Can you guess a shape from its shadows?

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This video explores the question of whether you can determine the shape of a 3D object by observing a few of its shadows. The results are surprising and beautifully rich!
I created the slides in PowerPoint, and I wrote the music using a trial version of Ableton Live 11.
For more on this topic, here are some resources from Hideki Tsuiki (‪@hidekitsuiki1551‬) :
- Video showing the 3D prints and their various shadows (Watch This!): • Shadows of Fractal Ima...
- Imaginary cubes webpage: u.kyoto-u.jp/icube
- Imaginary cube sculptures and Latin squares: archive.bridgesmathart.org/20...
- Imaginary cubes and fractals: archive.bridgesmathart.org/20...
- Imaginary cubes and packing puzzles: www.mdpi.com/1999-4893/5/2/273
- Imaginary cubes and hypercubes: link.springer.com/chapter/10....
Special thanks to ‪@feynmanschicken‬ for offering feedback during the creation process.
0:00 - Introduction
2:48 - Imaginary cube patterns
4:32 - Latin squares
5:43 - The replacement trick
6:22 - Fractals
7:44 - Further exploration
#SoME3

Опубликовано:

3 авг 2024

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Комментарии : 1 тыс.

@PrimerBlobs 11 месяцев назад

Nice video! Impressive that you also made the music.

@TripPy_Poly 11 месяцев назад

Hi primer, the evolution simulation content creator (idk)

@pirilon78 11 месяцев назад

The man himself

@LadyTink 11 месяцев назад

Imagine having 166 subscribers, and having Primerblobs comment on your video >.< Huge fan btw >.>

@kaininjago6161 11 месяцев назад

it is the man!

@BurningShipFractal 11 месяцев назад

@syriuszb8611 11 месяцев назад

You can make imaginary sphere as simple as just making 3 discs parallel to the shadows they supposed to recreate.

@DisguisedParrot 11 месяцев назад

Indeed, but that really be able to be a stable object? Also love the idea!

@BryanLu0 11 месяцев назад

@@DisguisedParrotYou can intersect the discs and it won't affect the shadows

@tokarak 11 месяцев назад

Notice that you can’t get rid of the three 1-spheres around the centre of the 3-ball, because shifting it will move it outside the 2-ball projection locus in at least one of the other projected dimensions.

@tokarak 11 месяцев назад

Also: the surface area of a unit hollow sphere (a 2-sphere) (SA = 2tau [tau 2pi]); the surface area of 3 disks (3 2-balls) (SA = 3/2tau). In addition, half of the 8 congruent “quadrants” of the 2-spheres can be removed, in a very similar way to the 8 “quadrants” of a cube in the video, getting the SA down to 1 tau.

@tokarak 11 месяцев назад

It’s interesting that we are using surface area, rather volume. But in the video, notice that under infinite recursion of the cube fractal, with the volume halving each time, you also get a shape with 0 volume, but with surface area (which is equal to the area of the projected square). I wonder what this class of fractals is called.

@Dysiode 11 месяцев назад

I gotta say, this felt almost Blue's Clues-y, but as the highest possible praise. The almost uncomfortably long pauses after "can you figure this shape?" and "see if you can make an argument..." got the cogs in my very adult brain churning. Very impressive how you made it more educationally engaging while still keeping the same high level of polish and clear explanation videos from Numberphile and Matt Parker are known for

@woodybob01 11 месяцев назад

I was so f-ing obsessed with blues clues when I was a kid

@vigilantcosmicpenguin8721 10 месяцев назад

This is accurate. Sometimes you need a little Blue's Clues-iness.

@tttITA10 10 дней назад

This guy likes when the book goes "we'll leave the demonstration as a puzzle to the reader".

@upsidedown-pug1974 11 месяцев назад

for that circle shadow one, a way you could do it is take any imaginary cube and place sphere inside and remove all parts that extend outside the sphere. This should make imaginary _~circles~_ from the shape and the correct angle

@bengobler 11 месяцев назад

Very clever!

@voidwyrm6149 11 месяцев назад

that should work with all imaginary cubes that are solid and continuous. for "granular" imaginary cubes, you may need to go back and patch up holes in the sillhouettes, and for 2d surfaces, it might not work at all (the intersection of a ball and hollow cube of the same width is just the midpoints of the six faces)

@Luna5829 11 месяцев назад

but it's not technically a circle, because if you zoom in far enough, you can see the zig-zags

@kaininjago6161 11 месяцев назад

@@Luna5829 it would be like taking a slice; there would be no zigzags

@Mikelaxo 11 месяцев назад

That would work with literally any shape in existence

@dyld921 11 месяцев назад

The thumbnail is misleading, I think. I was expecting this to be about how to contruct a 3D object from any given set of 3 shadows.

@proxagonal5954 3 месяца назад

That's not possible unless the object is given to be convex

@williamhoyle6644 3 месяца назад

The title also plays into that. It was still a very interesting video! But not at all what I was hoping to watch.

@shelly8779 2 месяца назад

/op womp womp

@FeWi-YT 13 дней назад

The thumbnail didn’t even say that and constructing said shape from 3 shadows requires logical thinking

@RocksAreEverythingInTheEnd 7 дней назад

I think it's cone with a square cutting it in half.

@sokijohnson1309 11 месяцев назад

This video is flawless, not too Mathy, not too long, a clear motivation even for non mathematicians, good interactions, links to go deeper, etc... I hope you get selected, good job! 😊

@pocarski 11 месяцев назад

I discovered this accidentally when I wanted to see what the bitwise XOR function does to a plane. If we map discrete points in space to (x, y, x XOR y), it forms a Sierpinski pyramid standing on its edge.

@HansLemurson 9 месяцев назад

Wow, that's really cool!

@weibrot6683 10 месяцев назад

If you want to know what the thumbnail shape would look like, imagine a cylinder with the round parts at the top and bottom, now squish one of the circles together to a line and keep it in the center, that's the shape that would make a circle, triangle and square shadow

@Sir_Gilbert 9 дней назад

Imagine like a toothpaste tube on its cap but it's really short

@unknowndeviceconnected 5 дней назад

Imagine like the bit of a flathead screwdriver

@mikeebrady 11 месяцев назад

How are you going to use one shape for the thumbnail and then never give the answer to that one in the video? Talk about click bait.

@hidekitsuiki1551 11 месяцев назад

Thank you for creating an excellent video! Ever since I discovered the H fractal and T fractal, I have been dedicated to raising awareness about them and their significance. I'm thrilled that you've become a part of this endeavor.

@RohitKulan 11 месяцев назад

H and T, your initials!

@wilczus222 11 месяцев назад

Wait, it's the man himself, I just realized!

@vigilantcosmicpenguin8721 10 месяцев назад

'Tis a noble cause.

@Llamaful 11 месяцев назад

I started the video thinking it was a very easy and obvious challenge but after the fractal reveal I was hooked. Really good job!

@HazhMcMoor 9 месяцев назад

I didnt watch the video because the thumbnail and title looks lame lmao. When 3b1b said it's about fractals instead, then I watch it.

@iau 11 месяцев назад

I think the only thing missing was an animation that showed how the fractal shape actually projects a cube from all directions simultaneously. I understood it _must_ obviously work. But I kinda felt robbed of the satisfaction of seeing it at work, and until I got it I was just _trusting_ your conclusion instead of seeing it with my own eyes.

@davidsorensen2116 10 месяцев назад

Even just the solid imaginary cube shapes before they became fractals would have helped. The demo with the 3D printed model was convincing that at least one possible projection was a square, but didn't show that the projections orthogonal to it were also squares.

@j.s.42822 11 месяцев назад

Fantastic content, narration, visuals and music. On top of that, I think that this is one of the few SoME videos that doesn't feel like it sacrificed any rigour in its reasoning. The mathematics is pitched perfectly for what you can communicate in a 10-minute (or so) video, and then executed expertly. Very well done.

@user-id2nr1zp1u 11 месяцев назад

I really like the clever trick at 6:00, also the visualization at 6:20 looks like those tiny trinkets or dice you can play around in your hand, they're just so lovely!

@Swagpion 11 месяцев назад

The imaginary sphere is the shape that comes from the intersection of 3 cylinders, each one perpendicular to eachother.

@jules325 11 месяцев назад

I thought at this in first, but it seems to "exceed" if you try to construct it mentally

@amaryllis0 11 месяцев назад

@@jules325 See wikipedia: Steinmetz_solid#Tricylinder

@jetison333 11 месяцев назад

@@jules325 the union of three cylinders is too big, but if you only take the parts that are part of all three cylinders you get a shape that succeeds.

@Swagpion 11 месяцев назад

@@jetison333 yup, I even have a 3D printed version of it. I made it in Tinkercad and got it made real.

@jaki1876 11 месяцев назад

@MemeSwag doesn’t that just make a sphere?

@jakobr_ 11 месяцев назад

I thought about this sphere thing before, and surprised myself with the conclusion that the “meet” of three mutually perpendicular cylinders isn’t actually a sphere. You get something resembling a rhombic dodecahedron or cube. I just looked it up, it’s called a “tricylinder”. The sphere is hidden inside this shape, only poking out around three equators. There’s still more to shave off on the corners before it becomes a sphere. I expect this to be the maximal shape that fits in those shadows.

@K-o-R 11 месяцев назад

If you think about the bit outside the cylinder, you see things like two arched ceilings intersecting to form a vaulted ceiling.

@0xEARTH 11 месяцев назад

dude the production value here is insane. clean, precise, and simple, while not assuming we don't know anything, with well-made visuals to match; i actually learned something that i might use for something with this! this is absolutely nutty, i'mma stick around to see what else you got!

@Khaktos 11 месяцев назад

I just love how approachable this video is. I could show this to an 8 year old and they would most likely understand everything. But it is not dumbed down, and even an adult can find interesting puzzles and problems behind this idea

@EleetCanoe 11 месяцев назад

This video is brilliant! I didn’t really get it but the presentation is on another level! If I think hard enough, eventually I think I’ll get the whole shadow thing.

@demitrischoenwald1436 11 месяцев назад

This was so amazingly comprehensive that it made complete sense. And I didn't get bored listening to a bunch of nonsense, because it used a simple mathematical concept to explain how it could work alternatively. Very cleanly done.

@koendos3 11 месяцев назад

Finally a math video that is refreshingly elegant and suprisingly simple! Love it. Kinda reminds me of those 3d-print, that displays 2 different words, depending on how you look at it.

@StrawEgg 11 месяцев назад

okay, but... what about the shape from the thumbnail?!

@Luigicat11 11 месяцев назад

Okay so take a cylinder, then angle the circles on the ends so they form the triangle.

@kingsley. 11 месяцев назад

@@Luigicat11how??

@spkrforthedead4844 11 месяцев назад

@@Luigicat11 That doesn't actually work. Try to picture transforming a cylinder into the shape you're suggesting while looking at it from the perspective of the light casting the square shadow. The sides of the square formed by the ends of the cylinder become curves and the other sides get shorter as the ends of the cylinder angle towards each other.

@Luigicat11 11 месяцев назад

@@spkrforthedead4844 You're imagining it wrong then. Or maybe I just worded it poorly. Would it be better to rephrase it as cutting along two lines that intersect on the surface of the cylinder? I could probably draw a picture (a poor-quality one) of the shape I'm thinking of, but I wouldn't be able to show it since you can't attach images in a RU-vid comment.

@Kromiball 11 месяцев назад

Take a cylinder and cut the curved side into a triangle shape

@imotvoksim 11 месяцев назад

This was both engaging, well visualized, and well executed from sound and speech perspective! Good job mate 🧠

@brambl3014 11 месяцев назад

Except the horrible click bait thumbnail

@brambl3014 11 месяцев назад

That doesn't even get explained in the video

@confusion5025 11 месяцев назад

This was an amazing video, you definitely deserve to win! The question was really interesting, and it was neat to see how the pattern of four cubes could be repeated inside itself to form a tetrahedron. Also, I really liked the animation style, it was aesthetic and also conveyed the mathematical ideas very well.

@KarmaKomet 11 месяцев назад

Really wonderful video! Great pacing and kept me interested the whole time.

@thecalculusofexplanations 11 месяцев назад

This is simply an amazing entry, you deserve a pi creature for this! And a compliment from Primer as well, epic. I will continue to aspire to this level of quality in my own videos. Well done sir.

@salxrn 8 месяцев назад

when you were talking about how there was one cube in each row, column and stack I was thinking about sudoku and then you immediately say exactly what I'm thinking about

@HomeofLawboy 11 месяцев назад

That ended up being much much much more interesting than I expected it to be from the title and thumbnail

@bastienpabiot3678 11 месяцев назад

having been lured in by the thumbnail i wonder if you have a solution for the triangle/circle/square shadows?

@sheepy403 11 месяцев назад

Anybody please correct me if I'm wrong, but I don't think there is actually a solution. The defining question I asked myself to reach this conclusion was, "at what elevation can any corner of the square shadow exist?" The triangle shadow tells us that such points can only exist at the lowest height. However, the circular shadow tells us they can only exist at the middle height. Therefore, no point in 3D space could be the corner of that square while also staying within the confines of both the triangle and the circle. Again, if anybody can prove otherwise, I would LOVE to be wrong on this. I hate it when thumbnails present unsolvable puzzles.

@brandonwillnecker8060 11 месяцев назад

@@sheepy403my first guess would be to extend the shapes along their respective axes into a prism shape. Then you could take the triple intersection. I don't know if this would work but it could be tested with something like Blender. The circle and square would produce a cylinder that recreates those two shadows but maybe the triangle messes it up.

@caspianmaclean8122 11 месяцев назад

@@sheepy403I think you're right that it is impossible. I'm curious what is the shape of the largest possible shadow instead of the square, if the triangle and circle shadows are as shown.

@sheepy403 11 месяцев назад

@@caspianmaclean8122 I found the shape, though I don't know if there's a name for it. If we say the square would be 1x1, the shape we get from the triangular prism and cylinder is the following: an ellipse with a major axis of 1 and a minor axis of 0.5, cut in half along the major axis and spaced with a 1x0.5 rectangle. The area of such a shape is 1/2+pi/8

@Sr.Estroncio38 9 месяцев назад

My solution would be a disc as a base then you make a cross section with a thin square and triangle, which should be posible if they have the same hight

@rodomify7681 11 месяцев назад

I remember a while ago finding the shape you get by literally cutting shapes from a cube in all three Directions. The one you get from a circle happens to have the same corner/edge structure as a Rhombic dodecahedron, and if you were to get a shadow from the corner it would end up being a perfect hexagon.

@CookiesRiot 11 месяцев назад

Tricylinder Steinmetz solid. Basically a chonky rhombic dodecahedron.

@thomasrad5202 10 месяцев назад

every engineer has become a professional at guessing shapes from their projections unintentionally

@Autoskip 11 месяцев назад

I saw part of the trick from the start - all of my answers were along the lines of "a cube would work" - but I didn't realise that a serpenski pyramid could do it. Once I saw it though, it made sense, and I managed to figure out that it was minimal shortly before you spelled it out. As for the 3 circles option, it's a bit unusual in that the most common expectation (the sphere) isn't the option with the most volume - that title belongs to the overlap of three perpendicular cylinders, which is a shape similar to a rounded rhombic dodecahedron, and has 8 sharp corners (and six points where four faces meet collinearly, which could be called corners, but are completely flat at the exact point that they meet). Also, I clicked hoping for an exploration as to why the circle/square/triangle shape from the thumbnail was impossible, but this was pretty interesting too.

@BarelyNoticeable 11 месяцев назад

You struck gold with this tone of voice and the animation style and the not dumbed down but simple enough for most to understand scripting in this video, keep doing what you do mate

@DisguisedParrot 11 месяцев назад

I love this video soo much!!! You are great at making them

@zanop15 11 месяцев назад

I absolutely loved the video! I am, particularly, very enthusiastic whenever the topic is mathematics but I could easily see any of my friends thinking this pretty cool too! The soundtrack, visualisation and explanation is great.

@caspermadlener4191 11 месяцев назад

As an IMO (2022) gold medal winner, I really appreciate elegant arguments like these! At first, I expected a video just explaining why this isn't possible in general, but this is way more elegant! Thinking about latin squares this ways proves that for a latin n×n and m×m square, it is also possible to construct an mn×mn square! Also, notice that it is always possible to "confexify" these fractals, without changing the shadows, if the shadows were confex to begin with. The tetrahedron is the confexification of the Sierpinski fractal, but you can also get the other shape by confexifying the fractal of a more symmetric variant of the minimal 3×3×3 cube than shown in the video.

@bengobler 11 месяцев назад

Excellent! Of course, you can replace the cubes in the Sierpinski pattern with any imaginary cubes of your choice (they don't even need to be all the same). In the video, I say that the Sierpinski pattern pairs well with the tetrahedron, and the reason is precisely that of convexification. Great catch!

@miskolinaccc 11 месяцев назад

Very nice video! The one in the thumbnail is a dizzy to imagine though, I had to sketch it out to see if it was possible and I'm still not sure if it is 😆

@luukthegamer 10 месяцев назад

Its a two faced triangle standing on a disc

@rubensabatini7265 11 месяцев назад

Wow, the part about latin squares converted into elevation maps is mind blowing, wonderful video!

@JaharNarishma 11 месяцев назад

I recommend you to look into _skyscraper sudoku_ It is a variant of sudoku which uses "elevation" to find the solution.

@blobofdespair 11 месяцев назад

This was so well made. The visualizations made it really easy to follow along and the presentation made it so interesting!

@blacklistnr1 11 месяцев назад

@5:50 The reason I care is that I got tricked by your shenanigans in the beginning, now I can rewatch the video and go "That is clearly an iteration of a fractal with minimal cubes!"

@PennyLapin 11 месяцев назад

I really like how excited you sound through the whole video! The best part of these events is that they inspire people to share about the things in mathematics that they love so much!

@KevinLubick 11 месяцев назад

Loved the animations and the explanation. A contender for at least an honorable mention in my eyes!

@yassinesafraoui 11 месяцев назад

I love how you make things crazy simple and yet they still feel fascinating, elegant!!

@henryzhang3961 Месяц назад

I was hoping that this video would solve the more general problem " Can you guess a shape from its shadows? " but this was fun anyway

@latehate1017 11 месяцев назад

Super underrated! I love the 3-d prints you have made for the video too, shows that what we learn in math can be applied in the real world. Continue making more videos!

@bengobler 11 месяцев назад

Thanks! The 3D prints were gifted to me by Hideki Tsuiki (@hidekitsuiki1551). Check out his channel for more videos about these shapes and their other shadows!

@redpepper74 11 месяцев назад

It’s always cool when you can make abstract concepts physical and tactile :)

@dimethylhexane 11 месяцев назад

this is a great video, but I still really want to know what shapes with shadows like in the thumbnail look like!

@lucaslevelups9592 22 дня назад

5:35 Say we only look at one row of a Latin square and try make that into a cube. While the process still works it leaves all these holes. But if we then pick one column and layer it on top of our row, because there is 1 number per column, and the amount of said numbers matches the dimensions of the grid, the remaining column will fill in the gaps, repeat that for every spot on our row and it will cast a full square shadow. This reasoning could also be applied to every direction, therefore casting a square shadow on all 3 walls.

@bowieinc 11 месяцев назад

This was WAY more interesting that I thought it would be:) great job!

@erikhaag4250 11 месяцев назад

in a mathematical "cad", you take the shadows you want to cast, and extrude them into an infinite prism. The set intersection of the 3 prisms will be the biggest set with this property, if the intersection is empty, then there is no set with these shadows. you can also add more shadows and change the angles between the shadows with no lose of generality. there is a video by maker's muse that goes into detail here: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-r-cNofvv8nk.html

@Tzizenorec 11 месяцев назад

You can't just check if the intersection is empty; you have to check if the intersection of the three sets actually casts those three shadows. In the case of the shadows {square, triangle, circle}, the intersection of those three prisms doesn't actually cast a square shadow (the shadows it casts are triangle, circle, and some sort of lopsided rounded rectangle).

@sirgregsalot 11 месяцев назад

I was really hoping someone would bring up the thumbnail - I was trying to figure how to solve it using CSG intersections. Take the intersection of the square and the triangle to get a triangular prism, and then take the circular intersection orthogonal to that. I can't quite picture the shape, but I can convince myself that it works, and that the order you take the intersections in doesn't matter.

@aspyse 11 месяцев назад

@@sirgregsalot The "base" face of the triangular prism is its only square part. When you intersect this with a cylinder, two of the face's edges are shaved off, making the "lopsided rounded rectangle" shadow they mentioned.

@nubdotdev 11 месяцев назад

This video is awesome! My first exposure to Latin squares was in an abstract algebra class, which got me wondering: What do the fractals of the multiplication tables of all the fundamental groups look like?

@bengobler 11 месяцев назад

That's a great question! I bet there are some nice ones. For starters, the multiplication tables for (Z_2)^n correspond with iterations of the Sierpinski pyramid pattern. The results will depend on how you order the rows and columns (this example uses the natural ordering).

@skylardeslypere9909 11 месяцев назад

This is a really fun video to watch. It's not difficult to follow, and it explains clearly why the thing that works, actually works. Nice

@TheScienceNerd100 10 месяцев назад

Saw the thumbnail and instantly went into Inventor Pro to CAD up what it would look like. Might 3D print it for fun if I get my printer working again.

@blinking_dodo 11 месяцев назад

Okay, but you *still* haven't shown us what shape created the shadow configuration from the thumbnail. Please show me.

@tesseract7586 11 месяцев назад

WHOSE THAT POKEMON! its a cube! *sirpinski tetrahedron* AAAAAAAA

@bengobler 11 месяцев назад

Lol!

@tesseract7586 22 дня назад

@@bengobler me when i actually get noticed by a youtuber:

@mange_1_kiwim1k96 11 месяцев назад

This reminds me of tomography (reconstructing an object from its projections). The main difference is that in tomography you typically know the "width" of the shadow, i.e. the object is semi-translucent and so at each point, the shadow can be of any color between white and black.

@Blueyzachary 11 месяцев назад

For the cube, I actually imagined it having another few faces and it still making those shadows

@ethanwinters1519 11 месяцев назад

Great work on this! What an interesting, yet fun and accessible topic : ) Perfect for SoME3, I'd say. Enjoyed how smooth and charming the visuals were too! Also, in answer to the question you ended on, my first thought was a tricylinder.

@Renteks- 11 месяцев назад

Did I miss the part where you explained what the shape from the thumbnail was? Or was it intentionally omitted?

@mastershooter64 11 месяцев назад

the premise is kinda like "Can you hear the shape of a drum" which gave rise to spectral geometry

@bengobler 11 месяцев назад

That's a great connection!

@BetaPlayTeam 11 месяцев назад

This video immediatly caught my attention as I had this question of whether you can be sure a object is a sphere by looking at its shadows. Now I need answers!!!

@Frizou 11 месяцев назад

You have- how much subscribers?? Less than 400?? This is quality well beyond most channels I've seen yet, truly an amazing video and subject! Your editing - both visual and audio - is absolutely amazing, it's captivating but doesn't distract from the subject. I cannot wait to see more

@ZoofyZoof 11 месяцев назад

Well he gained 70 from this video, or more since you said less than 400

@Jellyjam14blas 11 месяцев назад

Awesome video!! Very entertaining and succinct. :D Another neat thing that's related to shapes and shadows is creating complex 3d shapes that spell out different words from different angles! I made one out of Lego with my name and the word hello, and had a lot of trouble fitting an "N" into the shape of an "O" and not having it break apart and fall over haha. I've also played a puzzle board game about Latin squares (though they don't call them that) where you build a tiny city to fit a specific shadow. Sadly I don't remember its name

@RecursiveTriforce 11 месяцев назад

Thank you for making a video with my 3-dimensional cousin and playing with him! He loved the experience, even if he thought the lights were a bit blinding.

@tyronorxy5646 11 месяцев назад

*The geometric approach:* 1. Given 'n' amount of lights, you can always just use 'n' amount of 2D shapes, each perpendicular to one light, to cast the shadows of any 3D object. 2. The amount of 2d shapes then can be reduced by stretching particular shapes and turning them in such a way that they enclose equal angels to multiple lights. 3. Then, if you want to turn your collection of 2D shapes into a single 3D object you just have to connect their edges with planes in such a way that said planes remain in the confines of the shadows of the 2D shapes. *The 2D shapes you need for the 3 circular shadows are:* 1 circle perpendicular to one light; 1 ellipse enclosing a 45° angle with the other two lights; Now you just have to connect the edges with some bent planes to get a 3D object.

@ericpeterson6520 11 месяцев назад

You really buried the lede with the title and thumbnail, I almost didn't click because I assumed it was just going to be that simple guessing game the whole time. Maybe a trio of square shadows and an indication that the mystery shape is NOT a cube would be more eye-catching and illustrate what's interesting about the video better

@JMurph2015 11 месяцев назад

Ok but what about the thumbnail challenge 😅?

@joshl.4358 11 месяцев назад

This was a great video. Well sequenced, well explained, and interesting.

@eigengrau7698 10 месяцев назад

When you link the explanation with sudoku, my brain went through the atmosphere

@ge-orc8286 11 месяцев назад

horrible clickbait. dont get me wrong, it was reasonably interesting, but the case from the thumbnail, with square, circle and triangle was not solved in the video.

@kxs7267 11 месяцев назад

From the thumbnail I expected a trivial (but fun) exercise in 3d visualisation. And instead I got a fascinating mathematical excursion into fractals. Nice!

@ac2bn 11 месяцев назад

Before clicking into this video, I looked at the cover and thought hard on the puzzle, I couldn't imagine what 3D shape will have triangle, circle and square shadows and was expecting explanation. Turns out the video is not about it😂. Now I'm curious what does it look like or whether possible or not. Despite this little misunderstanding on my end. The video is really high quality, fun and extremely smooth to keep track of.

@VCLegos 11 месяцев назад

You are a good teacher, this was explained in a very easy to understand way. This is how teaching is supposed to be done, thank you.

@nuclearduck13 11 месяцев назад

The thumbnail shape with silhouettes of a square, circle, and triangle would look like a really short, fat toothpaste tube

@deanthe3684 11 месяцев назад

In middle school, I once cadded a shape which was essentially a cube cut by a cylinder on each axis to have 3 circular shadows. It also had the property of rolling on a grid. It looked like a hackey sack sewn of 12 rhombi. Pretty cool shape.

@mikeflowerdew7877 11 месяцев назад

Very nice! The link to Latin squares was unexpected and very well explained

@jonuuh 10 месяцев назад

Really fantastic video, was totally blindsided by the connection to sudoku. Love this style of video and would love to see more!

@elementalearth1237 11 месяцев назад

i literally said "oh, just like sudoku" out loud immediately before you said that it might be familiar if we've ever played sudoku

@Atomas69 11 месяцев назад

this is really cool! Brings up a cool concept that can be played with in further complexity! I also love how enthusiastic you sound in this, makes anyone watching feel the same sort of wonder, encouraging the discovery of new things this newfound topic

@hymanimy 11 месяцев назад

This was so awesome. Perfect pauses taken before reveals - kept me as the viewer primed for the next thing.

@random832 11 месяцев назад

the easiest example of "three circular shadows, but not a sphere" is the Steinmetz solid - the intersection of three cylinders.

@GarryDumblowski 11 месяцев назад

To be honest this isn't where I was expecting this to go, I was thinking you would show a pattern and then it would be revealed that no shape can make that pattern with the shadows.

@aepokkvulpex 10 месяцев назад

That's right, this shape fits in the square shadow!

@robharwood3538 11 месяцев назад

Nice one! Good progression from basic concepts to more advanced, in a gradual pacing.

@BsktImp 11 месяцев назад

Wow! What a great punchy little video on a fascinating new-to-me topic. Quite aside from the SoME competition, this hits all the right notes on immediacy of engaement, piquing curiosity and leaving me asking more questions. And the revelation that this was done in ye olde PowerPoint _and_ you wrote the music too...! I salute you.

@bengobler 11 месяцев назад

Ha! Old but mighty. The "morph" transition is a workhorse. Without it, I'd have to learn how to animate for real...

@jerecakes1 11 месяцев назад

i genuinely love the catch you introduced at the beginning, i was really flabbergasted and made me watch the entire video which, said video was really concise and full of interesting points and/or realizations what i loved most was the fact that you can interchage the shapes between the cubes, really obvious info once i got it but it sent me how non-square like you can get them to look like LOL

@odysseasv7734 11 месяцев назад

This was an amazing video, very consise and motivating to learn more and create some imaginary cubes (or tessaracts ?!). I particularly liked the real life videos of the shapes and the pauses you did to make us think. Good luck in the competition!

@duskyrc1373 11 месяцев назад

What I thought was going to be a discussion of back-projection turned out to be a thought provoking video on fractal structures. 👍

@Sahir_Here 11 месяцев назад

I thought this was a quizy video to see how smart you are, but this actually transition into a math lesson very smoothly. 10/10 video

@DroCaMk3 11 месяцев назад

Interesting topic, great visuals, great explanation, catchy background music! Very well done!

@ray_jewelzz 10 месяцев назад

i thought i was going to watch a simple quiz-like video, instead, i learned something new! thank you!

@L4Vo5 11 месяцев назад

For me, it still wasn't entirely obvious that the other "base" shapes are imaginary cubes, I just had to take your word for it. Would've been nice to have an animated visual of that.

@MilanTheAngel 11 месяцев назад

Seeing this video I assumed you were a big math channel, since the quality is top notch!! You're definitely gonna get there if you make more, its good stuff!

@kipchickensout 11 месяцев назад

"well it looks like a square but it's too easy so I guess he'll give me some lesson now"

@ebenenspinne4713 11 месяцев назад

One possible shape would be a disc, which is at an angle (maybe 45°, but I'm not sure). The highest point of the disc could be at the bottom left side of a cube imagined in the place of the sphere and the highest point would be on the top right side.

@citratune7830 9 месяцев назад

My immediate guess was that if you made it concave at all, you could not. And this kinda was true for any of the shapes you showed that tiled

@dariofagotto4047 11 месяцев назад

For the sphere I guess one of the simplest convex cases is just taking the trivial solid with these shadows (that in fact it's not a sphere, we think of sphere just cause we like it not cause it's logical) just by taking the intersection of the cylinders made by the 3 shadows

@tricanico 11 месяцев назад

This is my favorite so far. Fresh and to the point.

@NickAndriadze 10 месяцев назад

That was such an unexpected yet great twist with the tetrahedron, I love it.

@MemeAnt 11 месяцев назад

This is very interesting. It’s rare I find a video like this. Fractals are cool, and I love geometry. Cudos.

@Xonatron 11 месяцев назад

I was in the demoscene and always wanted to create a demo effect like this. Not with shadows but with points that look like different objects from different perspectives.