The hardest problem on the hardest test

[@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😂

[@bartbroek9695]

I know right? If you're gonna assume the axiom of choice, at least make it explicit.

[@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.

[@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

[@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.

[@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

[@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.

[@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

[@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

[@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

[@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?

[@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

[@wavy582]

How’s the degree going?

[@matthewgeary1811]

@@wavy582 I graduate in May 🙏

[@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

[@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

[@夜遊1128]

This is the first time I see you without 100 likes

[@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.

[@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)

[@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

[@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

[@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

[@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.

[@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

[@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

[@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.....

[@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.

[@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

[@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...

[@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

[@QuantumDivergence]

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

[@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 😂😂

[@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

[@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!

[@Flow86767]

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

[@Silk0926]

So true

[@livingivr]

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 .... 😀😀

[@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]

@@3ka-MC Sad but true..

[@butcherpete9252]

@@beangobernador tf is you talking bout

[@Whatever37393]

@@butcherpete9252 LMAOO

[@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

[@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.

[@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

[@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

[@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

[@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.

[@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.

[@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.

[@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.

[@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👍🏼

[@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

[@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.

[@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!

[@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

[@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

[@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

[@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

[@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

[@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.

[@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 ; )

[@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.

[@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? :|

[@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

[@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?

[@lucaciucci7719]

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

[@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

[@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*

[@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

[@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! 🥰

[@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.

[@JohnSmith-dm1ev]

It’s weird how I’m an expert at math as long as the instructor keeps talking.

[@phoenixx888]

Wait so can u get correct answers?

[@vulcan792]

No contento con tener un restaurante o con ese cuero cabelludo envidiable

[@liveen]

John, that's what it's like to be taught by a good teacher. If you don't always feel like this when learning, or like it's an adventure or super fun challenge, and you just HAVE to keep going, then you aren't learning in the way that works best for you, and there IS a way for you

[@adrienpinder1406]

Nah word lol

[@preshenkumar5632]

@@liveen Hey LiV do since im in grade 5 do you have any tips on studying subjects?

[@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

[@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.

[@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.

[@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

[@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.

[@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.

[@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?

[@ChosenPlaysYT]

4 minutes in and I’ve concluded that I am not gifted mathematically lol it’s crazy how smart some people are.

[@NovaWarrior77]

hey! i'm the equivalent of the police for people who doubt their own mathematical ability. you can do it!

[@NovaWarrior77]

@@vivek-zo2yy Just have fun with it. You will learn more than you think.

[@dagmwitmelkamu9470]

me too

[@mostlikelyaperson6940]

No way i just gave up after 4 minutes as well

[@giladkay3761]

He actually explains it better towards the end of the video

[@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.

[@parth-the-artist]

My friend told me about this exact problem about a circle and three random points. My argument is that if you take a triangle ABC inscribed in that circle such that it contains the center, consider points D,E,F that are diametrically opposite to A,B and C respectively. Now, for every such ∆ABC, there exist three triangles named BDC, AEC and AFB and they are uniquely attached to this triangle ABC there is no way you can get the same three triangles with different such center containing triangle Hence there are three no center containing triangles for every center containing triangle so probability should be 1/4

[@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

[@verycool7424]

Schools: "Write that down, write that down!"

[@mateuscr1915]

lol

[@sameersamrat3568]

CHARLES THE FRENCH:😂👍

[@jayveeaurea9091]

OH HELL NAW!😭🥲🤣

[@rocketmanfossel1174]

Nope. As long as my school wants high grades from students to show off and bait parents, they ain't making math harder

[@kirankumar7923]

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

[@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

[@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

[@vijayn2363]

This test is so hard that I didn't even understand the question

[@keine_ahnung_wie_der_heisst]

For me its just a asmr

[@amuffins6644]

same 😂

[@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

[@aaronherman1056]

I'm kicking myself. I tried thinking about this on my own for a bit, but I couldn't get my head around it even in two dimensions. So I simplified this problem down to ONE dimension and then understood it perfectly: given an interval and two random numbers within the interval, the center of the interval is only between the two random numbers if they're on opposite sides of the interval, which has a probability of 1/2. Then I couldn't figure out how to generalize to multiple dimensions, got lost, tried to think about properties of triangles, and thought, "Now I'm going to watch the rest of the video and realize I had a really hard problem by the neck and couldn't do the final step" - and it was true! Three points on a circle contain the center if two of the points are on the opposite side of the circle from the third! Four points on a sphere contain the center if three of them are on the opposite side of the sphere from the fourth!

[@apshanlimbu2153]

Kid: gets 119/120 on this test Asian parents: why didn't you study

[@slimey_37]

Ya apshan, why didnt you study?

[@joshuachoi_5609]

Ummm.. true from particular parents tho.. not all I suppose

[@beforeikillyou7430]

@@joshuachoi_5609 no bruh... All of em

[@justjohnnywu4771]

@@beforeikillyou7430 yep

[@teRRmann]

Turkish parents same...

[@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...

[@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

[@anonymanonym5901]

I don't know how it's possible, but I was able to find the solution to the 2D problem after just few minutes, when I first saw it I thought "I def need to put this in 2D". I didn't solve the whole problem, 'cause I got bored and just wanted to see the solution, plus I'm in the second year of highschool and we didn't have probabilities yet. Still I'm very happy I figured out the first easier half, since in school I'm average at math.

[@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

[@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”

[@vlsparrowlv3396]

The study guide: Tom has four pillows. How many pillows does he have? The test: how many atoms are in my cat’s left kidney

[@stalinsdog679]

vl Sparrow lv and if so identify how many electrons are also in it and how fast their going

[@rjc.05]

Stalin’s Dog damn dogs are smart

[@Darkesturnover]

then solve for the amount of kinetic energy being produced

[@haxan8113]

Thus give the probability of a kidney stone forms in the next century

[@Champ_7298]

@@Darkesturnover kinetic energy is only produced by motion but i guess that could still work

[@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

[@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--

[@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

[@annablue1237]

me : * barely scraping maths* also me: i bet i could do this

[@adriannanad4675]

haven't done maths in 10 years also me: i bet i can do this with my pure primary school mathematics

[@tone-deafbard3247]

Tamanna Kareem lol same

[@a.bagasm.7253]

OnO

[@thomy2562]

@@adriannanad4675 A thing i like abaut this probelm is that you can "oraly" solve it with just almost no understanding in mathematics.

[@stevecoffman2559]

Being brilliant at maths is one thing. Being brilliant at perception/framing is a completely different skill. Good video!

[@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

[@avocados9110]

There’s no way I’m smart enough to be on this side of youtube

[@ronnie2cap728]

Big fax

[@jamal9884]

@50 200*

[@lobster5364]

@@jamal9884 *250

[@unironicirony9741]

@@lobster5364 3.5e+3*

[@lobster5364]

@@unironicirony9741 1092e+12

[@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

[@MichaLenard-mv7ek]

I've managed to solve it on my own in a very different method. Just at the beginning i want to adress that it's not a great method because it doesn't prove the concept but manages to give a "proposition" of the answer. My method involved solving this problem in different dimensions. Instead of solving the 3D sphere with 4 points, I solved the 2D circle with 3 points, 1D line with 2 points, and 0D point with one point. I assumed that the number of points would be the case because 0D point has max 1 point and line has 2. After that, for a point it was 100% obviously and in a line 50%. The only hard part of this method for me was solving the 2D version because im not very good with probabilities but after a while i realised that we just choose a random number between 0-1, and then the probability is this number squared. I then proceeded to square the average of 0-1, one half, so the probability came as a quarter, 0,25. The only thing left for me to do was notice the pattern, 0D - 1/1, 1D - 1/2, 2D- 1/4, 3D -1/8 (1 over 2 to the power of the number of dimensions for this problem)