when the author likes math

[@copywright5635]

If you were confused about Asano's Method. I Made a video covering it in depth on Patreon (it's free and public). I just posted it on there as it isn't the content I want on the main YT Channel. www.patreon.com/Phanimations Look for the video titled "Asano Method". And if you like it and want to support me... well I won't complain. But seriously, keep your money unless you really want to give it to me. Thanks!

[@PhillipAmthor]

Does this also account for the free space which cant be occupied from any sphere because it would Intersect with another sphere or is this space irrelevant?

[@MelvinSowah]

​@@PhillipAmthorthe spheres themselves are irrelevant. They are there just to represent the points we're interested in. This confused me as well: the point of making the spheres so big was to make it easier to show that the size of the domains of each point are the same, and therefore the sum of the intersections of the domains with the cube is equal to the domain of the center point

[@SK-Rocks-y8r]

It is more like the Cristal structure we studied in college

[@Wulk]

Math getting so difficult you need the power of friendship to solve it 💀

[@NiLi_]

that's called cheating xD

[@ShoreyardAri]

University math classes call it the study group.

[@dissonanceparadiddle]

@@NiLi_ that's called academia and publishing papers built on the shoulders of other papers. TRUE collegiate studies and not the high school 2 student debt boogaloo is about further humanity's knowledge. True, you learn how to learn as a bachelor, but that then prepares you to learn things that have never been known before by any one person.

[@Paulo594]

I know a lot of people that only graduated because of the power of friendship *wink wink*

[@ookjannesplanting1296]

Yea it took Newton and Leibniz working together to invent calculus

[@beast7842]

"Karma literally solves a math problem with the power of friendship" HAHAHAHA anime's power of friendship strikes again.

[@ibrahimihsan2090]

Except here, it makes total sense. It's not a power up, it's just a changed mindset.

[@blacklight683]

I read that exsactly as he was saying it, the power of friendship ship is too powerful

[@hiddendrifts]

@@ibrahimihsan2090 it's really funny how well this demonstrates the power of perspective. nothing changes, it's just two different ways of approaching a problem, one dramatically more efficient than the other

[@ibrahimihsan2090]

@@hiddendrifts You know it.

[@ultrio325]

I straight up do not remember this episode of Assasination Classroom, and I absolutely hate that I can't remember this masterpiece of an episode

[@copywright5635]

@@ultrio325 time for a rewatch?

[@detaggable9271]

ULTRIO WHAT ARE YOU DOING HERE

[@suwacco]

@@detaggable9271 what are you doing here too? (mint)

[@detaggable9271]

@@suwacco i never found an explanation for the final problem in ansakyou that i could understand so i watched this and i finally understand 😭😭

[@roylim1169]

same here bud, I was so young and dumb with shounen brain rot, I could not process this absolute marvel of math + story telling

[@noo6423]

The way karma put it was so easy to understand, second you showed the infinite lattice I immediately understood what he meant by that and it just clicked, that’s genius of the show

[@Bruhecc]

I know! Really makes me want to read and watch it one more time

[@Mutrax4706]

i didnt realise it till a little after

[@pyropulseIXXI]

There is no genius here or in the show

[@sorrynotsorry2573]

I was so lost and never understood that

[@copywright5635]

I'm sorry, it is something that's a little difficult to comprehend, especially in 3D. Try to understand the 2D example first, then move upwards.

[@kazukawasaki97]

​​@@copywright5635so instead of doing 1/2×(a/2)²×4, understanding the real area under question is just the entire lattic's /2 directly simplifies to a²/2, which is not that different in 2d, but in 3d dealing with pyramids and weird wedges, a cube is way simpler,so cool you picked this eg you not only gave me the thrikl but also the motivation to check this anime out as well

[@kinfthaderp5045]

@@copywright5635 i don't really wanna speak for others, but i think they meant the past tense, your video is a great explanation and visualization :)

[@yumyum366]

@@copywright5635 I honestly don't remember learning this and was lost the second "domain" was brought up and brushed over like it was an understood term. I remember taking Calc I, Calc II in college, and don't remember learning anything like this before.

[@K1nighty]

⁠@@yumyum366I can tell you this was not a topic in calculus 1 or 2. Maybe in higher division math classes

[@TVISE]

I never expected any show to actually incorporate any math accurately and also being related to the plot of the show. I think the author noticed this problem first, and then decided to make the entire show around it, it's just that good. Thanks for making a video on it.

[@RobinClower]

Futurama and the Simpsons are both written by a bunch of mathematicians. Futurama has an episode involving body swapping (where you can't swap with a person twice) that they wrote a mathematical proof that you need at most 2 extra people to ensure everybody gets back to their own bodies.

[@hiiprocrastinate6138]

as far as i remember in the physical manga the author said he asked someone to make a problem that can be solved with just middle schooler's math knowledge but is hard enough to be college level, still amazing that he can link the method to solving it to the characters though

[@haveiszalfaroqie1628]

First animator vs. geometry, and now a nostalgic trip back to an old masterpiece. What a time to be a nerd.

[@chilyfun9067]

more like anime vs. geometry

[@lailoutherand]

​@@chilyfun9067bro 😭😭

[@LordOfBananans]

Holy yap

[@noaag]

​@@LordOfBananansSomeone woke up under the wrong side of the bridge 😂 Jealous you don't feel included as a math nerd or something?

[@LordOfBananans]

@@noaag yez ;-;

[@nanamacapagal8342]

Absolutely love it when something as innocuous as a math problem completely shows how different characters think, not just in the way they do math but also in the way they act. BTW, final question w/answer: ASANO (Bisecting Lines) The length between points is a, and the length of each bisector is sqrt(3)a. Since the bisected points form an equilateral triangle, the area is 1/2 * b * h = 1/2 * sqrt(3)a * 3a/2 = 3sqrt(3)/4 * a^2. KARMA (Symmetry) Because the points lie on a hexagonal lattice, each domain around every point is symmetrical. Because of the symmetry of the setup and the nature of bisecting, the area closer to any blue point surrounding the "center" takes up exactly the same amount of space as the area closer to the center. For the area in question, consider adding extra red points inside each hexagon, so the grid becomes triangular. The distance between a red and blue point is the same as the distance between two blue points: a. The area of a bounding hexagon with 3 blue points outside and one blue point inside is 6 equilateral triangles with area sqrt(3)/4 * a^2, so 3sqrt(3)/2 * a. Half of that would be 3sqrt(3)/4 * a. BONUS: You can use a similar trick to figure out the volume of a rhombic dodecahedron. This solid tiles 3d space, because it's essentially the inside-out of a cube with 6 of its corners at the "centers" and the other 8 at "corners". If you tile 3d space this way you still get a grid of corners, but only half of the cubes formed by those corners also have centers. Its area is therefore 2 * the area of the cube. The edges of said cube are the long diagonals of each rhombus face, and the side length of the rhombus faces are the distance from the corner of the cube to the center. If the side of a rhombus face is a, the side of its long diagonal is 2sqrt(3)/3 * a, and the area of the solid is 16sqrt(3)/9 * a^3.

[@copywright5635]

Pinned! You noticed a similar symmetry with the rhombic dodecahedron. I'm not sure if you know this, but the shape in the video is referred to as a truncated octahedron (you can see this as it's an octahedron with the corners shaved off at 1/3 the side length). We found it's volume by utilizing the fact that it's the Wigner Seitz cell for the lattice in this example, this is referred to as a BCC (Or body centered cubic lattice). For the rhombic dodecahedron you mentioned, it's actually the Wigner Seitz cell for another very common lattice called the FCC lattice, which actually has optimal packing in 3D space. These spaces as I mentioned are very important in crystallography, so bravo for mentioning it. I'm probably going to do a short on this exact topic sometime in the near future. Very Nice!

[@jin_cotl]

You had me absolutely tweaking when I saw your equations 😊

[@Pyonner]

Yeah

[@mogaming163]

I assume for karma’s method you forgot to include ^2 for the last 2 equations of the paragraph?

[@nanamacapagal8342]

@@mogaming163 yes

[@nonbread7911]

AssClass holds a special place in my heart, thank you for explaining one of Karma's biggest flexes

[@zkte]

AssClass 💀

[@st.altair4936]

Please never call it "AssClass" ever again 💀💀 If you need to abbreviate it just say AC, though that does get confusing

[@Th3-WhOwOl3y-TrEeNiT3a]

Do not cook again.

[@detectivefischer6396]

That looks like a gay movie title

[@nonbread7911]

aint my problem none of you have ever seen it called assclass lmao

[@Gidiotic]

when the youtuber likes math

[@copywright5635]

Well I won't deny it...

[@Aliaska9816]

when the viewer likes math

[@leiii05]

The test scenes were one of my favorites in the anime bc holy fucking shit how did you make an analogy of solving math akin to FIGHTING A MONSTER IN A COLISEUM

[@rexellerainbow1173]

I KNOW RIGHTTT now every time i have a math test i keep thinking about those scenes lmaoo

[@CielArtem]

I'm way too dumb to understand any of this, but good job either way

[@OatmealTheCrazy]

Basically, find a point where no other center/corner of a square/cube is closer to yours' center (or any center) Gonna proceed for only square though. This will always be the midpoint between the two points because anywhere else is closer to one. if you focus only on one quarter of a square and draw where each is equally close, you just make a line down the middle and split it into two triangles. so, you literally only lose half of the area of that quarter, and that's true for every quarter so, the answer is half the area... or (the area)/2 in the video that's a cube with side length a so (a^3)/2 since cube area is a^3

[@mrowlsss]

​@@OatmealTheCrazywhat is the math problem here

[@greentea_DP]

​@@mrowlsss you're a center in a square, calculate area that are nearer to you more than the 4 corner of the square. Karma realize that the area that are nearer to a single corner only has a volume of 1/4th compare to his own, 4 of those corner will finally make it so it has the same volume as you, which is why in the anime he say he takes half the square and the "you" (corners) take half the square. which make it a^3(total area of a square) divided by half!

[@Taedrin]

Blowing up the dots had me confused at first, because I thought you were saying that the shape of the domain was circular/spherical under Karma's method, which is inconsistent with the complex shape under Asano's brute-force method. What made it easier for me to understand was realizing that under Karma's method, you don't have to care about the actual shape of the domain at all.

[@Bryan-ep4qj]

I was wondering about the same thing. I was wondering how the spheres can be working if there is space in-between. I just understood it because of your comment

[@ikeu6433]

I was staring at the screen for like 10 minutes before I came to this conclusion 😂 bruh I was flustered.

[@perrolmao]

because regardless of the size of a person's domain (life) it will still be a corner to someone else's domain (life)

[@hiddendrifts]

7:35 there's nothing "wrong" with brute forcing a problem, but i believe the point is how effective karma's solution is. simple and efficient, meanwhile asano's is complicated and time consuming. it's a really great message about the power of perspective, how approaching a problem from a different angle can yield much better solutions

[@MathematicFanatic]

This is absolutely gorgeous!! I am pleased I found the symmetry solution because I could not fathom the shape of the region. What a beautiful and interesting shape! And I suppose they tesselate perfectly in a sort of doubled up cubic lattice! Very very nice excellent content to watch on youtube

[@copywright5635]

Yes thank you so much! I didn't mention it, but if you look at the geometry calculation I do on paper, you'll see that the shape is actually an Octohedron with the points cut off at 1/3 of the edge length. This shape is actually super important in Crystallography and Solid State physics, as I mentioned it's referred to as the Wigner Seitz cell. In reciprocal space (or k-space), which I also did a video on, it forms what's referred to as the 1st Brillouin Zone. Here's a good video by david miller about it. kzbin.info/www/bejne/nYq7amOOgsmLp68 It's also a nice little exercise to try to prove that it is the smallest volume that can tesselate a given lattice (though not necessarily the only shape). Honestly, I think it's pretty cool that this show, which has nothing to do with math, includes such an interesting problem. Cheers!

[@Righthand_]

The fact that both of them are middle schoolers. I cannot comprehend their genius mindsets

[@sabin1999]

THEY ARE MIDDLE SCHOOLERS

[@DeadlyBlaze]

Easier solution: We know the domain is the same for each volume. Therefore the volume of one will be the total volume divided by the number of atoms The lattice is essentially two cubic lattices imposed on each other, meaning the atoms are packed twice as dense. The volume of each atom in a cubic lattice is a^3 and so our final volume is a^3/2

[@copywright5635]

Yes of course, this is a clever solution. It is however not as easily generalizable to other lattices.

[@prigoryan]

​@@copywright5635Really? I thought it generalizes quite nicely. To use the hexagonal lattice example from the video, each hexagon has 6 vertices, and each vertex is shared by three hexagons, which means that there are two points per each hexagon in the lattice. Since the domain of each point has the same area, its area should be half the area of a single hexagon, or 3sqrt(3)/4 * a^2. This method should work for any lattice where domains of each point have the same area/volume.

[@copywright5635]

@@prigoryan well yes, that’s exactly the argument made in the video. OP had a nice solution as well, honesty they’re just all slight variations on the symmetrical theme

[@prigoryan]

@@copywright5635 sure, I was just a little confused as to why you said it wasn't as easily generalizable

[@the_lazy_hat]

That is kind of solution which immediately struck on me when I saw the answer is a^3/2, but your solution is incomplete. The problem is you can't consider infinite number of particles since such lattice would have infinite volume and you can't draw conclusions by dividing infinity in 2 equal parts. So you have to consider finite number of particles. But there is no way to just pick some finite number of particles that all requested bodies around them form cube with side a*n for some natural n. I see 2 ways to go around that: 1. You may consider 1 lattice of n^3 particles and other lattice of n^3 particles shifted by 0.5a by each axis. To prove that sum of requested bodies for them is exactly (na)^3 you need to state that their cumulative volume is equal to volume of cube with side of a*n. For this you need to consider protruding volume on half facets of n*a cube and lacking volume on opposing facets and see, that they are equal. It is not easy to see and ultimately will lead to solution similar to solution number 2 in the video. 2. Instead you may consider 1 lattice of n^3 particles (cude with side a*(n-1)) and other lattice of (n-1)^3 particles - centers of (n-1)^3 cubes (n - large natural number) and requested bodies for all of them. From global perspective cumulative volume of them is between ((n-3)*a)^3 and ((n+1)*a)^3 (I added a layer of cubes on each side to limit protruding parts and removed a layer of cubes in second case to limit lacking parts). Clearly requested volume is c * a^3 for some constant 0

[@mksk4395]

"Did you study for the exam?" "No, but I am believing in the power of friendship" *Gets a 100

[@angelmarques3124]

Then the teacher will mark karma’s answer as incorrect because he didn’t use the method explained in class

[@felix30471]

Dunno, everyone on the internet seems to have had this experience, but for me it's never been a problem to solve something in an unorthodox way, even if it was arguably less elegant and convenient than what we learned in class, as long as the steps I've taken and the logic behind them were clear.

[@wryyy2841]

blud did NOT write his working down😭

[@terdragontra8900]

@@felix30471 It’s because a lot of the time, unlike you, people who complain about this are really complaining about getting the right answer with a wrong method

[@jinclay4354]

@@terdragontra8900 Actually, though, I saw that happen first-hand several times at school. Teachers marking answers as only "half-correct" because the student didn't use the method they were supposed to. Personally, I got away with that all the time because I was in the advanced Mathematics extra classes, so they knew that I knew what I was doing, but I saw many colleagues doing the same thing and being punished by the teachers. A well-prepared and well-paid teacher knows the importance of incentivizing students to invent solutions for Mathematics problems. But an overworked and financially unstable teacher really is not looking too hard into what they're doing, only recognizing patterns.

[@terdragontra8900]

@@jinclay4354 You’re right. I don’t think it’s important to teach math well to students that don’t care, though, the world is going to end anyways.

[@Kofhiliphus]

As much as I hate math, Geometry definitely took me into a deep fascination into it. The visualization just made it easier to see numbers and dimensions. So when I first watched the episode back from 2018. I was so immersed in the visual representation of the test. But when I rewatched the anime in 2023, I became more intrigue by this newly found knowledge as I grew up. It is very funny that this video was specifically in my recommended.

[@lunyxappocalypse7071]

We often are taught route learning first, so enthusiastic learning is difficult.

[@TheRedBeet]

1:28 Expansion

[@LionSnob]

Nah I'd win

[@konchu4u608]

I saw this comment as soon as he said domain lol

[@creeperfun12]

I have no idea about what this video is about and was looking for this

[@Devoidy]

7:08 evangelion reference

[@copywright5635]

@@Devoidy ayyy first one to notice it

[@kamilocastillo5816]

True, the "omedetou" flew* above my head

[@marselo1316]

Congratulations! Congratulations! Congratulations! Congratulations!

[@danielenriquez7910]

TLDR: breakdown of domain expansions. 😂

[@FarzanaFathima-t4e]

2:20 Look a *truncated octahedron* !

[@copywright5635]

bingo!

[@FroenTsk]

4:24 this is NOT primary school stuff

[@ShahTalks]

Great video man, would love to see Maths appear more in Fiction.I'm surprised in Magical School type anime , there's no Teacher that focuses on Math and applications to magic

[@hamondorf9355]

I think it's cause there's very few writers if any who understand high level math and communicate it to an audience. Also given that most audiences don't like math they probably don't bother anyway lol. I definitely would love to see someone work out a whole system of mathematics and then translate it into magic. That would very cool. Math tends to be so rigid it makes it hard to go in with a desired result and make a system that gives it to you, unless said system is very simple.

[@Datscrazi231]

There's veryyy little overlap between manga author and mathematician/math nerd + there's low demand for such types of magic

[@Kofhiliphus]

There are a few magical mangas that incorporates math and science into play. However, most of it are basic and some are systematically wrong but was played well due to it being "fiction."

[@osbourn5772]

A few years ago I played around with a Minecraft mod called Psi, which basically combined programming, math, and kinematics into a spell creation system. I watched the anime (Irregular at Magic High School) it was based on, and was extremely disappointed to find that there was basically no math in the show.

[@neztech.]

this makes me really want to see or design a low-magic fantasy world where the distribution of mana throughout the body is so small that mages must abuse mathematical concepts to make their spells useful in combat. like for example, a small, weak fireball could be generated by simply pouring your mana into a small enough area. but by coming at the problem differently, maybe a different mage would create high friction within air molecules to create the same effect with a much much needed reduction in mana cost. i know there wouldn't be any material for the fire to burn, but the example could be used for a lot of different things. i've always liked magic systems in stories but most of them don't really delve too deeply into the hows and whys of the systems and its honestly such a shame

[@zartigana]

Bro it’s crazy how I see this video while studying this exact thing for my material technology exam tomorrow kinda crazy

[@george9371]

what the fuck even is a domain lmao I understood nothing but good video chief 💯

[@OnePieceFan4765]

Basically just another word for an area in this situation. “The domain of all points inside a fence” would just be all the space within the fence

[@alan62036]

Yeah, it's worded stupidly and uses unnecessary symbols. Domain is just the area of the atom. And the areas are not spheres but honeycombs pressed against each other perfectly, leaving no gaps

[@rhi4091]

Ah yes, I'm watching this instead of studying for my calculus exam that's in a few hours

[@JoBrew32]

I'm so glad someone is talking about this scene! It is still one of my favorites of all time!

[@Heifof]

Next time in your chemistry class when you start the crystallography chapter and the body-centered cubic cell shows up…

[@zekiz774]

Honestly, I don’t even comprehend the question

[@Mr_RandomCommenter]

Wonderful video mate, I had a hard time still understanding even during rewatches probably because I was grasping Asano's method at once too. It really is so simple that you'd wish you knew sooner, the corners are only 1/8 of the point we see or have, and if you put the square on the corner point, our original point becomes the corner and the same logic applying. Since all areas combined is the area of the cube, and the corners combined are half of it when added (8/8) and our point is as well (also 8/8), our area is just half of the total area (a^3/2). It's beautiful how math was integrated into the story to show the progress of Karma's character, and at the same time it's cool how there's the easy alternative to the popular solution that is as valid to the other just from approaching it differently which is I argue one of the reasons why many find math fascinating at times.

[@emberthecatgirl8796]

Think of it that way: when you extend the pattern into infinity, the amount of cubes is the same as the amount of center-atoms. Each cube has 8 corner-atoms and each corner-atom touches 8 cubes. Therefore, there are twice as many atoms as cubes. Each atom’s domain is identical and exclusive with other domains, and there are no unoccupied spots.

[@johnpaulcross424]

You deserve millions of subs, amazing storytelling, animation, and editing. I would love to see you tackle more series with interesting problems or perspectives

[@inigoobien8910]

This analysis just made me appreciate this series that I love more than I already have. Major kudos to you, Phanimations-sensei~! ✌️😁

[@computerzero2681]

Finally, a youtuber explained this math problem

[@ghyro2848]

I can't remember this from either the show or the manga. This is 100% gonna go into my next dnd campaign.

[@copywright5635]

thats so evil 😭

[@KinuTheDragon]

After the problem was posed, I tried my hand at it: Due to the symmetry of the problem, we can focus on just one octant of the cube with a cube-corner at one octant-corner and the cube-center at the opposite octant-corner. Due to the symmetry here, half the points must be closer to the cube-center than the cube-corner. To see why, imagine flipping the points' roles and then rotating 180 degrees: the cube looks the same, but the points' roles are the opposite. Since any octant has half its points closer to the cube-center, the answer is half the volume of the cube.

[@alansmithee419]

I love how this is like a blend of both of the anime characters' solutions.

[@Slugfox-lg2fg]

well hello Assasination Classroom, I didn't expect to find you on my KZbin feed

[@russaz09]

Love the “out of the box thinking”

[@dokchampa9324]

One thing I dislike about the explanation is the fact that the shape of the area changes between examples. In the first "shooting corners" method the shape if of a diamond/square, but in the "everyone is their own centre" method the shape is a sphere/circle. I know that the math checks out but this discrepancy really makes it hard to follow

[@drdca8263]

I think it is because the person thinking about the symmetry doesn’t need to think about what the shape specifically is?

[@copywrite9396]

I apologize for this. In hindsight I should have gone back to the 3d example and shown how it works for that. To be clear, the symmetrical argument is independent of shape. In the 2D example, 1/4 of the corners are inside the square. In the 3d example 1/8th are inside the square. In both cases they contribute to 2 total spheres, and thus we have the same argument

[@zaek2144]

In Karma's method the shape of the domain is irrelevant, because you only concern yourself with the volume of a given domain with respect to the volume of a cube (which is a³). By Karma's reasoning we know that in a cube we can exactly fit two domains D_0 and D_1 and because the volume of every domain is the same no matter which atom you choose in the lattice, that means that two times the volume of a given domain is equal to the volume of a cube (a³). Thus, the volume of a domain is a³/2. As it was previously said, you dont really have to concern yourself with the shape of the domain for this specific method, just with its volume. It's one of the reasons why Karma's method is such a beautiful and elegant solution: you simplify and abstract the problem in such a way that the shape of the domains doesn't matter and you just have to deal with the most essential part of the problem. This abstraction also allows you to easily solve this problem for any lattice (in the 2d case the area of the domain would be the area of the polygon that spans the lattice divided by 2 and in the 3d case it would be the volume of the polyhedron that spans the lattice divided by 2)

[@nickitori]

Man, I would never have thought of Asano's method 😭 it's too hard. This video made me appreciate what the author was trying to convey about him. As soon as you drew lines to the corners I was like, hey look triangles that form an equal square (cube). Bam, a3/2.

[@MaxxYurri]

It only took me till my junior year as a civil engineering major to understand this problem, when I had to solve for Atomic Packing Factor of a crystal lattice ._.

[@sonicya]

This is one of my all time favorite series. A timeless show with timeless messages about the time you have left. Thank you for this video! It reminded me of why I love assassination classroom and math so much.

[@faizanhussaini9658]

Theres a somewhat triv solution if we divide the cube into 8 octants. The points in each octrant are closer to the corner in that octant than to any other corner so we jsut need to determine which are closer to the center and which are clsoer to the corner of the quadrant. The center and the corner of each quadrant are opposite corners of the quadrants so they are both closer to half the points. Thus the vloume of points closest to the center is half the volume of the cube.

[@apple8ees]

this episode lives in my head forever - especially when i find out i could have solved a problem with much, much less steps than i had tried to

[@Dragonyy-sb51]

When you added all of the lines at 5:30 the grid became that illusion with the black dots lol

[@x3no]

Great video! Thanks for taking the time to highlight this

[@radagamchannel8565]

this video convince me to watch Assasination Classroom

[@Gojiradogzillagodzilla]

"Math" 0:11 bro is literally having a test about the crystalline structures i'm seeing in my materials science engineering classes LMFAO

[@diht]

This was my favourite math problem as a kid lol It demonstrates a fundamental quality of maths that makes it so unique and beautiful.

[@Ikxi]

Just one video and I love this channel already!! In the show I didn't pay much attention to the math, but when you showed the expanded grid here in the video, I instantly reliazed "ohh holy shit" the outer areas are just each 1/4 of the inner domain/volume freaking beautiful, when math can be shown in such a simple way but math teachers would still want us to write a full proof lmao, would fail so hard at that

[@copywright5635]

Thank you! Yes, math teachers (especially in middle school) might want you to do some geometric method like Asano. However, in higher education, if you were to write out the reasoning Karma has, that would also be given full credit. It's just important that you show the reasoning, whatever it is. Otherwise how can we trust your answer?

[@ArchiXBelidercene]

We got anime 3blue1brown before gta6 💀

[@saftheartist6137]

Excellent video, hope you find more examples in media that highlight math lessons as well as this one.

[@copywright5635]

@@saftheartist6137 if you have any suggestions I’d be open to them!

[@saftheartist6137]

@@copywright5635 I could only think of one example it was pretty brief. The scene is from “No Ordinary Family” and it involved a boy in high school doing math (because his power is super intelligence).

[@Boko-Maru]

The music picks and animation in your videos absolutely slaps!

[@benjaminlee985]

I've been obsessed with this scene too ever since I saw it, and I'm really happy someone else is too.

[@Wakwise]

never heard of this anime, nor do i watch anime in general... but a recent materials science class taught me how to solve this type of problem and now i'm happy to watch regardless!

[@pinethetree]

That was beautiful. Using symmetry to solve the problem more easily and the metaphor between symmetry and empathy. :)

[@supermonkeyqwerty]

amazing anime, and amazing analysis of it as a math major, I appreciate looking for that elegant and easy solution so much

[@sarasousa6949]

when watched this anime was before starting a chemistry degree and seen this video now made me remember how hard was to understand and i thought that was not possible to calculate and its funny because now i know how to do. thanks for the video its really good to see an anime that show math correctly and applied to chemy + characters

[@philosopherkingzant2037]

Smart character written smartly

[@eerieeyesred7359]

Thank you thank you so much for explaining this I’ve been confused for SO MANY YEARS

[@anonymousrandomness1374]

AssClass was the first anime I watched completely, probably as a middle schooler or high school freshman, and this scene stuck with me as much as any of Nagisa's most dramatic scenes. I didn't get much from Asano's method at the time, but I knew Karma had realized it was half the volume of the cube. When I took the SAT (around half a decade ago), there was a question which - if I understood and am remembering it correctly - was exactly the 2D version of this one. I remembered this scene, and I felt... a lot of positive things, it's hard to define. Of course, the 2D Asano method isn't nearly as bad as the 3D, and I don't remember what I actually gave as an answer (and they don't give those tests back afterward). I also wasted precious moments just feeling great about it. But maybe that experience helped me somehow, because I did score well. And in the end, what matters are two things: consider other people and their perspectives, and watch/read/etc fictional media to have fun and feel good.

[@abeautifulduwang]

yeah that math is definitely spot on cause I never wouldve understood it if I were in class and I still don't understand it now

[@harsyakiarraathallah2222]

Man if only i can see Math like this... I could Probably at least be calmer in doing it.

[@diegosierra1951]

I solved the problem in a different way from the two you explained in the video. The cube can be divided in 8 cubes of side a/2 formed by a corner of the initial cube and the center point. Half of the volume of each of these smaller cubes belongs to the domain you try to calculate, since you can draw a plane that's perpendicular to the diagonal formed by drawing a line joining the corner and the center of the initial cube and bisects the cube through the middle point of the diagonal. Since there are 8 cubes like that, multiply the half the volume of a small cube times eight to obtain the number you were looking for. ((a³/8)/2)*8=a³/2

[@DrizzingSakuras]

I LOVED THIS EPISODE, LIKE BRO WAS TRYING TO SHOOT THE FUCKING MATH I CANT-

[@Jacobjones762]

I never realized how this showed how his mindsets changed from the beginning of the year also crystology seems pretty cool wish they thought it here.

[@memesalldayjack3267]

those animations were awesome, I doubt I'd understand stuff without it

[@shahproductionsuser2965]

I remember when I read this part in the manga, I solved the problem myself before moving on and seeing how the characters did so

[@scottygg8550]

i think that is now one of my favorite math problems of all time now, thank you.

[@Jazzimus]

no joke this has to be one of the ebst videos iv seen on youtube, extremely well put together

[@copywright5635]

Thanks!

[@notcyfhr]

This content reminds me of watching 2b3b or whatever the channel name is I always forget but I had to cram calculus with his KZbin series on calculus. It worked but I have to refresh for the next one

[@copywright5635]

2b3b is crazy lmao. Thanks for watching

[@СарраКарагозян]

Thank you so much for this video! Read the manga a long time ago, when I didn't appreciate the math problems, so this is a delightful throwback! Using the real math to show a character's growth is genuinely genius. Also I wouldn't be able to find such beautiful solution on my own either, so thank you again! Power of friendship and anime 🤝 Karma's approach is so simple and elegant.

[@chrisbmxbrandt9495]

This was genuinely interesting

[@sebjink.9037]

I always come back to this episode, and it was nice to finally see the explination

[@amanemisaki4046]

my favorite type of yt video (random math) + my favorite anime? subscribed.

[@Beast_the_smash_guy]

Assassination Classroom was a top-tier anime. I highly recommend it to EVERYONE, as it changed my life during Covid

[@anarchosnowflakist786]

very cool ! I didn't notice this was an actual important math problem back when I watched assassination classroom so I didn't remember it but I learned the second method in a crystallography class last year !

[@Squid_less01]

Omg this is such a unique video! I love Assassination classroom and math so this was such a good watch! I wish more videos were like this

[@mensem2405]

insanely entertaining, yet insightful video. Please make more content bruhh

[@copywright5635]

Of course lol. It's gonna be about half "math in media" stuff like this. And half just cool math/physics stuff!

[@umbraemilitos]

Plenty of shows do not get math, or math hidden under the logic of the plot, correct. I imagine many videos could be made from that content.

[@Bee-g4s]

Damn, anime can really solve anything with the power of friendship.

[@MagnificentCreature]

AssClass holds a special place in my heart, I didn’t think too deeply about this when I first saw it, but I felt it made much thematic and mathematical sense. Absolutely amazing video covering two of my favourite things. Math and Anime, you earned my sub tdy

[@catherineluk2414]

just wanted to share my appreciation for this video. i forgot how much i loved the themes presented in assassination classroom. the animations and visuals you added to explain this theory were super well done.

[@hungrypizzafox]

It's so cool seeing stuff like this in shows, they put soo much thought into both the topic and the interpret it into the story. I wish more anime did this, but I also wish all shows did this. It just makes the show seem more real. I love this anime.

[@mattmerced1148]

This is why the real math exam was the friends we made along the way.

[@user-zl1jh6jm6d]

I've been stuck on this problem for years I won't lie. The way you broke it down was so simple and I'm glad that people who watch the show for the first time now and have questions abt this scene have a simple and great video coming to their aid!

[@sorvetedemadeira9717]

thank you so much for this video, this was sooo cooool

[@ansa2197]

Finally, thank you for explaining this! I understand the question + answers of this math problem in this episode 😭

[@alexicon2006]

If I had to explain it :- 1) The sum of the domains of all the corner points and the center point of the cube would be the total volume of the cube, ie, a³. That much is obvious. 2) Let the domain volume of the center point be K. Now, when we take the Karma Approach, we can see that the total domain of all the cornerpoints is the same as the domain of the centerpoint, ie, K. But out of the entire domain, ONLY 1/8TH of that is INSIDE the cube. Once you know what Im talking about, it is VERY easy to visualise. 3) So we know that each corner points' domain volume inside the cube is K/8. There are 8 such points so their domains inside the cube have a total volume of K. Combine that with the center point's domain volume of K and we get that the sum of all domains in the cube is 2K. 4) Back from point 1, we know that the sum of all domains is obviously equal to the total volume of the cube. That is a³. Thus, we finally get 2K = a³, and hence, K=a³/2, where K is the domain volume of the center point. 5) Thus, the answer should be a³/2.

[@gimoff578]

thank you now I finally get it

[@alexicon2006]

@@gimoff578No problem!!! Was my explanation sufficient and proper?

[@alexicon2006]

Also reading this explanation now after Ive woken up (I wrote this while half asleep) not to toot my own horn or anything but as a Mathematics Student whose literal job is shit like this I kinda cooked with this explanation here like sheesh.

[@iwack]

Bit lost on how the sum of all the domains is equal to the total volume, everything else seems obvious to me but idk having a weird time wrapping my head around it probably because of the wacky visualisation in the video.

[@alexicon2006]

@@iwack Think of it this way. Wbat is a domain? Its the area of volume in which all the points are closer to one specific corner or center than any other. Now think. If in a cube, there are 9 points of which domains can be taken, and we take every point which is closest to one corner, then every point which is closest to anotber corner, all the way to every point which is closest to the center, wont all 9 of those domains totally cover the inside of the cube like that? And this is the REAL kicker. If there is ANY point inside a cube, then dont you think it will HAVE to be closer to one corner or the center than others? Because think about it. Is there ANY point in a cube which is equally distant from all 8 corners and the center? Once you visualise it, you'll find out that such a point is obviously impossible and cannot exist. And if such a point cannot exist, then a point which is outsode all 9 domains and still is in the cube cannot exist. And thus, conversely, and finally, all 9 domains would HAVE to cover the entirety of the cube's volume. Every point inside the cube would HAVE to have one point it is closest to out of all the corners and center point. Out of all the 9 points, there WILL be one point to which any point inside the cube is closest to. Hope that helps!!! I KNOW this explanation is trash, but this is what I could think off the top of my head only so sry about that 🙇‍♂️ ^_^

[@niraqw5908]

I actually paused and opened an Onshape document to help me visualize the problem.

[@jonathany1240]

Ngl reading this chapter when i was doing my intro to metallurgy felt like i was on the trueman show. The tetrakaidecahedron is a useful result for FEA and idealised grain-formation calculations but for volume? yeah you have to rely on the translational symmetry inherent in lattice structures. At this point in reading it I realised i was in college and these were middle schoolers

[@thephoenix8421]

This was one of the earlier anime’s I watched in my anime watching career. I absolutely loved it and fell in love with the combat and teaching/wisdom oriented anime’s I still binge to this day nearly two years after.

[@AsyncMusic]

This is really interesting! It's something I went over in a modern physics class when covering crystalography

[@Gravitatis]

3:47 " All knowledge presupposes Subject and Object. Even self-consciousness (Selbstbewusstsein) therefore, is not absolutely simple, but, like our consciousness of all other things it is subdivided into that which is known and that which knows. The Subject accordingly knows itself exclusively as willing, but not as knowing. For the ego which represents, never can itself become representation or Object, since it conditions all representations as their necessary correlate. "

[@Trigun99]

I remember seeing it in the Manga and not really understanding it, then watching it in the anime and having it make a lot more sense. Thank you for the reminder of one of my favorite anime.

[@imnotjesper]

I actually can't think of any other show/story that uses math like this. But, to be fair, from what I remember of Ass Class, Asano and Karma are basically some of the best high schoolers at math in the country. So this problem should probably be fairly straight forward for them.

[@azraeltom]

iirc when I read the manga long ago, the author added a footnote that he asked a few friends to come up with university level problems that could be solved by high schoolers (or something along the lines)