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

[@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

[@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

[@Gidiotic]

when the youtuber likes math

[@copywright5635]

Well I won't deny it...

[@Aliaska9816]

when the viewer likes math

[@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

[@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 😭😭

[@PlushMonki]

Holy yap

[@noaag]

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

[@PlushMonki]

@@noaag yez ;-;

[@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

[@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)

[@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!

[@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

[@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

[@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

[@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!

[@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.

[@mksk4395]

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

[@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.

[@FarzanaFathima-t4e]

2:20 Look a *truncated octahedron* !

[@copywright5635]

bingo!

[@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)

[@zekiz774]

Honestly, I don’t even comprehend the question

[@FroenTsk]

4:24 this is NOT primary school stuff

[@cursedstarflight]

i remember watching this scene with my friend a few years ago and one of us had yelled something along the lines of "sir SIR WHAT ARE THEY TEACHING CHILDREN IN JAPAN"

[@danielenriquez7910]

TLDR: breakdown of domain expansions. 😂

[@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.

[@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…

[@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

[@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!

[@Dragonyy-sb51]

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

[@syan2240]

Oh yeah i just realized

[@thedra9ongod]

i loved this scene in the show but didn’t understand the math behind it so thank you for making this video and showing off the attention to detail that was put into the show

[@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

[@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.

[@zartigana]

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

[@rhi4091]

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

[@Potato6480]

same bro I have my calc 2 exam tomorrow 😭

[@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

[@ramonemiliochaconperdomo7225]

@@alan62036”The area of a atom” it’s no the accurate description here, because there’s an add condition: that area must not overlap of the other atoms, an that’s the same that saying the set of all points closer to that atom than any other. It’s not unnecessary use of word, but certainly can be confusing if you don’t know terms like “Domain” or “set of all points”

[@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.

[@computerzero2681]

Finally, a youtuber explained this math problem

[@ArchiXBelidercene]

We got anime 3blue1brown before gta6 💀

[@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.

[@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 😭

[@russaz09]

Love the “out of the box thinking”

[@amorfatikhb]

this anime holds such a special place on my heart. this math problem demonstrating different viewpoints was beautiful.

[@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

[@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).

[@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.

[@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 ._.

[@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.

[@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.

[@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

[@Slugfox-lg2fg]

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

[@inigoobien8910]

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

[@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

[@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?

[@Gojiradogzillagodzilla]

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

[@harsyakiarraathallah2222]

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

[@philosopherkingzant2037]

Smart character written smartly

[@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

[@mujtabaalam5907]

For the cubic lattice: Each center point has eight vertex points, and each vertex points has eight center points, thus they are both equally common and thus share area equally This generalizes to other regular lattices: consider the 2d lattice of hexagons, with points at the vertices and centers of the hexagons. The centers have 6 asdociated vertex points while veryex points have 3 associated center points, thus the vertex points are twice as common and thus theor domains take up 2/3 of the area

[@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.

[@benjaminlee985]

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

[@supermonkeyqwerty]

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

[@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

[@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!

[@pinethetree]

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

[@Bee-g4s]

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

[@chaincat33]

I find in this kind of math, if you're doing a lot of tedious work and geometry, you are missing something. Yes, you will get the answer. But there is almost always some kind of elegant solution that is incredibly simple and ties everything up in a neat bow. That said, for a problem that has inscribed spheres, I am kinda surprised that pi doesn't show up.

[@memesalldayjack3267]

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

[@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. "

[@radagamchannel8565]

this video convince me to watch Assasination Classroom

[@niraqw5908]

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

[@scottygg8550]

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

[@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.

[@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!

[@eerieeyesred7359]

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

[@YuutoGaming]

If you have never make this video, I never knew is kind of friendship in Math problems exists!

[@copywright5635]

That was the purpose, glad you enjoyed

[@juliangst]

This episode always gives me flashbacks to solid-state physics class

[@muffinssupreme84]

I'm not that good at math, and I got stuck at the 5:05 part. I don't know why ''you should be able to see that it has sidelength a/root2'' thanks for the help in advance anyone.

[@willdebest432]

45-45-90 triangles

[@antonioduarte4370]

Pythagorean theorem. The sidelenght is the hypotenuse.

[@casinoroyalelover]

Look at the black triangles. They are 45-45-90. So each side of the 90 has length a/2 since it's half of the larger square side a. Then by Pythagorean Theorem: (a/2)^2+(a/2)^2=c^2. That becomes 2a^2/4=c^2 and reduces down to a/root2=c

[@x3no]

Great video! Thanks for taking the time to highlight this

[@sylfthesoundyoulongfor8363]

Rare footage of Math elegant resolution process serving a narative done right. GG for catupring it bro ❤

[@Beast_the_smash_guy]

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

[@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.

[@blandile]

i randomly remembered how cool this scene was and ended up rewatching the entire series

[@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

[@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)

[@mattmerced1148]

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

[@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.

[@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

[@triacontahedron]

My own method (that I came up with after finishing the video) was to simply split the cube into 8 equal sections. Each section is a cube where 2 opposite vertices are the center and corner of the original cube. The section would then necessarily be split in half, and therefore so would the cube. This can be generalized to a lot of shapes (I'm to tired right now to figure out the exact criteria.) It's pretty much the same as Karma's method, but I find it to be far simpler and more intuitive (which is saying something, because that method is brilliant.)

[@starfurystudionl4732]

Assassination classroom actually helped me with geometry, not kidding. Had watched the test episode a day or two before my own math test and learned that picturing the problems like how they did it helped me with math. Test day comes, I use my new think method, boom, I aced it.

[@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.

[@emberthecatgirl8796]

Paused, and shooting my shot: Volume is equal to (a^3)/2. The atoms in the middle create an identical square lattice to the one highlighted, thus we can simply look at 1 “corner” of a cell and multiply it by 8 (for each corner of a cube). In this case it has to be a 50/50 split of volume, therefore an entire atom’s domain volume is equal to half of the cube’s volume. Or simpler: For each cube volume there exist two atoms, and each atom needs to have an identical domain for periodicity to happen, so the domain must be equal to half of ‘a’ cubed.

[@greentea_DP]

this was a tad bit hard to understand but karma method is really eye opening, by realizing that only a 1/4th of it own domain has entered your space, it also meant it only equal to 1/4th of your own domain if you consider it to have the same volume as your own. for easier understanding i think as triangle that took 1/8th of a square and then i realized it prob similar to Asano way of thinking.

[@rexellerainbow1173]

everytime im sitting for a test, i think about this show specifically the whole final exams arc. but i never really understood it until now. i just hope my final exam for this senior year wont have that question. if i see that on my paper ill genuinely cry as i try to remember this vid lol

[@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 !

[@jasonmaserton]

I appreciate the headphone warnings

[@N_skyV]

I watched the show when I was in middle school so when I watched this scene and was confused, I didn’t give it much thought cause at the time, the characters were two years older than me. Now, I watched the show again last few months as a third year dental student and the fact that I still don’t know what tf is going on is becoming slightly concerning😭😂