]

Everywhere I go I see your face 😂

[@gamercatt1235]

Heyy

[@富冈义勇-l7u]

This is the first time I see you without 100 likes

[@Galactic_15]

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

[@kukokeko]

truly. where was this guy in 6th grade?

[@seal2560]

@@kukokeko Where was this guy during my entire schooling career (so far)

[@valediction9174]

facts bro why can’t teachers be like this

[@Forward.4]

Exactly. Teachers should be taught how to teach first

[@smirfbroil6934]

@@valediction9174 ;( we getting there, but teachers still payed like shit and not actually taught how to teach, just to show

[@TudorLaurini]

what a beautiful mindfuck

[@paxera2913]

xD

[@Malik-im8zg]

I changed this so you will never now why those people are crying

[@minglei779]

@@Malik-im8zgchill brub

[@thenumberfour6455]

@@Malik-im8zg you do realize that "useless comments" make up 99% of youtube right?

[@abstrakt8709]

The Number Four too true

[@cheese5065]

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!

[@joshyoung1440]

What do you mean seeing this video as a write-off?

[@shanedsouza189]

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".

[@momgay2118]

This is not for average university students

[@ElusiveEel]

​@@joshyoung1440 missing prereqs I'm guessing, I'd do the same if I saw a abstract algebra video (I only recently learned what group, ring and field mean, but am prioritising linear algebra)

[@elijahcole6786]

High school teachers be pulling this out then saying “This is a college level class, it only gets harder from here”

[@azdirtnaper]

TRUEEEEE

[@cheesefries7174]

💀

[@thegrim418]

That's actually a great idea. April fools will be brutal next year.

[@thedarksaber]

@@thegrim418 oh no

[@mosio.2504]

My math teacher did a huge ass equation and said "Its primary school knowledge" I don't even know how to deal with fractions

[@nicholastorres603]

teacher: im just gonna skip this question, u guys should have learned this last year

[@atikshsingh1598]

teacher last year: im just gonna skip this question, u guys should learn this next year

[@unknownvulture6189]

@@atikshsingh1598 😂

[@classymuffin4589]

Why is this situation so damn relatable...

[@rithanipriyanka2393]

teacher who taught us the previous year : I'm just gonna skip this question, u guys should have learnt this last year

[@mattjohnson4013]

@@rithanipriyanka2393 teacher: this ones self explanatory

[@ADeep007]

50% chance. It either does or it doesn’t. Problem solved.

[@nikj1178]

That's not how this works, that's not how any of this works!

[@thevigamerpixerlator]

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)

[@krakatoadude4231]

Let's imagine a world where everybody gets the irony

[@ADeep007]

Krakatoa Dude congrats on taking a post too serious. You win.

[@lightskinche]

@@krakatoadude4231 And then we have that one guy...

[@QuantumDivergence]

Wow, the animation, and music, the way you explained all of this. This is a work of art. Well done.

[@matthewganun4444]

Imagine taking this test only to see some kid start flipping a coin

[@TheBrickagon]

😂😂😂😂

[@muhammadumar8903]

I'd defo start laughing at him and myself

[@nataliegrayhandle]

Gotta be creative to figure it out

[@onlygrumpycat8380]

Whenever you realize it’s not multiple choice😰

[@luketaylor1305]

@@kellycong8388 i think he understands the joke mate.

[@MaxMiesen]

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.

[@monsieurbobblehead3854]

Yeah

[@connorschultz9022]

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

[@frostflakejr6324]

@@alycias7345 yes it does, atleast for me.

[@frostflakejr6324]

@@connorschultz9022 I know it's really sad to see, and to top it all off the teachers most of the time do.

[@GoonCommander]

Why teach one class, When he can teach the world with his KZbin channel.

[@non123y5]

I probably watched this 100 times Now i have started to understand what an tetrahedron is

[@nusretakbulut7159]

😂😂😂😂

[@iqbaltrojan]

a 3d triangle

[@non123y5]

Ahhhh!This was suppose to be a joke

[@malikhafez8056]

HAHAHAHAHA

[@the_rover1]

I still wonder. what is it actually? :|

[@TheSurprises711]

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! 🥰

[@Jj-gq3sl]

Him: Explains hardcore math What I learned: ah yes moving lines inside circle very nice

[@salwaabdullah1682]

LOL😭

[@erikhalvorseth3950]

Youre not alone Sir. Still I wish I could have had a math teacher like him

[@Slekejkwls-1819]

Same

[@NeelTigers]

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..

[@ahnrho]

Damn. I remember when 3blue had fewer than 200k. Wasn't too long ago, either. How it's all grown.

[@sinan.7328]

Teacher: "The test won't be that hard." *The test:*

[@bluegamer07]

Bratans Bratuchas 1.7k likes but no comments?

[@sinan.7328]

@@bluegamer07 yes, whats up with that?

[@bluegamer07]

Bratans Bratuchas strange.... well whatever I am glad to be the first one I guess lmao.

[@sinan.7328]

@@bluegamer07 it isnt strange at all I bought 2500 likes first then the other 200 came by themselves

[@MK-sc9le]

Bratans Bratuchas why would u buy likes though?

[@ApenstaartjeYT]

Girl: I don’t get why he doesn’t get my signals Her signals:

[@lunaa9512]

lolllllllll

[@centralprocessingunit2564]

AHAHAHAHAHHAHAA

[@momov4060]

damn I didnt think id find something this accurate out here

[@manifestationhappiness705]

Lololol

[@omniyambot9876]

G: he is cheating His boyfriend:

[@meingutername2158]

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.

[@BurgoYT]

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!

[@enricoiraldo9057]

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

[@anasmaher4783]

I swear i do 1 plus 1 and things like that on calculator

[@suk6556]

me.

[@olegdobinda8354]

That’s just sad 😦

[@Mike_Toreno]

6 divided by 2? It's so easy lol, It's 12 *Checks in calculator* Oh...

[@TheBrickagon]

I once got 9,90 points out of 10 on a test just because I wrote 6/3=3 😂😂

[@m1-]

I literally have no clue what hes talking about, but it sounds smart

[@sslasherwolf1]

U know something wrong with a text when the smartest kid say what is this

[@bluelegion9812]

Me too, took half the video to ask why im even watching this

[@philippezevenberg1332]

issa pyramid in a sphere.

[@jaydencoffman1856]

Well it a test. I think

[@somedude2662]

*SMORT*

[@cheesiesticks]

He’s literally solving the meaning of life and I’m trying to make sure that 3+4 is 7 just in case

[@ea8455]

Using two calculators because you don't trust the first one

[@ahmedkhaled581]

@@ea8455 😂

[@jonathan0225]

@@ea8455 was looking for this comment, and was not disappointed. 😆. A man of culture indeed.

[@karlspasst2235]

Enes Akbulut you cracked me up HAHAHHAHAHAHAHAH

[@raydarable]

Same.

[@tundraxd4896]

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.

[@TheSteinbitt]

But you need to know the rules before you can play.

[@sknn]

*In class:* 2 x 2 = 4 4 ÷ 2 = 2 *In test:* The circumference of a circle is 92cm, the radius of a circle is 83cm. What is in my back garden?

[@dsdsspp7130]

dirt

[@hue5693]

The Demon King Stan

[@lilpurmp4981]

Lol Advanced Placement is just like that

[@ghexhsdhujvcfbsdhucvrej5452]

*the real answer*= 25²

[@cesarperezargota]

Catherine x The area of a sphere can't be 92mm. Smh.

[@Flow86767]

“Take a moment to digest the question” Me : *What is a tetrahedron?*

[@Silk0926]

So true

[@adeenala]

And now Im dead thanks hahahaha

[@ariwang8613]

If you're actually wondering it's a triangular pyramid with 4 faces lol

[@Flow86767]

Ari Wang Thank you kind stranger!

[@_____......_____]

U shouldn't be here .... 😀😀

[@RingtoneCentral]

*In class:* The solar system has 8 planets *In tests:* exactly how many stars are there in the universe

[@manuel-no5zb]

you have spoken the truth

[@pao2725]

Probably 24 stars

[@masteryooda9087]

I actually don’t know lol. Something like 2,000,000,000,000 x 100,000,000,000

[@slattypatty9982]

Nova nah maybe like 17 24 seems like too much

[@pao2725]

But why are we here just to suffer? Hm i guess 17 is more scientifically possible than 24... Thanks

[@owenbechtel]

I am taking a Putnam exam prep seminar and this problem was on our homework for this week. I solved it a few days ago. My solution wasn't quite as elegant as the one in this video; I used a triple integral to find the average area of a spherical triangle, making use of a symmetry in the "area of a spherical triangle" function to avoid having to actually find a formula for it. In hindsight, I could have made use of even more symmetries (specifically, the fact that there are always seven other triangles that add up to the whole sphere), which is more or less what you did. My solution: When we choose three random points on a sphere, we get three random variables that we can use to calculate the triangle's area: θ₁ = angle along arc from point A to point B θ₂ = angle along arc from point A to point C ϕ = angle at point A between the two arcs All three variables are in the range [0, π]. They are independent with probability densities sin(θ₁)/2, sin(θ₂)/2, and 1/π. Let Area(θ₁, θ₂, ϕ) denote the area of a spherical triangle, where the area of the whole sphere is taken to be 1. Note that Area(θ₁, θ₂, ϕ) + Area(π - θ₁, π - θ₂, ϕ) = ϕ/2π, since together these two triangles fill up the region between two meridians ϕ radians apart. The average area of a spherical triangle is ∫ ∫ ∫ (sin(θ₁)/2) (sin(θ₂)/2) (1/π) Area(θ₁, θ₂, ϕ) dθ₁ dθ₂ dϕ = (1/4π) ∫ ∫ ∫ sin(θ₁) sin(θ₂) Area(θ₁, θ₂, ϕ) dθ₁ dθ₂ dϕ = (1/8π) ∫ ∫ ∫ (sin(θ₁) sin(θ₂) Area(θ₁, θ₂, ϕ) + sin(π - θ₁) sin(π - θ₂) Area(π - θ₁, π - θ₂, ϕ)) dθ₁ dθ₂ dϕ = (1/8π) ∫ ∫ ∫ sin(θ₁) sin(θ₂) (Area(θ₁, θ₂, ϕ) + Area(π - θ₁, π - θ₂, ϕ)) dθ₁ dθ₂ dϕ = (1/16π²) ∫ ∫ ∫ sin(θ₁) sin(θ₂) ϕ dθ₁ dθ₂ dϕ = (1/16π²) ∫ sin(θ₁) dθ₁ ∫ sin(θ₂) dθ₂ ∫ ϕ dϕ = (1/16π²) * 2 * 2 * (π²/2) = 1/8. (All of the integrals are from 0 to π.)

[@AbrarAKhan-rk1ls]

Bro, there are more integrals in your solutions then there are in the quantum wave function.

[@tobe4336]

Me after 3 mins: I understand Me after 6 mins: I understandn't

[@Hahny]

Me: after 2 seconds i understand Me: after 1 min. Im'nt understand

[@SPlompie]

Damn this is underrated

[@nickbilly7329]

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

[@romilgoel4191]

Did you understand ?? *Yesn't*

[@Rookie1706]

Ye

[@pic5637]

What I learned from this video: 1.) simplify the questions you’re being asked 2.) ask simpler versions of the question 3.) If you don’t get it right, it doesn’t mean you’re not smart. It just shows you what you still don’t know yet. 4.) it doesn’t take away from your Value as a human

[@draggin]

I think the last point is the most important to remember

[@OmerMD]

@@draggin I damn agree

[@sad_hedgehog]

aw.

[@calvinhobbzz9787]

I'm gonna start writing that as an answer on my exams. "I still don't know yet"

[@ArashArfaee]

You don't know it, probably because you are not seeing the right angle to look at it. I think that is the main lesson he is trying to teach.

[@AnupSingh-kw3ww]

Imagine solving questions like this with just pen and paper.

[@z.e....3175]

You write and scribble.

[@pommes1287]

@@z.e....3175 and flip a coin

[@lukeskywalker691]

This is Mathematical Olympiad

[@pin2398]

For eg.. JEE

[@AnupSingh-kw3ww]

@@pin2398 I'm preparing for the same ; )

[@EvilNinja182]

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

[@remy629]

As a wise turtle once said..... “I don’t know”

[@aulalivre5481]

Nem eu.

[@DP-ot6zf]

If a turtle said that to you, it's time to check your meds.

[@TaranVH]

this video slowly blew my mind.

[@ChipterLP]

Heres a problem for you Taran, say if you have 104 keys on a keyboard, how many macros could you bind if you could press 10 buttons at once to make a shortcut.

[@TaranVH]

Answer: Nice try. Even if you could remember them all, it's impossible to accurately press down 10 arbitrary keys simultaneously. Even two keys simultaneously is a bad idea, unless one of them is a modifier key. If it's macros you're after, a secondary keyboard is the way to go. In that case, more than one modifier key at a time is usually inefficient. Also, WIN and ALT are dangerous under most circumstances. Therefore, only CTRL and SHIFT remain. Therefore, the most macros you can safely get out of a 104-key keyboard is: 104 - 8 modifier keys x 3 (CTRL, SHIFT, and unmodified) = 288 macros. 384 If you include the double-tapping of a single key. (Tapdancing) Of course, it's easier just to add another keyboard rather than use modifiers in this way, which is, of course, why I have 3 keyboards and counting. Yeah, totally took the bait on that one.

[@ChipterLP]

Try binding U +2 +3 +5 together, tnt should work as a trigger if packed densely enough (and if you use egg shaped warheads). Heard Cesium is pretty common in the trigger aswell.

[@Michael-xm4ux]

Slow blowing is the best

[@CoolJoe330]

Daddy Taran

[@iceborneuprize3998]

I must be doing something right to have gotten this on my reccomended.

[@OKayD3N]

Nope you have anime pfp

[@james68279]

For sure it ain't spelling 😏

[@OKayD3N]

@@jesse406 ok.. you’re subscribed to “dloow”

[@christiancy2514]

@@OKayD3N wtf do u have against people who put anime pics as their pfp? they just like anime

[@OKayD3N]

@@jesse406 What’s the issue with me being subbed to Carson?

[@JefffMocha]

in 1D, the 'circle' is a line segment. Imagining point A is fixed, point B could be closer to the center or closer to point A. if B is closer to point A, the center is not contained. if its closer to the center, it is contained. since B could be on either side of the center, and the center splits the line segment into 2 equal pieces, the odds are 1 in 2. This aligns with the pattern found in the 2D and 3D cases, where the probability is 1/2^D where D is the dimension.

[@radian2.012]

Me watching this: *"Hmm yes, tetrahedron."*

[@justaman7124]

Hahaha

[@eddiemartinez8277]

Bro that was the moment when i realized "yea i shouldnt be here"

[@Royal-sp9pb]

exactly my reaction lmfao, this comment made my day

[@asianalliancebs6474]

hmm yes, 10 times 12 is 120

[@toneasyy]

Bruh exactly lmao

[@antihero8214]

teacher: cmon guys i taught u this

[@dharmang]

Haha yes fucking teachers be like "Common peeps i just literally taught you THIS exact problem yesterday"

[@Quarkee]

us: Noo, you taught the nerds that. The rest of us were busy raising our hands, waiting for our turn to ask for help..

[@luukabrassart7635]

You had this 3 years ago...

[@anuronchakraborty1202]

Man the solution was amazing ... Although speaking as an undergrad math student I swear I wouldn't have understood it at all without the fantastic 3D visuals

[@Cuumerr]

Good luck with ur career

[@steamyninja8881]

R u a masochist?

[@cotton3399]

@ً bruh he shortened undergrad on purpose

[@adriano760]

@ً ????

[@ayanokoji5594]

@ً math doesn't require grammer so gtfo grammar Nazi

[@Ajbolt89]

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!

[@mynameisjeff5397]

You know shit is real when the kid with photographic memory starts re-reading his notes

[@tShuka_]

*god help us*

[@arandomcowjustchilling4237]

@Lil Quack Satan has left the chat

[@jasongrenbox6997]

Wait.. then whos left?

[@mynameisjeff5397]

@@jasongrenbox6997 Zeus?

[@keanux5906]

@@mynameisjeff5397 Zeus has left the chat

[@day99988]

teacher: “no calculators for question 5!” the question:

[@Ryan-wp6vr]

He did all of this without a calculator...

[@parallelogrum7967]

@@Ryan-wp6vr Yeah he did, if you exclude the graphing software

[@oscDaBeast]

@@parallelogrum7967 that was for the video not for the answer

[@joeyhardin5903]

i dont think a calculator would help you with this question

[@hendric6149]

even with calculator i wouldn't even know how to use against this question

[@DBJ99_]

Me only a few minutes into the video: “What’s a tetrahedron?”

[@casperthegamer7176]

Not related but go pack go

[@DBJ99_]

@@casperthegamer7176 hell yeah GPG!

[@frds_skce]

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

[@OsinakiKun]

I am so not understand any of this... But I still watched

[@bobcostas6272]

Build more pylons

[@wren5291]

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👍🏼

[@h4brid992]

Professor's: Put's effort making a hard question Me: **Leaves it blank**

[@cozmos1553]

He'll be sad

[@user-bz1xk3pm2v]

Oh I see what you did... your pfp

[@mabo_lombo1533]

Profesor: (ur profile Pic)

[@mateusribeiro9384]

My monography be like

[@Crazylom]

Put is You made a _greeeeat_ mistake

[@dizzy212]

Dawg why did the KZbin algorithm send me here I’m dumb asf

[@ez-boys4268]

Literally was watching highlights of football and the next vid was this

[@kayymini]

Felt this😭

[@stfuernie]

fax im only tryna listen to Carti snippets

[@lij9724]

@@ez-boys4268 i was watching highlights of football to

[@localdreamer13]

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.

[@nickh29]

Somewhere between 0-100%. Looks like I got it right

[@1brainonsteroids244]

um not negative 1%

[@masonkane5884]

partial credit

[@magosexploratoradeon6409]

@@masonkane5884 in this test I consider that a godsend.

[@jessechalif2428]

Idiot you don’t know how to do math

[@jessechalif2428]

@@nw3473 r/woooosh i was making a joke by pretending to not get the joke

[@jorgerivera5003]

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

[@ankit_singh2704]

Me: Watching cute cat videos KZbin: So I have heard you like tetrahedrons

[@andreasfDE]

Your cat watched this video about tetrahedrons.

[@momgo6533]

Andreas F they’re only one step closer to world domination

[@Steven-nq7fx]

CreamHeroes? I know it's cringe, but I'm just curious

[@justhingalit9780]

Same HHAAHAH

[@jonathanshapiro6593]

I am c a c k l i n g

[@awesomekb3065]

Me at school: "ugh maths is boring" What I watch when I go home:

[@beangobernador]

it boring cuz u too slow git gud noob B) my PB: 7 minutes 38 seconds 12 milliseconds git gud

[@itsatrap3703]

Awesome 🤣🤣

[@itsatrap3703]

@@deleted-user-82u3ht92 Sad but true..

[@butcherpete9252]

@@beangobernador tf is you talking bout

[@Hamsters_areCute]

@@butcherpete9252 LMAOO

[@abdullahdaone]

Took me about 4 hours to fully understand the question Then I realized that the actual question was for a sphere

[@aidenchoe4971]

@Barney hi there that's not a probabillity

[@XandiXDs]

Barney hi there A circle doesn‘t have volume 🙃

[@Jayden-ds1xz]

he meant area, but yeah thats not probability

[@isaacgaleao]

@Barney hi there you actually don't have the tetrahedron volume--

[@Ashborne002]

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

[@pidgy8927]

I like math when it's simple and straight forward, with set in stone rules I can keep in mind and follow easily. But then there are these confusing things. Things you actually have to think about, and that's where I start to fail. Because while I get good grades usually, I'm actually stupid.

[@Raven-bz8kl]

@Si0NE thats the most intelligent thing ive ever heard somebody say

[@queenkoko8686]

I agree. Though it's satisfying to figure out confusing things once you understand the foundations for those things.

[@alexreidzero1357]

What happen when u r forced to study math by urself starting from +1 due to online class which is useless and have to solved it by urself

[@coronasir3857]

@XxZomBiE_SlaYa115xX Do you get the grades? Coz at the end of days that's what matter when it comes to academic purposes. Makes your life go smoothly. Although to succeed in life you must understand the concepts. There, grades doesn't matter as long as you're good at grasping things quickly. It's like a tricky paradox.

[@pialalmamun2453]

Man tbh with u i have to said that even if someone might be smarter as long as u work hard for the knowledge you're going to "become smarter" maybe u work more for it but in the end if u do learn it u become smarter in the eys of peole Edit: realize someone said something like that 😅😂

[@7Dok]

Me: Watching Minecraft KZbin: So i herd u leik polygons

[@eggrolltheillegal6201]

This is at the same level of some minecraft redstone.

[@Ja-sm7sz]

I was just watching minecraft then saw this

[@joleeen]

I've just watched a minecraft vid, wtf.

[@holyfknsmokesigotmymoneyup]

Timothy Moore same

[@juliourigunera9748]

Same dude.

[@ElectricYoshiHD]

Class: 2 + 5 = ? Homework: (y-1)2x-3y = 64 Exam: You have 5 apples, you give one away, calculate the mass of the sun.

[@profitmarketingandonlineea320]

ElectricYoshiHD 😂😂😂

[@vipneat7265]

ElectricYoshiHD I'm deddd 😂😂😂

[@wasqrsul8097]

😂😂😂😂

[@jonnytap]

Is this how college is like?

[@stanleylim4458]

Yup real talk. Im in engineering

[@goblinsharky]

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

[@kirankumar7923]

This is a gem. The visuals, the content and the explanation are just awesome👍. You are phenomenal.

[@piromansadran]

I swear every elegant solution of a math problem is basically a big bruh moment

[@clipkos3009]

so true doe

[@membranekeyboard781]

*when you get your test back*

[@hiro_6015]

yeah i always think for so long only to find out the solution could be found out by a third grader

[@debroopghosh7845]

Maths is really beautiful tough problems have simple solutions but complex understandings

[@rayankasam4784]

Under what circumstance would anyone be able to find this.

[@slackfazed5788]

It's all cool in the exam until the atheist kid starts praying

[@ten1162]

asian atheist kid*

[@kittenmimi5326]

@@ten1162 uhmm that might mean the apocalypse is coming

[@nicknawd7757]

That’s me lmao

[@zzztriplezzz5264]

@@قصيالجوابره-ط3ك what’s wrong with believing or not believing in god? Can people just get over it?

[@richardbernadino6449]

@@قصيالجوابره-ط3ك whether god is real or not no one knows! Doesn’t matter to much, just live a live after your own morals

[@sarimshaikh5224]

A good teacher is very important in every student's life,you are absolute good teacher 👍

[@jxllx9996]

Im out here still figuring out how to read the clock

[@clipit4503]

😂😭

[@bradbrandon2506]

I'm out here still figuring out how to read your comment.

[@bradbrandon2506]

@Andrew Young A roast of myself? Yes. A roast of this guy? No.

[@Bossix84]

It will come with time. I'm 42 and finally learned how to do it :)

[@moisteagle6556]

42 is the answer to everything!

[@kalpitahatode8596]

The horses name is friday

[@wouterfransen9771]

Kalpita Hatode i remember the answer but i have no idea what the question was

[@danceartist8203]

@@wouterfransen9771 A cowboy rides into town on Friday, he stays for three days and leaves on Friday. How is this possible?

[@wouterfransen9771]

Dance Artist thank you

[@bongojongo7380]

@@V-xox well then whats on second?

[@Ferb747]

Kalpita Hatode iCarly

[@furikusu]

Lecture: 1 + 1 = 2 Homework: 1 + 2 x 3 = ? Exam: The train's velocity is 160mph and an apple rolled on the ground with a distance of 2.35 meters, calculate the mass of the sun.

[@alvarezz7986]

Mass weights around same as deez nuts

[@Anyting9OnTopGrrr]

@@alvarezz7986 the sun aint that light my bro

[@BadUsernameKing]

Lmaoooo this comment section

[@BadUsernameKing]

@@alvarezz7986 bro how did you get a mass of almost 0 as your answer??

[@freddyman7967]

This why I never did homework

[@kerrywsmyth]

When I was in college we had a “project” that was due in a week. We were tasked to write a simple program that enabled the user to enter three, 3-coordinate points in space and have the output give you the area of the triangle. I solved it in one day and my answer was given on a single side of a single sheet of paper. The following week, all my classmates turned in these huge packets with dozens of pages in them. The following Monday the professor gave back all the graded papers except for mine. He held up my single sheet answer and told the whole class that their work was shit and that this is how your answer should look. I felt like a million bucks.

[@nalat1suket4nk0]

Lmao

[@xxneweraxx7422]

tbf ur class really was stupid then, this is incredibly easy

[@sunnyk7893]

Wow nice job, what was your solution

[@xxneweraxx7422]

@@sunnyk7893 given that the area or a triangle is (base * height)/2, all he did was probs calculate the vectors using the coordinates of the points given, to deduce the base and height of the triangle, and then output it, it's really nothing complicated to code on top of that, this is more logic than actaul coding

[@kerrywsmyth]

@xxNewEraxx it requires 3 dimensional calculus, so unless you’ve taken advanced calculus of the type you only see in Engjneering or Mathematics majors in college, it isn’t that simple. I’m fact, everyone else in the course started their project with the same failed premise as you and that’s why it took them piles of useless paper and theory to attempt to solve it. With 3D Calculus it has a simple and elegant solution.

[@sebastianvazquez2242]

It feels so cool having the problem just "click" in my head as you explain it. Like you were talking about the importance of the 1/4th chance and then I just got so excited cause I finally got it

[@baserbasgut5358]

sike! that's wrong number

[@willtalscoot7876]

Last question: Are the signals she’s giving me real?

[@andib1005]

No its your mind playing tricks on you

[@oscarbustillo4451]

You really can't tell, maybe she is Canadian and she is just being polite.

[@ohyeahyeah1955]

@@oscarbustillo4451 lol

[@geoffreymystery]

Oscar Bustillo nice lol casually explained reference.

[@ahmoodaa]

Simple answer: no

[@luismanuelvera7848]

And remember: This was just ONE QUESTION. FROM A WHOLE TEST

[@M3rcuryMan]

in germany we are getting kind of used to this kind of questions. often the solutions are even longer

[@kattenelvis1778]

@@M3rcuryMan Only if you're doing a masters/phd in math in Germany.

[@erfan9749]

@@M3rcuryMan Bist du sicher!? haha

[@whateveryh2119]

@@M3rcuryMan I don't belive you.

[@beetlejuice8147]

@@whateveryh2119 actually we do, this test is hard but not extreme, our education system is hard

[@lucaciucci7719]

Years later I needed this result for a seemingly unrelated problem. I instantly remembered that 3b1b made a video on that!

[@lucaspont6659]

Yeah mate I first have to figure out what the question means lol.

[@Hi-uu7pk]

Lucas Pont I can't even read the question help pls

[@bangtanhoe5386]

LMAO I KNOWWWWW

[@jessechalif2428]

Lucas Pont idiot

[@acurefordeath]

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

[@AbdulIsik]

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.

[@shubhamtokas5995]

you're just taking the assumption that it can be cubed. there needs to be serious proof behind it.

[@minecrafting_il]

@@shubhamtokas5995 but that might be easier than the original question

[@kennethluo4934]

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

[@jordanliu9747]

@@kennethluo4934 1/2^n It's correct in every dimension. It's the proof that's the hard part though

[@loliabuzer]

I'm here to comment on how this man didn't even make a 10 minute vieo for the revenue. True passion displayed right here.

[@jpmohan96]

Is it at least 10mins?

[@smayansahu1070]

He doesn't put ads on his vids.

[@elbranlo4727]

is this bait

[@shaw5118]

@@smayansahu1070 ^

[@bobbyfr911]

there's no ads for the first month the videos up but after there's a very few ads

[@Qawa]

My take on the problem at the end of the video: Each person will have two people adjacent to them. They have a 50% chance of not being cheated off of from each, so you multiply 0.5 by 0.5. That means each student will have a 1/4 chance of not being cheated off of from both. Multiply that by 8, then the expected number would be 2.

[@AaronRichardsMusic]

Now to take it one step further, what is the probability that those 2 students will not end up not being cheated on as opposed to any other possible answer.

[@iamthinking2252_]

huh, all I got was that for 3 students... let's say student 1 looks at student 2 - If student 2 looks at student 1 (1/2 all cases), then student 3 will never be cheated off (expected number 1) - If student 2 looks at student 3 (1/2 all cases), student 3 looking back at s2 means s1 never cheated off (1/4 all cases) - s3 looking at s1 means everybody spied on. 3/4 chance of having 1 student spied on, expected is 75% for 3 students. Can't have 2 students not spied off, as who can the third student spy on (nobody)

[@wren_.]

i got 1.2. first, I drew out all the points in a little octagon and randomly selected a few to circle. I reasoned that you can’t have three people circled in a row, because then the person in the middle isn’t able to spy on anyone. this means that you cannot have 5 people not being spied on, since somewhere on that octagon, there will have to be a group of 3. two circled people in a row is allowed though, meaning you cannot have any more than 4 people not getting spied on. that means that there are five possible cases. One where everyone is being spied on, one where one person is not, one where two people are not, one where three people aren’t, and one where 4 people aren’t being spied on. taking the average of all five of those possibilities gets you 1.2, or basically one. therefore, the expected amount of people not getting cheated on is one.

[@holo23]

2 is correct. You can express this in mathematical terms by saying X_i is the indicator random variable that the ith student has no one spying on him, with the distribution Bern(1/4). Then E(X) = E(X_1 + X_2 + ... + X_8) = 8E(X_1) by linearity, therefore 8/4 is 2. Anyone that has a little bit of probability theory knowledge can solve this. However, that wouldn't be fun, as the video specifically stated that shifts in perspective is what makes solutions elegant.

[@riccardosarti3234]

@@wren_. I'm afraid you're doing it wrong... each of the cases that you calculate can appear in different ways, that also need to be calculated if you want to procede this way. For example, if A1...A8 are the eight students, there are 4 ways that exactly 4 students are not spied on (which is the number of ways to choose 2 pairs of adjacent students - the not spied on - and the other 2 pairs of adjacent students - the spied on, i.e. not spied on: (A1, A2, A5, A6), (A2, A3, A6, A7), (A3, A4, A7, A8), (A4, A5, A8, A1)). Note that this was a simple case, because once you choose the spied and not spied students, all the graph is automatically determined, but in the case of 3 not spied on students, you have some freedom in selecting how the students are lookin at the others... Briefly, this way of calculating is insane and definitely not the elegant way suggested by 3b1b! See other comments that prove why 2 is the expected number (each student has a priori probability of 1/4 of not being spied, thus on average you expect 1/4*8=2 students. Try with 3 and 4 students by listing out all the possible 8 and 16 cases respectively and you'll be more convinced!

[@MrF18]

Imagine if a kid asks how you would need this in real life.

[@joshuaoconnor8505]

How you would need this in real life?

[@mihir6181]

@@joshuaoconnor8505 To brag 😅🤣

[@kritedz]

@@jootpepet dude he aint an idiot for making a joke

[@onyxflicku610]

They would get shot on sight

[@SilverShark8554]

Maybe if you want to be a physicist

[@victorvila1056]

Bruh why am I so addicted to videos that I can't understand???

[@disadadi8958]

And what part didn't you understand on this video? I mean the math wasn't that complicated at all.

[@eduardoizquierdo309]

Because you have an anime profile pic

[@daraobongisonguyo]

@@disadadi8958 stfu

[@mikeztecha3808]

Because people have always had an interest in understanding things they can't, that's why we're where we are today

[@tb_mrpanda1908]

@@disadadi8958 😳 you good bro

[@ninjabunny101]

i don’t understand a single word you’re saying but for some reason i can’t stop watching

[@pardeepgarg2640]

Me too He makes so good that we can't stop

[@maybeso8513]

lmao same

[@alejrandom6592]

7:07 this moment is what I love about math. That moment in which suddenly everything clicks and makes sense. It's just beautiful.

[@Darkmage1293]

"Some of you with some multi-variable calculus under your belt..." "...uh....yeah, I got tons of that. Need a bigger belt even."

[@zentempo7902]

Yeah same i need a huge belt for all of the multivariable calculus

[@lamarjackson9736]

😭😭😭😭

[@jamespeck10]

um

[@Alex-gp5xl]

In class: whats a circle Homework: what's a circumference Test: the book is 3 inches tall what's the name of the author

[@alimustafa4753]

Alex Yan well you have to take into account the length of the letters

[@grieferjones2237]

haha get it it’s funny because i hate school please give me likes

[@hipeople9856]

Well... it could be Cassandra Clare, Rick Riordan, or even J.K. Rowling. We need more information to solve this problem, such as what is in the last room on the left in your house 😂.

[@Elliephant_]

I did the research, it’s probably either Stephen King or George RR Martin.

[@drago5801]

Definitely Lev Tolstoy with his “War and peace”

[@xatnu]

Around 7 minutes in I just had to pause the video and start laughing out loud because I realised what you were about to do. Brilliant. It's just so elegant!!!

[@coscorrodrift]

Dude same, I was like "fuck no mate that's too much for me, this shit's SMART" YOOOOO these are the worst problems, the ones that are a massive Ooooooohhhhhhhhhh AFTER you've had it explained. so clever, the people who make up these problems are some smart motherfuckers lmao

[@AtticusFinch65]

around 7 min? i realized 0.1 seconds in

[@calvinlin5753]

Try 2005 A6 (paper at the start of the video) > Let n be given, n 4, and suppose that P1;P2; : : : ;Pn are n randomly, independently and uniformly, chosen points on a circle. Consider the convex n-gon whose vertices are the Pi. What is the probability that at least one of the vertex angles of this polygon is acute? There's a smart way to tackle this problem, similar in idea to this video.

[@joshhill4760]

When 3B1B suggested to break the problem down to just the lines and not the dots, at 6 mins, the thing about the 4 arcs, and thus the 8 parts of the circle just clicked and I had it, such a good feeling.

[@DMSG1981]

Kyle Horne, you're such a hero.

[@kaygur._.]

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.

[@georgefarah9214]

Fastest 3 things in the universe: 1- light 2- universe expansion 3-me clicking on a 3blue1brown notification

[@SupLuiKir]

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

[@Kelly_Jane]

· 0xFFF1 I was going to make a similar, but less considered point.

[@AtticusFinch65]

· 0xFFF1 why does it depend on how far apart two points are? And what is the semantics of your hexadecimal username?

[@alexnope2180]

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

[@jongyon7192p]

Alex Nope yeah the universe is expanding faster than the speed of light, pretty much

[@SleepySeal121]

As someone with a creative writing degree, this went WAY over my head. And yet it had me on the edge of my seat.

[@bobcostas6272]

“Creative writing ‘degree’” lol

[@RyanKOnk]

"creative writing degree" lol

[@BlackDragon-tf6rv]

What is that?

[@Tyrosine0910]

@@Inkripted Why not?

[@BadUsernameKing]

Lol

[@antrikshsharma8793]

Well, only if I had a 3D Imagination with scales and graphs

[@gabeengel8142]

Antriksh Sharma that’s big facts. If you had the stuff he uses to explain it as tools it would be a heck of a lot easier

[@3User]

Its just not fair, some questions just can't be solved mentally, specific tools are required.

[@juztjip6802]

Well if you know that the answer is 1/4 in 2D you take the square root of that giving you 1/2 in 1D, now (1/2)^3 giving you 1/8 in 3D.

[@bogdansavianu6658]

Nipun Sharma There is a formula. Let's take 2 triangles whose angles are the same value (I don't know how to say that in English, maybe similar triangles but idk) and divide one edge by the corresponding edge of the other triangle and the result is k. Now if you divide the area of the first triangle by the area of the second triangle, that's k^2. If you go even further and make one tetrahedron out of each triangle and divide their volumes, that's k^3.

[@glorytofathersonandholyspirit]

In class: 1+1=2 On final: The Putnam

[@Nikola.Tesla369]

Ahhaha That's right

[@seanwang1540]

Think your class taught how to prove 1+1=2

[@thagabagoop6115]

Dude, idek what the Putnam is

[@thenotoriusbp]

Taylor Blair the whole entire video: am i a joke to you

[@thagabagoop6115]

@MrBigEnchilada thnx

[@Jake-ds9sw]

Me who forgot how to do long division: Interesting...

[@ubberJakerz]

He didn't even use long division here tho?

[@baguettegott3409]

tbh I forgot long division as well. Multivariable calculus, sure, but don't expect me to actually *calculate* anything lol

[@imnotfunny2995]

As a 26 year old, I just relearned how to do long division about a month ago.

[@Morizzoo]

Imma be honest, I have never even heard about long division

[@kawosdhdos]

@@Morizzoo how old are you

[@davudpivac]

"how you might have stumbled across the solution yourself" Didn't know this was a comedy channel

[@devonpederson919]

Especially for this problem

[@aceott8690]

Devon Pederson you’re supposed to type “LOL” not make the joke worse

[@yushpi]

😂😂

[@enjerth78]

I figured it out before he introduced the 2 dimension example. All points of the sphere are equal and so the average of random distribution cuts the sphere in half 3 times over, the same likelihood as 3 heads in a row. Doesn't work with 5 points unless working in 4 dimensions, dividing each vector of the dimensions, which is 1/16th or 4 heads in a row. I don't have a high school education.

[@yushpi]

@@enjerth78 how old are you? Where r u from?

[@derekfordyce9]

I took this exact test in college. I remember this question and it's great to finally see the solution.

[@KejriwalBhakt]

And what was your score? Has anyone scored 100 percentage?

[@derekfordyce9]

@@KejriwalBhakt haha, 0

[@joechen8082]

Math questions be like: Jimmy has 21 oranges He is 2 hours late for school Solve for the mass of the sun

[@kkaaii177]

Not really

[@proddamien]

@@kkaaii177 it be like that

[@dingyworm]

okay but we can actually calculate the mass of the sun despite the unrelated information given

[@josephikrakowski6526]

@@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

[@jouljoker9684]

@@dingyworm yes of course