Mathematician REACTS To 'Animation Vs Geometry' | (Math Explained)

hi welcome to the mathemagic channel So today we're going to be reacting to animation V geometry and I have to say I'm really pumped and excited about this one uh so you know I'm really happy to be doing this video with you guys and I wanted to First give you a big shout out and say a big thank you for all the absolutely amazing positive comments that you guys left on my animation vmath video so if you haven't watched it yet please go ahead and watch it it's a good video and uh you guys have been so incredibly supportive I've really appreciated it and uh yeah I just wanted to say that first and so today we're reacting to animation V geometry by popular demand you guys just asked for it so I'm going to be doing my best to do it justice I look at Alan Becka's videos like something which uh you know is a little bit like a super cool puzzle where you have to unlock all the hidden meanings inside of it so without further Ado let's Jump Right In and uh enjoy the video thank [Music] you okay I guess we're good to go let's see it I'm excited I hope you guys are too [Music] [Music] this is just an advert though maybe I need to get one of those pretty cool [Music] what [Music] [Music] this might this might seem like nothing but from the second coming or Stickman or orange or whatever you want to call him appearing we've gone from zero Dimensions which is a DOT to one Dimensions or or one dimension which is just a straight line to two dimensional uh object so this is pretty cool [Music] so this is either going to be a vector or [Music] aray and if you're doing high school geometry this uh these are vertically opposite angles when you have two secant lines like this you get vertical angles and they're equal so nice representation of that [Music] I love how he's thinking about it he's like what do I do with my angles like imagine he was like an old Greek man trying to discover mathematics this is pretty cool um and then here you have angles on a straight line which are 180 and which give you two 90 degree angles on the other side uh introduction of ratios so if you have a ratio of one to one it means that really you have two sections 1 plus 1 is equal to two and uh in school like a lot of kids struggle with this so make sure that if you're doing maths at school if this is you and you're doing ratios add them together and then you have one half and one half you can change it into a fraction so one out of two parts and one out of two parts introduction of ratios is good here [Music] [Music] wow so the introduction of the letter five the golden ratio of 1.618 super super cool let's talk about it so what is the number five so fi is 1.618 and it's a solution to this quadratic equation which is x^2 - x - 1al 0 which you can solve with the quadratic formula uh it's equal to 1.61803398875 what's really interesting about it is if you're to do uh one over five so the reciprocal of five you actually get the the same string of decimals which is shocking for irrational numbers it doesn't happen very often um and it's named by Mark bar in 1914 after a Greek sculptor called fidus um yeah and we use it to denote the golden section or the divine mean so the way that you can think about it and this is the Fibonacci um rectangles for you is that if you have a sequence which goes one one two three and the way you construct that sequence is you do 1 + 1 to get two 2 + 1 to get three 3 + 2 to get five 5 + 3 to get 8 8 + 5 to get 13 13 + 8 to get 21 it's the Fibonacci sequence um what's really cool about this sequence is that as you um go to bigger and bigger numbers and you divide one number by the previous one you get very close to the golden ratio so if you do two ided by one you get two if you do three divided two you get 1.5 if you do five divide by three you get 1.6 recurring if you get 8 divided by 5 you get 1.6 and you go all the way through to 21 divided by 13 which is about 1.65 and you can check that out and so you get closer and closer to 1.618 um yeah so this is a Fibonacci Sequence and it's supposed to make things very pleasing to the eye and so we've used it in music U we see that pattern in famous paintings a lot even in like modern AI paintings look at this one beautiful spiral uh and so yeah you'll see this Fibonacci spal um everywhere pretty much and here's a representation even of the Taj Mahal with again the beautiful Fibonacci spiral and so f is the solution or one of the solutions to x² - x - 1 equal 0 you can use the quadratic formula to solve it and you'll get 1 +un 5 2 and 1 - TK 5 over 2 1 +un 5 over 2 is 5 1 - TK 5 over 2 is which is another Greek letter root five is 3 uh is sorry 2236 and if you to add one to this you get 3236 and if you divide that by two you get your 1.618 which is five and let's go back to the video [Music] notice route three which is 1732 just a little bit bigger than 1.618 [Music] help oh that was sweet he helped him out now is the 30 6090 triangle that's one of the special triangles and it has side lengths too root three and one very nice to see it showcased [Music] here that is a 90° rotation clockwise that's a geometrical transformation so it's good to see that showcased as well that is a reflection about the x axis so nice to see that happen as well an 150 degree rotation [Music] it's nice to see all the angles on the inside like as we go through you know all the different polygons here and you've got like your Pentagon octagon heptagon and so on how far are we going do you guys want to count how much that is I'm going to say maybe it's 100 sides which would be like hectagon maybe I'm off maybe this is a lot less than 100 you guys can count but if it was 100 it would be a hecton like in hectogram and if it was a thousand no actually 10,000 it would be a myriagon I really like that word so uh because Myriad means a lot of something right uh but you wouldn't to the naked eye it would just look like a circle and we have a circle so this is golden not because it's a Golden Triangle I don't think um at the bottom notice you have pifi which would suggest the perimeter of the shape is pifi so that means the diameter uh so the length across is actually five so the length across would be 1.618 and then the whole perimeter would be Pi * 5 this is also show showcasing the um one of ID's theorems which is if you stick a triangle inside of a semicircle it's right angled so it's nice to see that triangle in a semicircle um shown here I suppose this is a golden Square because the side lengths are five [Music] he's so happy he can swim in it this is one of the 370 proofs of Pythagoras Theorem beautiful to see it showcased here [Music] he says go fetch that [Music] square this is another proof to Pythagoras Theorem very good did you see that this is pretty cool so five to the^ 0 which is 1 + 5 is equal to 5^ 2 so what's that all about so you can actually take the quadratic uh formula solution for five uh 1+ root 5 over two and if you had to add one to it so if you add two over two to this you get 3 +un 5 over two and if you calculate 5^ 2 you also see that this is 3 +un 5/2 so 5^2 is indeed equal to 5 + 1 so you can do this numerically and you can do this uh using Pythagoras Theorem as well so pretty cool to see that being showcased here they're friends now whoa what's that whatever it is looks pretty angry okay I feel like we need to talk about this now that is a seriously angry 4D object so why am I thinking that it's a four-dimensional object well first of all when you look at a three-dimensional object and you rotate it like this Cube it stays fixed in space almost you can see that there's no like bits of it like folding onto itself or whatever so this looks a lot like a four-dimensional object because there's this internal type of movement um and also in the video we started in zero dimensions and then First Dimension second dimension three dimension so it's normal that we're just increasing in in Dimensions I don't know how far we're going to go uh if we're talking about string theory and you know 11 dimensional spaces and so on and folds uh so we could go really far with this and let's see later what happens in the video um in terms of uh four-dimensional objects you can see here a tesseract which is a 4D Cube and here you can see that it's like almost like you have a light that's pointing at the object and projecting it in the back and then from different angles and it's kind of folding onto itself and this kind of movement can only happen with four dimensional objects or higher so that's why inferring that the shape in the video is a four-dimensional object object is probably quite accurate um a bigger shape would be a 24 cell polytope so this could be definitely something that's very close to what we're looking at but even this seems to be a little bit too organized although it could be a good villain for the video it seems to be a little bit too organized for what we're looking at which looks really chaotic uh actually it might be just like a random shape that doesn't have you know like a structure inside so I was thinking maybe it's the Metatron Cube Cube uh who's just really angry and the Metatron cube is a Divine shape in sacred geometry where you have you know all the all the platonic shapes contained inside of it so in in Metatron Cube you will have the tetron the Octon the doc cedron and so on so these all contained within this shape and there is kind of not a Biblical but a uh I think it's in the talmood a cabalistic uh reference to this where Metatron was an AR Angel and it's not very clear whether he's a force of good or a force of evil you guys can look it up uh please don't cancel me in the comments below so please don't go blitzing my comment uh because of this but you know maybe this is what it is so do you think that it's a polytope do you think it it's Metatron Cube I don't know so um I I think both of these are wild guesses which could both be a little bit accurate but you know I'd like to put this forward to you uh it is a beautiful shape and by the either way it sounds a lot like Megatron who's the head of the Decepticons and Transformers so he's a bad guy and so the Cub's a bad guy I don't know you can go ahead and and tell me what you think in the comments below now also I wanted to point your attention to the sapinsky carpet that's being left behind it's very cool like the way that this shape is constructed like you see some iterations here where you have uh you know a square and then you make a hole in the middle and then you take the other squares and you make holes in the middle of those and then you keep doing that all the way to Infinity so you see up to C4 here but you can do it up to C you know trillions or millions and then the cool thing about this is it's like in a fractal Zoom where you can just keep zooming in on the shape and it just repeats onto itself to Infinity um so without trying to break your brain here's a fractal Zoom of a cinsky carpet and you can see how incredible this is anyway I think it's great to see those references in the video and I'm very I'm very glad that these were included uh let's get back to the animation run Stickman oh very cool this is the fractional representation recurring fractions representation of F his shots are getting deflected at some funny angles I don't know if that means [Music] anything that's our spiral from earlier [Music] is this like a hoverboard or you say that's like a a unicycle more like a unicycle right because it's in the middle [Music] all right all right back up a little bit here okay so this shape this is not a random shape so um actually these tiles are not random at all and if you saw the angles it was 727272 144 we call this the kite um and then you have the dot which you see on the right um and that's 36 216 3672 and so he's using uh I'm not sure if he was using actually the kite order dot as a paraglider I have to check the video again but this was um something that Roger penro Roger Penrose came up with and those are two tiles that you can so if you you have to set them in a specific order but given that specific tiling so there's only one way that you're allowed to tile them they will make what we call an AP periodic pattern so a pattern that doesn't repeat itself and that's very unique um so it's pretty incredible that that's showcased here and this is something that came up in the 70s so here's a Penrose tiling and as you can see there's like these star shapes and there's other shapes that we call Kings and things names named after a deck of cards actually uh you can look these up these are pretty cool uh but you can see that like the placement of the Stars doesn't really like repeat itself it's just kind of random and all over the place so yeah this is a nice reference in the video I think to Penrose tilings now one more thing that I'd like to share with you about Penrose tilings and this will blow your mind is that if you take and this is not a joke you can you you can look it up the limit as n tends to Infinity of the number of kites divided by the number of dots so the number of kite shapes divided by the number of dot shapes you get five true story so that's kind of incredible to see that mentioned in the video and I'm wondering if it's a little wink to the fact that five is actually not only inside of the shapes but also in the number of shapes divided by each other which is absolutely incredible right [Music] he's shooting octahedrons this is insane [Music] this is like a Divine uh sacred pentagon with a pentagram on the inside lots of golden ratios rallying [Music] up it's nice to see like the fractal on the side of the of the Pentagon there look at these circles there there's like tangents to the circle and inscribe triangles actually no like just just a piece of the triangle is inscribed very very cool dumping golden rectangles on him he doesn't like it though like the golden stuff seems to hit him a little bit okay so if you trap him in a cube you can make him go away this really reminds me you guys and I apologize for the super old film reference but of when uh in Superman one when we trap General Zod and send him into space um yeah maybe that's what this is referring to [Music] oh he's pissed he's really angry [Music] so trapping him in a pyramid here which is a tetrahedron wrap him in a [Music] [Music] cube this is going to be the iosa hedra um [Applause] so we threw the DOA hedron at him and now you have these beautiful Dragon curves amazing very very cool so these are the the platonic solids that we just threw it in I think this is extremely intentional um so if you look at the different platonic solids you have your you know triangular base pyramid which is a tetrahedron then you have your octahedron hexahedron which is a cube icosahedron which is the 20 side and then doc cedron which is 12-sided and so it looks like we threw fire at the at the villain right and it didn't work and then we trapped him with air and it didn't work and then we trapped him with Earth and it didn't work and then we trapped him with water and it didn't work and by the way Plato the way he looked at platonic solids is that um you know one turns into the other so like air will um turn into water and then water will turn into Earth and then Earth and air will turn into fire and then they'll all like turn into each other however ether means the universe and so when he throws the universe then suddenly that works because the universe is just like the most powerful thing and so he threw the universe at this sort of chaotic shape all this Metatron or whatever it is I still don't know what it is and uh and that worked so yeah the dodecahedron seems to be the most powerful shape um and it's it's the golden doca hedron as well and took like the power he harvested the power of more like golden ratios before he threw it very very cool oh my God absolutely amazing this was in fact so cool I'd love to watch it again absolutely [Music] incredible so he steps into the docah hedron and these shapes now they don't look 3D or 4D anymore they look like maybe they extra like look at that blue shape here like was that I forgot which one it was was that the icosahedron the the blue one it looks like there's a lot more stuff happening inside so maybe it's a higher dimensional object so instead of like three or four dimensions I'll put an example here um of like a ninth dimension nine-dimensional object just for you to get a a reference as to all these different interlocking points here also if he's in the Multiverse and if this is like a wink at at String Theory um then are these like different version versions of himself in like different universes and then everything all the elements are going towards some Central light like is that the center of the universe what's going on with that oh if you've got any ideas please let me know in the comments below okay so this is like a reference to animation V physics is this like imagine that he's um he's a mathematician he studies geometry but in an alternate universe he would have been a physicist [Music] and if you met your Alter Ego from an alternate universe a little bit like an Interstellar when he goes into that Library you probably fall off your chair like he just fell off the the do do [Music] decahedron the end and I have of course I don't want this to end oh my God but there's a couple of things to say about this okay so here's my take on the ending here um there was an article published in 2003 inside of physics World which I've just pulled up here uh which suggested that the Universe might be a docah hedron and this is uh coming off measurements of the W map which stands for the Wilkinson probe which was sent into space and by the way all the measurements for the Wilkinson probe have now been recorded and all the studies have been completed so until we have a you know further kind of studies this is where we're at in terms of humanity um and so we're looking to find the topology of the universe and you know we managed to establish a certain number of things like the amount of dark matter or the number of atoms and things like that um and so in terms of the shape it suggested that if it was a doc aedon it would agree with uh the formations of the cosmic microwave background what we call CMB radiation um and so you can read this article um and go and figure it out for yourselves maybe but I think this is a wink to that uh yeah so very very smart in the video um I think and if you're not convinced this is what a pank do cedral space with multiple Earths might look like and if you watch the end of the video again don't you think this looks really similar so I think that this is definitely what Alan Becka's team is hinting at um yeah I'll play the end of the video again for you maybe you can you can think about it so let's take another look at this now [Music] what [Music] [Music] so thanks for being uh with me and uh following me on this adventure through this whole video I just want to leave you with one closing thought here because I think it's uh it's a cool one do you think the point of the video is to say that Plato 400 years before Christ correctly predicted the shape of the Universe um as a dodecahedron which he called ether saying it's the universe wouldn't that be incredible imagine if he's right like how powerful would that be and uh to finish I just want to say isn't math just beautiful don't you guys think anyway please make sure to um support our Channel and I shall see you on the next one bye-bye thanks than you [Music]

Channel: The Mathemagic Channel

Views: 19,363

Keywords: reaction video, math reaction, animation vs math, math, math videos for kids, math video, educational videos, maths for kids, learn math, how to be good at math, how to become a math genius, how to understand math, a math person, how to learn math, they know the best, creative thinking, animation vs math explained, animation vs geometry, animation vs geometry explained, animation vs geometry analysis

Id: SJV4Y7gSqg0

Length: 34min 9sec (2049 seconds)

Published: Mon Jul 08 2024