And we're at last. Nice. Hi everyone. This is Gichu. Welcome to my channel and welcome to another live stream. Today, today is November 14, 2022. And we're back at it, doing our math drop-and-tutoring sessions. And this is number 81. For the last, I guess, three years maybe. All together. Maybe less. Maybe two years, maybe four years. I can't remember now. We're doing a lot of math sessions. We weren't numbering them. So we've been at this doing live streaming on Twitch. That's where we're live streaming these sessions over here. For about four years now. Basically, this is a foundation of why it is that I started making videos and live streaming and whatnot. Specifically making videos back in 2007.  So this is the foundation of what my work is about. So thank you very much. What the bug? The 07 is now following. Thanks for the follow. Salut, salut. Now give me a siggy. How are you doing? So if you're catching these math streams, just know that everything that I do is basically layered on mathematics in some form or another. And if it's not as obvious as it can be, at some point we will make it obvious. Some of the stuff we already did. And for those of you that want to know what this work is about, you can follow my work on Patreon, Substack, and SubscribeStar. For those of you that are supporting, we've got people supporting us from multiple platforms, but Patreon, Substack, and Twitch are the three main ones where it's mainly because of the support we're getting on these platforms that we're able to do what it is that we are doing. So everything done, it is sort of a business model. It may not be a corporate business model, but it is a chicho business model. Maladras, how are you doing? Chicho business model of what I had in mind when I started creating content back in 2005, writing blogs, 2006. There was no form of monetization other than advertising back then. And I didn't partake in the advertising really. But I knew at some point there would be a movement where content creators were lifted up and supported by the community. It was inevitable. It was inevitable. And one of the indications for me that this was the case was from Robert Anton Wilson. But we can talk about that event at a future date. For those of you that are here, I hope you enjoy the work, the math. You can also follow the work on Gettrvk, Gap, Parler, Mines, and BitCloud.  Eat a salad. Right now you're eating salad right now. Nice. Yummy. I got my walnuts and raisins going on again. Slayer, Darth, how are you doing? I am disabled and was told as a kid that I would never be good at math. That's because they don't want you to be good at math. They lie. Years after leaving secondary school, I decided to teach myself math from scratch. The stereotype is true. It is all about confidence. It is all about confidence, support. A good curriculum. People that care. And as Krishnamurti would say, it's about the love it is really. That's all it is. And any institution, anybody out there that's listening to this, if you've been told by centralized power that you will never be good at math or math is not your forte and good luck, you shouldn't take higher level math or whatever it is. If centralized power is telling you this, they're lying. They're lying. Give me a city says after school system that you have to do you have to do to do you. Yeah, exactly. The best educator in your life is going to be you for sure. Find great teachers and stuff like this. But experience is 90 90% of wisdom. Okay. Experience is 90% of wisdom. When you see those people that are only academics and have never experimented in some of the philosophies, core philosophies that they study, they're about 10%, about 10% know what's going on. The ones who are in the field doing work, doing their own business, working for someone else is fine. Doing research, educating yourself. That's the 90 90% that really gets done. Right. Slayer d'arth. I have a geometry question. If that's okay for sure, lay it on us. Crack. How are you doing? Good afternoon. Misty yesterday. Crack. I did, we did a current event stream, but I had two comic book hauls. There weren't comic books, but you'll have to wait for the video to be uploaded for you to see what they were. You're going to laugh. Afternoon. Afternoon, everyone. So Cheryl, how are you doing? Hope you're doing well. Slayer d'arth with a question. What math are you doing? Any math, any questions that come up? George from Peru, how are you doing? Allerga's in the house. Allerga's in the house. Not how to distinguish the triangular prism. Crack. Damn. I'll check it out when it comes up for sure. I'll break it up as well. So let's read the Slayer d'arth. I gotta finish my intro, but let's read Slayer d'arth, the question we read again. How do I calculate the volume? Oh, you can't give me the, is that a link? Slayer d'arth? You can't post links in the chat, the triple star, if it is, but I'm going to read you a question. You'll have to send that to either Cheryl or Allerga. Oh, there it is. You took the HTTP. Okay, good, good, good, good. How do I calculate the volume? I've been told that I should split the shape into a rectangular, rectangle, and triangular prism. Compute the volumes for each, then add them together. Yeah, that would be probably it, but we'll take a look at it. Gang, I'm going to finish off this live stream's intro pretty fast. For last year's, we don't have any visuals. We do today. We do upload the audio to soundcloud.com forward slash chichu as a podcast, and those podcasts should be available in your favorite podcasting platform, including Spotify, iTunes, Google Play, and whatnot. This full live stream is mathematics. We'll keep politics on politics. We'll be loaded on censor two on Bichu and Rumble and on Odyssey. And we do have a Gilded server. You're definitely welcome to join us on Gilded and participate in our little community. And we do have a sub-math section as well. We have heavy topics, light topics, and a math area, where you can share math information. Everything's, as I said, is layered on mathematics. Aside from that gang, let's do a little bit of mathematics. Let me take these guys down. I'm going to see if I can open up here, because all we need is the image. I can just come up with my own image. Let's see. Oh, yes, I do remember. I do remember. I should have prepped. I wish you sent me a little notice earlier in the morning. I would have had something here to do. I totally forgot I was running around doing stuff. But we will. We will do this game just for now.  But there is something that we have to do right now, because it is, it is, it is, happy birthday to you. Happy birthday to you. Happy birthday dear Cheryl. Happy birthday to you. It's, for what I understand, when Aldi got dropped on us yesterday, it's Cheryl's birthday today. I hope I got it right. Is it okay? Perfect. Awesome. Fantastic. Good, good, good, good. Blushing. Awesome. Awesome. You can tell I'm blushing as well. I'm a little hot here. And there's the virtual cakes popping up. For sure, Cheryl. Happy birthday and all the best. Seriously. Fantastic, fantastic. And thank you for being here on your birthday. What an honor. What an honor. Like seriously, same with Aldi God. Aldi God was here for his birthday and we had a little cake. I was munching on Munchies cakes and Aldi God set us up nicely. Cheryl's quiet about this stuff. She didn't let me know. We had to hear it from a second third. Another mod, right? But awesome, Cheryl. Awesome. Many, many, many more. Okay, healthy more, of course. Healthy more, of course. Oops, there we go. Hold on. Let me find this thing. Let's see if this image will pop up. Not many, great. Okay, hold on. It's not popping up. The link don't like it. Let's do it that way with HTTP. No math intervention. That just goes to it. For some reason, it's not popping up for me. I'll put a WDW in front of it. Nope. I'll take the S out of it. Confirm, draggy, not a butt. Okay, we'll do it. Sorry, gang, if I'm not catching the chat. I just want to see if I can bring up this image. No, it's not doing it for me. It's not doing it for me. But I know the type of shape you're talking about. Slayer Darth. Slayer Darth. So we'll just make a shape and you tell me if we're accurate or not. Baseman, how are you doing? Good evening from the northeast. Winter is coming. Winter is here. Winter is here. Slayer there. My understanding is that the prism have flat faces, identical edges, and the same cross section along the entirety of it. It's like, yeah, and that is the definition of prism, right? That is the definition of prism. Crap. Really glad to duck in for a bit. I'll take a virtual slice of cake as well, crack says. Trying my best to cut down on sugar. Yeah, me too a little bit. I got to get back at the shape a little bit. Slayer the Geometry is one of those weird branches of math for me where I can look up most of it. But then it can also get pretty complicated. Replace dot with, oh yeah, I didn't replace dot with, I didn't even see it. I just copied the whole thing. I just did that to bypass. Oh, okay, okay, okay. Hey, my man, buddy. Good afternoon, Lark Bark. How are you doing? Let me try that again. Let's get the full picture. Thank you for, oh, there is a dot there. I just looked at the front. Let's check it out. Bring on the, oh, still doesn't do it. Oh, there's another dot there. I forgot the dots. Dot. Dot. Come on. Okay, try this again. Oh, there it is. Sweetness, excellence. We see this image. Gang, oh yeah, I'm going to share the link in chat so everyone knows it. We got a link. We got an image. Here's the image. I'll post that. And you know what? I'm going to pin this as well because I'm going to make sure we have the link in the description of the video when we upload it. So let me just draw this gang. I'm going to bring up the chat just in case I'm missing something. You guys can correct me on the stuff. Weird. Oops. Hey, don't do that. Weird sloping square. Weird sloping. But it's not yeah, it's just a prism. It wasn't a, yeah, this one's, here, let me draw this to you. And I'll give you a little lowdown before we do this, right? So the question is, what was the question again? Let me pop up. Darth, darth, darth. Well, I'm going to bring out a better pen. What color do we want? Darth, darth, darth, darth. Oh, I missed it, missed it, missed it. How do I calculate the volume? Been told that I should split the square into a rectangle? No, you don't need to do that. You can, I'll show you how to calculate the volume without having to split everything up. But you can, yeah, sure. Triangular prism, compute the volume for each, then add them together. Yeah, basically. So basically the question here is, let's do, let's do light blue, new pen. Let's see how this works. So the question is geometry related, right? And we have the following shape and then we'll draw the same thing in the back and then we'll connect them up. My 3D drawings are the same. Let me bring up, let me take a look at it from what you guys see. Oh yeah, I got a little mutated piece here. Let's correct it a little bit here. We'll correct it a little bit. I don't know if that's much better, but a little bit I guess, right? None of my drawings are to scale, not to scale, not to scale here. We'll flatten this guy up too, or raise this guy up as well. Let's make it more pretty anyway. At least make those parallel, sort of, right? Mr. RoboDope, good afternoon, Chicha. Unfortunately, I have to run to the gym, but looking forward to watching later.  You too, as well. Have a great workout, Mr. RoboDope. Work hard, make sure you replenish and drink fluids, and have a little bit of protein to build back your muscle ASAP, right? So, here's the dimensions of this thing. Oh, I keep on closing that thing. Here's the dimensions. What do we got? We got 1.3 meters, 1.3 meters on the top of the height. We got 1 meter here. We got 2 meters here. 2 meters here. And we got 0.5 meters here. 0.5 meters here. Okay. Now, the way it works is we don't need anything. We don't need any other information for that thing, so I'm going to bring it down. Giving a sticky diagram itself in the picture states that it isn't actually drawn, so your doesn't have to be perfectly there. Yeah, so not to scale, right? If that's 0.5, then 1.5 would have been, you know, a little bit bigger than this, or 1.3 would have been a little bit bigger than this and stuff, right? So, take a look at this thing. Think about geometry in the following form. Start off with a point, right? So, all shapes consider it, and we're thinking, like, we live in a four-dimensional world, right? One of the dimensions being time, but we live in a three-dimensional spatial dimensional world, right? So, we have, you know, this way, we got up and down, and we got in and out, right? So, those are the three dimensions that we have, and this is a three-dimensional object, so it's got three directions, right? But start off with a point. Let's say you have a point, right? A point in space has zero dimensions, 0D, right? It's not 1, 2, 3, 0D. It's before we get into the dimensions, right? So, this is 0D, okay? And this is a point in space, point in space. 0D has no units either, right? And then you can take your point, stretch it out in one direction, and you have a line or a distance, right? Line or a distance. And this is in one direction, hence it's one directional 1D, right? And then you can take your point, start off the point, right? Start a point, draw a line, go a certain distance, and then take that line, the distance, and zoom it up, right? You got this. What you have here now is two directions, right? Remember, this was one direction, this is one direction, and this is the other direction. Now, we've got 2D, right? Two directions, and this is a surface or an area, right? Surface or area. It could be a map or whatever it is, right? So, if you want to find the area of this thing, you measure this distance, and then you scan this up, right? It's just like a scanner. It goes up. That gives you the area. And the way you do that is you multiply this times this. That's how you do it, right? You multiply the two directions together, as long as they were 90 degrees. If it's not 90 degrees, then form it like an area a little bit, but you're still really just multiplying the two directions together. Go along this way and go zoom up, then you get the area. Start off with the same point. Make a line, take that line, turn it into a surface, right? Now you have an area of something, right? That's what this is, an area, right? And then what you can do, if you want to go in a third direction, let's say this thing now is a box, right? So, you have one direction, you got two directions, that's this guy and this guy, and then you got three directions, right? So, if you got 3D, that means you're multiplying three different directions together. And visually, the way it works is you start off with a point, generate a line, take this line, scan up, you got a surface, take the surface, scan in, right? Go along this distance and you got a volume, right? That's a surface, you got a volume. You got a 3D shape or prism, if you want to think about it, right? Prism. Well, prism can exist. You can calculate the area of a prism or something, but let's just call it volume. Okay, let's just call it volume. As now, with three dimensions, we can occupy any point in space. And now, with three dimensions, we can occupy any space. We occupy the whole space, if you want to think about it that way, with the volume, right? So, for this, what you need to do is you don't necessarily need to, because this is a prism. And by the way, these are any shape like this is called a prism where one surface appears on the other side, where you can just scan it in and you generate a three-dimensional object, right? So, for example, you could have a triangular prism. There's your triangle and then zoom it into the page and you get a prism, right? You can get a cylindrical prism, create a square circle, right? And then zoom that circle in and you get a cylinder, right? So, this shape appears on the other shape just by tracking along this dimension, right? This shape appears on the other side as long as you track along here. So, over here, right? I call the triangular prism a tubular, a roll-on-bar, yum, dark chocolate one is the best. First time chat, how are you doing? Swift swath, not sure if I'm going to say that, what you wrote, right? A free Julian Assange gang, free Assange, free Assange, free Assange, Julian Assange publisher and journalist that has been crucified for trying to be transparent in accountability of capitalist poverty, humanity. For more information, see wikileaks.org, defend.wikileaks.org or our Julian Assange and Wikileaks playlist on censor 2. And if you need those links, you can come to our chat anytime you want on Twitch and type an exclamation mark, free Assange right up here. And what I just said with the links will appear, right? Just a little side track from doing a little mathematics because this is very, very important, very, very important, right? Now, this that we have here is a prism, right? Because this shape appears on the back side, right? Now, if, for example, this distance was smaller than that distance, you couldn't consider it a prism, right? For example, if this was this distance here was let's say 0.75, then you couldn't consider this a prism because this length was longer than this length. So you couldn't just scan in one side to get the other side, right? But they are the same. They told us that by saying it was a prism, okay? So all we really need to do is find the area here and multiply it by this, which happens to be 1. And that will give us our volume, right? So our issue right now is we're not really going to calculate two volumes and add them together. We're going to calculate two different areas and add them together. Now, there are formulas for shapes like this, right? That you can, that you can do, right? Calculate. But because we have these distances, we can actually, we don't need a special formula beyond a rectangle and a triangle. Because what we can do, we can take this thing. Let's transpose this shape here, right? So we took this, right? The surface that we're looking for, the surface that appears on the back side, right? And we made a work area for us. And it's okay to do this. You don't have to cram everything on here, right? Do your work. Spread your work out if you need to, right? Don't spread out your train of thought, though. If you're working on a problem in mathematics, keep it orderly, okay? First time chat. Wall bottle, yes. Let's free him so we can try. You're not very informed. You're not very informed. Put it right by yourself. You're not very informed. What's your name? Wall bottle? You need to, you need to, you need to find some other sources of information. Now, I highly recommend you don't get involved with politics too much, really. If you've been fooled by the propaganda, I think you should stick with mathematics personally. Build up the critical thought process a little bit. Joe Chichot, wouldn't a formula for any shape be derived from splitting the shape into triangles and rectangles? 100% or circles and circles as well, right? Or spheres or whatever, right? So what we do is put down the length here. So this is 1.3. That's that guy. This is 2. That's that guy. This is 0.5. Now, one thing that you notice, I'm not putting in the units anymore, because they're all the same units. In the final answer, you're going to include the units, right? So how are we going to break this up? The simplest way to break this up, the way you, you know, the only way right now for this shape, we're going to really break it up, is to go start here and come along here. Oh my god, this is, my line is wiggly, right? Trying to go slow on the white board is difficult, right? Chichot, but isn't the formula for circle derived from splitting the circle into an infinite number? Yeah, then you need calculus. We're trying to stay away from the calculus aspect of it. Keep it simpler, right? So all we do, we just say, okay, there's one more level, one more formula we need, which is a circle, which is two more formulas, the circumference of a circle and the area of a circle, right? 2 pi r and pi r squared, right? So we don't have to go into the calculus level. Now, what we got here is this is 0.5, so this has got to be 0.5, right? Easy peasy. If that's 0.5, then we've got this guy. We know what this is, right? 0.1.3 minus 0.5 is 0.8, 0.8, 0.8, right? So this part is zero point here. I'll put it on the other side. So this part here is, oh, I got a little small eraser. This point here is, we'll take this out. This is 0.8, 0.8, right? Okay, cool. This we know is two, right? Easy peasy. So area of rectangle, area of, let's call this one, area of one is length times width, length times width, which is length and width, I guess, 2 times 0.5, which is equal to 1. What are the units? 1 meter, okay? What's an area of the second shape, which is a triangle? Well, area of the second shape is really area of a rectangle divided by 2, right? Because if you break this in half diagonally, you get a triangle. It's the same deal as this, right? Same deal as that, but we only want half of it. So we can go this times this divided by 2, because you just want half of it. So Joe, to go back to your question, the area formula, even the triangle comes from this, right? So this is going to be 1.5 length times width, or they call it base times height. They change the letters around. So they go 1.5 base times height. There is the base, there is the height. So it's going to be 2 times 0.8 divided by 2, 2 kills 2. So this area is 0.8 meters, wink, and then this was 1. So this is 1, and this is 0.8. That's the total area of this duickey. So total area of this duickey is 1.8. This is 1.8. That's the area of this duickey. How do we figure out the volume of this thing? Well, we multiply 1.8 by 1. So 1.8 times 1 is equal to 1.8. The area was meters squared. Oh, I should put meters squared, meters squared, mind bad. So meters squared for the area, for the volume, because you're multiplying by another meters, meters cubed. So the total volume of this thing would be 1.8 meters cubed. Slayers are things that I understand all this. Cool. I was just struggling to visualize how 1.3 mine creates a triangle. Oh, so we see here, right? That's how it creates the triangle. You eliminate this part from this, and you got yourself a triangle here. And it's, look, gang, when it comes to geometry, it's pretty cool. It's just my experience from working with a lot of students over the last two plus decades, 25 years or so. There are some kids that might not be good in some of the other algebra, like just doing simple algebra or hard algebra. It doesn't make a difference. But they do phenomenal with geometry. And then there are people who are really good with algebra that have a hard time with geometry. There are some people that have a hard time visualizing the stuff. They have a harder time just seeing how it looks. That's why, in my personal opinion, any math test you write or any math test that's given to anyone, when there's work problems, they should also have a drawing of the work problem. Because English is not everyone's forte. If you're going to test them for their math abilities, you shouldn't be testing them for their ability to translate from English to the language of mathematics. If it is, then you should specify that is one of the requirements for the exam, for the course. So squares are the fundamental shape in geometry. That's why area is measured in squares. I guess so, yeah, square units, yeah, meters squared, you call them, I guess. I've never really looked into where meters squared, like the square comes from. And if that's really related to a square, it must be. It has to be. But I don't want to make that assumption. And, yeah, I believe so. If you go, I would say circle is a fundamental shape as well, really. But the problem with circle is, or the reason I would say is a fundamental shape is because that way you don't need calculus to get to the circle, right? Slayer d'arth. I'm good with all other branches of math except certain aspects of geometry. Yeah, so you're one of those people. This is Slayer d'arth. You're one of those people that's not good with the shapes, right? Here's my recommendation. Here's my recommendation. Play Tetris, really, old school Tetris or 3D Tetris. 3D Tetris was interesting as well, N64. But old school Tetris, preferably the best Tetris I ever played was, again, N64. The new Tetris was absolutely phenomenal. One of the greatest games ever created. I actually knew some of the people that worked on that game, that designed that game. New Tetris and N64. New Tetris was absolutely brilliant. You could get lost for hours upon hours in that game. Just get into an amazing zone with the beautiful colors and the shapes. It's fantastic. So I would say start playing. If you want to get better at geometry, start playing games that are shape-oriented. And there are other ones God, I can't remember their names. I know I've played some. I just can't remember the names such as this. Slayer d'arth. I find it difficult to visualize problems such as this in terms of the formation of the triangular prism. Yeah, well, it's literally just there where 3D a hybrid shape that gets stuck on to a certain degree. But there is it is valid to challenge people to try to break down crazy shapes and to have more fundamental shapes that they could piece together. But I think they should make it more interesting than what they do usually. Give me a siggy. Geometry, would geometry wars? Yeah, geometry wars. Fantastic. Yellen of Troy. How are you doing? And welcome to our live stream. Salute, Salute. Arcana nuke. First time chat, I really like geometry. Whenever I find a way to turn weird problems into geometry, they feel way easier. Cool. Very cool. And geometry is one of the fundamental aspects of mathematics. Salute, Salute Yellen. And Arcana, Arcana nuke. Just so you know, there's actually a calculus book out there. And I've seen it. I saw it a few, it came across it a few years ago. I didn't write down the name. I didn't write down the author's name. And I can't believe it because I've had a hard time trying to find that book again. But I know there's a calculus book out there that teaches calculus specifically by only using geometry. Like literally. I looked at a few pages of it, I was like, oh, that is brilliant. Right? That is brilliant. And I didn't make notes of the book. I planned on buying it and I don't have it. And I can't remember what it is. And if you do find what it is, anybody, gang, if you know this book, come to our Gilded Server and please post a link for us either in heavy books, light books in the math section or in general anywhere. Just tag me as a chichou and say chichou. I found this book. I'll hop on it and buy it. And if it's out of print, I most likely will be out of print. I'll try to track it down online and get a copy and we can take a look at it. Okay. Give me a siggy. Topology is very interesting. Topology is, in another life, I would have explored the realm of topology. It twists my mind. I have a hard time with it. I really do. So I would love to explore it. Slare the chichou. Three blue, one brown is pretty good in terms of visualizing calculus concepts geometrically. Yeah. And his work is fantastic, by the way, gang. I've watched some of his videos long, long time ago. I haven't seen what he's been doing lately. I do follow him on sub-stack on Patreon. I think he's a sub-stack too. No, no, not sub-stack. He's on Patreon. I do follow his work on Patreon, but I haven't checked him out for a very long time. He's been really, he was putting on a lot more videos in the past. He's been a little slow going at it. I think he explained why, but I forget. But his work is fantastic, really. Kudos to him, man. Kudos to him. He's doing an amazing job spreading the love of mathematics. And that, anybody that does that, is a friend of mine. All right. Allerga, describe the book again. Allerga, it's a book. And I think the author, the reason I came across it, because I believe the author is Armenian, right? If I recall correctly, it's a book, introductory book on calculus and teaches calculus using geometry. Just geometry. None of these crazy calculus formulas. And it's got a lot of shapes and stuff like this. It just looked good. And that's all I remember. Sorry. Alalora. Alaloro. Laura is a punctuester. First time chat. Cannot believe I've just stumbled upon Chicho. Haha. I used to watch you years ago on YouTube. Wow. I'm so happy. Still making liqueurs. Still making liqueurs. I wasn't going to say this, but this is Blackberry liqueur with soda and ice in it. I put one ice in it. I just felt like drinking something soda with Blackberry liqueur. Indeed. Indeed. I think I'm going to continue reading. Nice to see you're still teaching the beauty of mathematics. Indeed. Indeed. I'm going to say Laura. Indeed, Laura. And thanks for popping in. And the love. Fantastic. I'm still going at it. I'm still going to go out until the end of my days. I love doing this, right? I love doing this. And I'm glad you're you. Did you make any liqueurs? Laura, did you make any liqueurs? Joe Chicho is all of calculus literally just finding the slope of a curve at a point and finding the area under a curve. Or is there more to it? Is there more to it? I'm going to say I can only talk about what I know of calculus and what I'm the amount of calculus I studied. That's basically how far I was going with it. But then you can take triple integrals and stuff like this and do applied mathematics. So the area implies a lot, right? So it's not just finding the area under the curve. It's understanding the units that you're functioning in and how the algebra, the mathematics, the graphs, relate to the real world. So for sure, you're finding points and areas and curves. And it's really the rate of change when you're taking the derivative. That's where you begin calculus, right? Introduction of time into mathematics. That's the way I like to describe it. Yes. So the basics of it is, yes, that's what we're doing. But the interpretation is a lot more. That's like saying, you know, algebra. Is algebra just adding? And you could say, yeah, algebra is just adding, right? So for example, oh yeah, this thing makes the board dirty. Let's check it out. Let's use a pink one on the next go. Let's see. Let's take this down. I'll leave this bottom part on here. We'll leave that on. Now, check this out. You could say is calculus really just adding and subtracting or is multiplication this or is this algebra? Because everything starts off with just adding, right? Adding to things is the beginning of really doing algebra, right? Doing calculations, right? You take two numbers and add them. Before this is counting, of course, right? And then the opposite of adding is subtracting. So subtracting is really just adding a negative number, right? That's all it is. So subtraction is just really adding. So you could come and say is subtraction just really adding? I would say yeah, subtraction is just really adding, but there's more to it, right? You could say, oh, multiplication is really adding the same thing again and again, right? Multiplication is adding the same number or the same variable multiple times. And that's multiplication. So if we add two plus two plus two plus two, we can just say, you know what, let's come up with a new symbol and call it two times four, right? Is dividing just subtracting, which is just adding? Yeah. Dividing is just subtracting out the same number from another number multiple times, right? And you just build it from there. Remember, the language of mathematics is built on five axioms. That's all. And the axioms are really just involved the equal sign in addition and multiplication. That's all, really, right? Or I could have knew same Laura, same Laura. Give me a second. Is it advanced calculus, a geometric view by Callahan? Give me a second. I don't think so. The name, it wasn't Callahan. Hello Lonely Piggy, how are you doing? Slayer, by the way, I recommend quick calculus, second edition by Daniel Klepner, which was published by Wiley. Thank you for the recommendation Slayer. Laura, my name is Allah. Allah is Arabic. Allah. Absolutely sensational. I cannot believe it. I never got around to it. I experienced them. Carelessly through you. Awesome. That's the liqueur. We've got to do a cleanup of the liqueurs. I made some fresh ones this year too. So at some point, we're going to do a liqueur stream probably next month, this month. Anyway, well within the next month, maybe do it for Christmas celebration or something. Holiday celebration. Controllers then, how are you doing? Cheecho, how do you UF, how do UFOs fly without our known means of propulsion? From what I understand, all UFOs are based, they're supposed to be based on anti-gravity propulsion, right? So our whole thing, look, this is the thing. Gravity is, you could use certain words that you could use a word that starts with a B or whatever it is. But gravity is a pain in the rear end of science, right? Gravity is really problematic for us. We really haven't figured out what gravity is. Some people say gravity is a pull. Some people say gravity is a push. Some people say there is no such thing as gravity, it's all just electromagnetics, right? Some people, Tesla had his own definition of what gravity was. Some people say we live in an ether, which is really why we experience gravity, because it's a fluid, right?  Some people say gravity is the weakest force there is. Some people say gravity is actually the strongest force there is. If you look into multi-universal universe jumping through membranes, it's the gravity that connects different membranes to the different dimensions. That's some of the strength theory stuff that I read like 20-something years ago, trying to wrap my head around the stuff, right? So from what I understand, in my opinion, there's UFOs. I see objects in the air that I cannot identify, so they're unidentified flying objects to me, right? Those UFOs that most people talk about, their propulsion system needs to be, must be, by all accounts, based on some kind of understanding of gravity that we, the general public, cannot grasp yet, right? That's just my take.  I don't know.  So everyone has the ability to do the math, 99% of the mathematics that you're going to need in your life. That's my take, right? Give me a siqi, best channel for math book recommendations. There's probably the math sorcerer. He has some good content on there too. He also has a decent amount of advanced courses on Udemy. There's an Albanian mathematician called Mamikon Menakaskarian, Albanian, so I wonder if he's got Armenian blood. He's got an IAN who worked on visual calculus. Might it have been him? Maybe because that sounds like an Armenian name. So it could have been an Albanian that I confused with an Armenian, right? My memory plays tricks, right? He has a book called New Horizons in Geometry. That might be, is that it? Joel, if you please, if you're on discord, please link it up. I'll take a look at it. I'll take a look at it. Not discord, gilded. If you're on our gilded server, link it up. Don't go to discord. I barely go there now. I just go there to announce I've uploaded videos and stuff. Okay. But yeah, gilded. I'll take a look. I would love to get my hands on it if that's the book, because I would love to teach mathematics using shapes only. That'd be super cool. I have a student that would really appreciate that. Oh my god. I keep running into calculus with analytic damage by Robert Alice. No, it's not that one either. I'm pretty sure it's not that one. Oh my god. I've seen Robert Alice. But link it up. Again, if you find this book, link it up on our gilded. I'll take a look. Hopefully it's one of them. Joe, Chicho. Oh, I mixed up Albanian and Armenian. Oops. Oh, what is this? Maybe. You could be an Albanian Armenian. Oh my god. Is it Allah or Allah? Allah. Allah. Allah. Allah. Allah. No one is bad at math. It just takes practice. I push math on my little brother, 10 years my youth, and he improves slightly year by year. Math has so many transferable skills, namely problem solving, 100%, 100%, critical thought of the yin-yang, right? Huge. Huge. Yeah. And it's just persistence and consistency. Putting effort in, right? Slayer d'arth. I don't know if you're aware of A levels here in the UK. They are taken by 16 to 19 year olds and are somewhat similar to AP in the US. Anyway, I have been self-studying for A level math off and on for the past few years, with an aim to eventually sitting A level math as a private candidate. Awesome. Good on you, Slayer d'arth. It takes a little getting used to the sort of, if they say AP level or A level math or whatever they call it, right? Because it's the questions that they give you that become difficult to translate. That's one of the issues. And there's a lot of gaps in what they teach. Like I've worked with students that, favorite students in the past, not in the last few years, but in the past, I went through a period for a few years where I had a lot of AP students and AP calculus and when I was teaching calculus and stuff like this. And I didn't like the courses, right? I didn't like the courses because they were very disjointed and there was a lot of holes. So the students I was working with, they were, you know, they would study this concept and then in the next class, you would do this and they were like, they were lost. They couldn't figure out how they went from here to here. So we'd be filling in the gaps and whatnot. They could be good, but you have to do those AP type of courses or A level courses. You have to be on the ball and you have to stay up to date. Make sure you're doing all the work, right? It's a serious commitment. Joe Chisholm, no, he is Armenian. I was right. That book was released in 2012 though, so it was fairly recent. Yeah, it could have been then because that's what I was looking at early 2010s. From what I understand, it was recent. I think I read some of the articles that he wrote before that. So that might be it. I gotta take a look at it. I hope you link that up for us when we yield it. Arkan Anukh, good luck Slayer. In my experience, past papers or your friends for A level, yeah, past exams, past papers, past assignments, are your friends for any of these special types of courses? Really? Because that gives you a sort of a picture into the mindset of the educators in the curriculum, which is something you have to know, right? Give me a siggy. Mathematics rightly viewed possesses not only truth but supreme beauty, a beauty cold and austere. Who is it? The physicist. Oh, I forgot his name. That sounds like one of his quotes. The beauty part anyway. Slayer at the Earth. Well, also on the spectrum, so I've had to learn very hard, very hard over the years to understand the context of certain words. Yeah, Slayer Darth, here's the thing with my students that I've had and I do have on the spectrum, all of a sudden you pick up a topic, you hit a topic they might have a hard time with and then you move on to another topic and they just absorb like a sponge. It's like you for me anyway, I can't feed them the information fast enough, right? So on the spectrum just says, to me, it really means you excel in certain topics and it takes a little bit of work for you to grasp certain other topics, which is really being a human being because we're not all made to fit inside the box of centralized education, right? Fun. Challenging, but man, makes you smarter than your average bear when you're, when you have to overcome challenges, right? Arcana Nuke. A-Levels feels a little better for that. D1 was the only module that felt like that for me and it's because decision isn't a type of, type of math you study before A-Level. So it was disjointed to a certain degree. Allah, my friend, where'd it go? Allah, my friend, unfortunately have to, my friend, I unfortunately have to depart. It's 9 a.m. here in Sydney, Australia. The day must commence. Have a great day. Chichu, you as well Allah. Thank you for popping in. Thank you for popping in and I'm glad you found us here. I'm glad you found us here. No longer have they did that, that, that. Allah, God, 2010. I was looking for it in 1980s. Yeah, it wasn't 1980s, Allah, God. It was either 2000s or 2010s, early 2010s, like during that period because I really started looking into it. Yeah, I think it was late 2000s that I looked into it. There must have been early 2010s when I was building some of the math curriculum I was building, right? Then I was looking into how I was going to teach calculus because I have looked into how I'm going to teach calculus, make a calculus module, right? Mathematics. We're still quite a ways away from that. I was planning on to have made it by this time but made other content instead. So we'll get to it at some point. I kind of knew fairs. I heard the x that is a math math. It's by a mathematician actually. Bertrand Russell. Bertrand Russell are fortunate. I really like that aspect of it. First time chat. First time chat.  End quote by Einstein. Possibly. We're apparently not sure. Yeah, there's a lot of stuff coded to Einstein and other people that aren't really true. Supposed to be the one about the, you know, if insects die, humans will die within that quote that everyone always says it's supposed to be Einstein. I don't think it's Einstein. Slayer dart. See, I just feel bad because the UK is such a classic society and to not do as well academically as my better off peers was very upsetting. Yeah, and it's not just the UK. There's many countries that are very classist or class based societies. India being one of them, right? The competition is fierce there. Fierce there. One bat, phoenix. I hope that was relevant. I just tuned in. Yeah, for sure. For sure. Quotes that make you think are always, always relevant. And I like that quote, actually. I've read it before. I've heard it before. El Ligar Ciccio. My android brain just recalls something on Discord from 2018. Yeah, yeah, yeah. Is it? We talked, I've talked about it before, but I can't, I don't think the book was linked or I didn't see it. Slayer dart. It was very unfortunate that I had a Lisp at school for which I got endless riddles. And it was, yeah, if you have anything physical that people, society groups, insecure peers that really have their own insecurities and the way they lash out is make fun of other people's insecurities or other people's whatever it might be, right? Differences. But Lisp is one. Lisp is one, for sure. Lisp is one. Made you stronger, slayer dart, I'm assuming. Made you have a, from our interaction, you got a pretty good perspective on life. So made you, made you a better human being, maybe. About math book, yeah, Al Ligar. Keep me a secret. Yeah, classism is a big problem in society. Huge problem in society, right? Bloodlines.  Crazy. First time chat, I use Wi-Fi. Is it possible for me to ask a question regarding data management? I'll try to answer. I'm not sure if I'll be able to answer it. I love data. I've worked with a lot of big data. I got my SAP certificate managing some data here. This is my, this is my SAP cup for FI for finance and work then. If I can, right? Thank you for the follow. Oh, I missed the name durr or something. It popped away. And if I can't, maybe someone else in the chat can, right? Give me a sec.  Yeah. I use Wi-Fi. Thank you for the follow. I still have the John L. Rose issue. Yeah, but it caused me all sorts of mental issues. Slayer d'arth. Yeah. For sure. For sure. For sure. It would. It would. For me, when I came to Canada, I didn't speak a word of English and I had to deal with that. I ended up getting into a lot of fights in elementary school, defending my rights. But kids, kids are kids, man.  I use Wi-Fi. Here's the question. I think this is a math course in my school and it's probably easy. However, I just started this course. The question is, quote, if three people are dealt one card from a deck of cards, it's three for one card, how many ways could all the cards be spades or face cards? This is combatorics. In general, I try to stay away from combatorics because I have a hard time with combatorics. Just try to understand the questions and stuff. Really, I have a hard time with combatorics, permutations with combatorics. But let's deal with it. Joe and all, I've never entered any math competitions like the Olympics and stuff like this. Again, because I have a hard time trying to interpret their questions. So we have a deck of cards. Here's a deck of cards. Here's a draw cards. Here's a deck of cards. We've got three people here. And the question is this. So we're going to, if three people are dealt one card from a deck of cards, and it's a deck of 52 cards, right? 52 cards. How many ways could all the cards be spades or face cards? So all we've got to do is figure out how many face cards there are and how many spades there are. So 13 spades, spades, right? And there's face cards in there. So we'll have to subtract those out. Okay, let me stay up with chat as well. The first time chat, dirt, dirt, listen, listen, lies. Dirtless surgeon? Dirtless surgeon? Salute first time chat. I'm not pronouncing this right. Thanks for popping in. Oh my god, at school every time someone asks me to say rain rabbit, someone got much hilarious.  Oh, thank you very much. Thank you for the love. See that? How are you doing? Ah, chichobab, love, awesome. So let's go back to this question. So we have 13 spades for this, right? Each person is going to get that one card, right? We've got 13 spades. And how many face cards do we have? Now we're not going to include the 10 as a face card because it's not a face card, right? So we've got four jacks, four queens, four kings, right? Three times four, we've got 12. We've got 12 face cards, 12 face cards, oops, cards. And three of these are spades, right? So we've got to take those out of this. Three spades, three spades, right? So we're going to bring this here and subtract three from 13. So we've got 10 only spade cards, and we've got 12 face cards. So in how many ways my teacher did, yeah, permutations, 12 choose three plus, and then you subtract the six, okay? 13 choose. However, I don't understand why they did minus six. The minus six would be this, right? The minus six is this, is three factorial, three factorial, which is three times two times one, which is six, which basically means you're eliminating the possibility of each of them getting like double, well not each of them, you're taking out the three spade face cards, right? But I wouldn't do it that way, maybe. I know this kind of not problem, probably a winning, probably a winning, yeah, this is probably a winning, right? How would I do end up doing this? Your first choice would be P, let's see this. So the solution the teacher gives is 12 P3 plus 13 P3 minus six, right? Yeah, that's what it is. And permutations, oh man, permutations, it's 12 facts for this one would be, let's write this out, that permutations has more probability, so correct me on the formula on this, okay? I'll have to look it up if we're not getting corrected. But permutations P is P and choose R, let's write it out nicer. I'm going by memory here all of it by the way. So if we have P and choose R, this is N factorial over R factorial. It's not N minus R factorial as well, is it? ID XT, that one would be combatorics. C and choose R would be N factorial over R factorial N minus R factorial. I gotta look this up. N minus R, okay, so it's N minus R, my bad. Thank you. So it's N minus R. So N minus R factorial, right? So for this, it would say this, 12 factorial over 12 minus 3 factorial plus 13 factorial over 13 minus 3 factorial minus 6, which would be 12 factorial over 9 factorial plus 13 factorial over 10 factorial minus 6 minus 6. And 12 factorial over 9 factorial is this, right? You go 12 factorial over 9 factorial. 12 factorial is 12 times 11 times 10 times 9 times 8, et cetera, all the way to 1. 9 factorial is 9 times 9 times 8 times 7 times 6 all the way to 1. So 9 to 8 kills that. So 12 over 12 factorial over 9 factorial is just 12 times 11 times 10, right? So this becomes 12 times 11 times 10 minus 13 over 10. If you do the same thing, you have 13, 12, 11, 10, and the 10 kills 10 factorial. They're gone. So this 13 factorial becomes 13 times 12 times 11, and then you got minus 6, whatever that ends up being. The reason I'm doing this is I want to do it in maybe the other way as well. So what is that? 12 times 11. Here, let's just punch it in. Let's see if we get this. Anybody else want to punch this in? Let's see. 12 times 11 is 132 times 10 is 1000. So this becomes 1320 minus 13 times 12. 12 times 13. Not minus. It should be plus, plus, plus. My bad. Equals that. So one, five, six, zero, and then add it to that. Subtract that. Okay. So one, three, eight, come on. One, three, two, zero, minus one, five, six, zero, minus six. So it's just going to be five, four, five, four. You get, oh, I subtracted. Zero plus one, five, five, four. You get two, eight, seven, four. So for this, you get an answer of two, eight, seven, four. That's how many different ways there are. Now, is there another way to do this? I wonder if we could do it this way. So that would be 22 choices. Let's try it. I'll see if we get the same answer. I'm heading up Chichou. Give me a siggy. It says, Chichou, have a nice rest of your day. You as well. Give me a siggy. Oh, what? My answer was 30, 30. Was it 30, 30? I'll try it again. Let's see. Let's see what the answer is if we do it the other way. The way I would approach it first, and I'm not sure if this is legit. All right. We want to deal out. We want to figure out how many different ways. Oh, 13 times 11 times 12 times 11. Oh, did I punch it in incorrectly? Let's check it out possibly. Let's see. 13 times 12 times. Oh, I forgot the 11 pooper scooper 11. Yes, indeed. This is way bigger. This is way bigger. Boink. Then that one should be. That one's huge. Oh, no, it's not. Oh, because we don't need the 10. That was being silly. 1716. All right.  Yeah, yeah. I multiplied by 10 accidentally. Silly me. 1320. 1320. Thank you for the corrections game. So 30, 30. Yeah. Boink. So this is 30, 30. 30, 30. Right? 3,030. So here's a quick way I would try it. And I always do this first, and I don't know if it's going to give us the right answer. If it doesn't, wrong. This is the way you do it. Right? I would say there are, from a deck of cards, there is 10 spades you can choose from, and 12 face cards, which includes the space face cards. So there's 22 different cards you can choose. So on the first card, you can have 22 different cards you can deal with. The next one is 21, and the next one is 20. Now what happens if we multiply all these together? Let's check it out. Let's check it out. Does that give us 30, 30? I hope it does, because that's a way easier way to do it. 22 times 21 times 20. It doesn't. Not even close. Oh, mine is way more. So we're not accounting for, so I'm not accounting for something using this. So this gives it to me. Probably the one thing I'm not accounting for is because what do you call it? Order doesn't matter in this. Right? Well, in this order doesn't matter in the other way. This gives me 9, 2, 9, 2, what? 9, 2, 4, 0. 9, 2, 4, 0, which is obviously wrong, right? Which is wrong. So I'm not sure what I'm not accounting for here in this mindset, right? Because I'm not very good at combinatorics or permutations. It's just my, I can't wrap my head around it for some reason, because the wording confuses me. Even though I understand the problem now, or we understand the problem now, right? There must, this must be part of the process. How many different ways, how many different ways are there? Let's read the question again. Now I'm all curious, what were we not accounting for? If three people are dealt one card from a deck of cards, how many ways could all the cards be space or face cards? I don't know why this doesn't work. I'm not sure what I would not be accounting for. It's a change in percentage as each card is chosen. All the God says. Could be 52 choose 22, and then 22 choose 3? No, that won't be it. I don't know. We can figure out what the minus 6 is, but I'm not sure why this doesn't work, and this does. Permutations, combinations. Permutations, order doesn't matter, right? Combinations, order matters. No, no, no. Combinations, order doesn't matter. Permutations, order matters. So why would order matter here? Sorry I use Wi-Fi. Is it right? No, it wasn't I use Wi-Fi that asked this question. It was, it was, it was, what was it? I forget what it was. Where'd it go? It wasn't Slayer that. Wombat Phoenix? Wombat Phoenix I think. It's a 6.24% chance of getting a face card if I'm, if I'm correct. Face card would be, no, it's got to be more than that. 12 divided by 52. The chance of getting a face card, right? Was 12 divided by 52. 12 divided by 52. 23% chance of getting a face card. That should be the probability. The chance of getting a face card The chance of getting, what's 0.6, what's 6.6? 0.24 times 52 times 52. How many cards does that give us? Oh Jesus, multiply divided by 100. What? Yeah, that doesn't make sense because that gives you 3.24 cards. I calculated for 3 people. Yuki, how are you doing? I hope you're doing well.  These types of problems give me a hard time. That's why in the description I say no hardcore calculus and no permutations and commentaries. I like algebra, I like graphic, I like functions. I love graphic, I love big data, I like crunching data. It's nice to do math again by the way. Live stream. I'm one of the reasons I haven't done this year, school year anyway, because I've ended up filling up my schedule a little bit with some students, so I needed to sort that out, get my rhythm down and then start making time for these live streams where we could do mathematics.  Let's see, let me, oh no, we need that shape. We need that shape. What else should we do? What else should we do in terms of mathematics? What did I look at recently? Which was super cool. I don't remember what I just did recently, which was very cool. It's that 52 times 51 times 50 thing maybe. I suddenly need to learn math probably, I know. I really, one thing with mathematics is, is Felix Unger? No, poker champion. Let me look this up. When I looked into this, there was only one person, poker. Is it Felix Unger? No, Felix Unger is the odd couple. World poker champion. World poker champion. World poker champion. World poker championships. Winners. Winners. Let's see, this is the World Poker Championship winners. Where is he? Where is he? Where is he? There was one person, Scotty Nien. Is that him? No, these guys. Okay, it wasn't World Poker Championships. It was something else. There was one poker champion in the world for the longest time where probably love math. There was one poker champion in the world that had only won the championship twice. I don't know if it was, it was a World Poker Championship. It was some other poker tournament. And he was, he was a bridge player. And he was a mathematician. And he was so good at bridge because bridge combinations, mathematics, permutations is Stu Unger. Is this Stu Unger? Stu Unger, maybe. Stu Unger. Felix Unger. That's what I'm talking about. Stu Unger. Is that him? I'm going to copy, I'm going to see if that's, that's his picture. Stu Unger. Stu Unger. That's picture. Yeah, that's him. Stu Unger. Stuart Errol Unger was an American professional poker blackjack and gin rummy player, widely regarded to have been the greatest gin player of all time. And one of the best Texas Holden players. Yeah. And at the time, I was really into Texas Holden, man. Huge, huge, huge. So this guy I have the high regards for, but he was on the spectrum for sure. And he, he basically was the only person that won whatever tournament that was twice, right? And he qualified for the final the third time and he never showed. He didn't even show up for it, right? Because those mental issues there for sure. And he didn't care about money. So he blew all his money and stuff like this. This is a good documentary I watched with him. I really like this guy. Man. I think I need to watch that documentary track down this documentary again. So Mathematist can take you a long way. I'm not sure. I'm slurred though. Can you teach us how to construct the unit circle from its principles? Yeah, for sure. Let's do it. Yeah, yeah, I love trig. Other gods. Standard deck of cards has 52 cards. It has four different suits, three space hearts club, space hearts clubs and diamonds. Each of these suits have three face cards. Jack, Queen, King. Therefore, in all, there are four times three 12 face cards, probably of getting one face card. 12 probably of getting two face cards is 11. Yeah, yeah, yeah. And probably of getting three face cards equals 12. Yeah, you multiply them together. You get 1% basically. I cheated. So check this out. The unit circle is this. Think about this, right? I've gone into this detail. I want to let this speedy Gonzales look. Check this out. Here's the thing you have to understand about the unit circle and why we study the unit circle. Us human beings, we're hardwired for problem solving. We want to analyze things. We want to break things down. We want to understand how things work. We want to do that because we want to optimize our lives and try to understand different systems in our world. Right? Initially, mainly associated with survival because we want to survive. Human nature is animal nature to want to survive. And the way you survive is you understand your surroundings better. Right? So mathematics is a language we came up with to try to understand the world around us better. And one of the systems that we encounter, which manifests itself in multiple different areas in our lives, is what's called cyclic systems. Right? Cycles. Things that repeat. Right? That's hardwired in life on this planet because the earth rotates around this axis. The earth rotates around the sun. Right? There are seasons that occur. Right? Our daily lives have routines associated with them. Right? So when we looked at the world, you know, mathematical perspective from mathematical perspective, and when we try to understand the cyclic system, we think to ourselves, well, we need to model this. And what's the best way to model a cyclic system? Right? What's something we can come up with that repeats? Right? And for us, the thing that we've come up with, the shape that we've come up with that repeats is obviously a circle. Right? So we can draw a circle and say, okay, a circle repeats. Like if you start off here, right? You move in this direction. Right? This is you. Depending on how fast you're going, you end up here again. Right? And then if you do it again, you end up there again. Do it again. End up there again. Wow. This is a cyclic system, an ideal cyclic system because from one understand, there are no such things as perfect circles in nature. Right? So we drew, we draw a perfect circle and we say, okay, let this circle represent a cyclic function, a cyclic system, something that repeats itself. You get up in the morning. You brush your teeth.   You come home. You do whatever it is you do at home for the rest of the day. You go to sleep. You wake up in the morning. You do again to a certain degree. You do again to a certain degree. You do again to a certain degree. You do again to a certain degree. Right? Now, now, my god, let's check it out. I remember doing this simpler math problem set with a situation of being chased by wolves over a mile with an additional wolf every 150 meters. Real question from a Chinese teacher. So if you're doing this and there's a wolf every 150 meters, how often you're going to encounter the wolf? Right? That's a cyclic function. Right? So for us human beings, when we try to understand a certain type of system, we try to break it down. Right? We take things apart. What? Reverse engineer things. Right? That's a legitimate thing. You reverse engineer something to be able to recreate that thing. Right? The famous story, sometimes when you take things apart, you can't recreate them. Right? The goose that laid the golden egg. Right? Supposedly there was a goose that was laying golden eggs. And the owners of this goose were very happy getting a golden egg a day. Right? Or a week. They're like, well, we've got a chunk of gold. You know, let this duck do its thing and we'll get tons of golden eggs. And then some genius came along and said, hey, let's take that thing apart and make more golden eggs a day. And the owner of the duck went, hey, what a great idea. Let's dissect this thing and find out how he lays golden eggs. They dissected it and didn't know how to make golden eggs. And their duck that laid golden eggs was no longer a duck. It was a dissected piece of thing on a table. Right? That could no longer lay golden eggs. Well, that wasn't a smart thing to do. Lucky for us, we can take a circle apart. We can break it into pieces and try to understand it better. And the way we break something into pieces, we go, okay, you know what? The most important thing about a circle is it's radius. Right? We'll call this R. Okay. And to simplify matters because we human beings like to simplify our problems so we can deal with them better. Right? So to simplify this problem, what we do, we say, you know what, let's call R. Let's give R the length of R a number that we can easily scale. Right? Now, we're not going to give it a length of 94 because that's who wants to deal with a radius of 94 or 72. Right? We're going to give R the easiest number that you can scale one. Right? So we're going to say this is a circle with a radius of one. This is the beginning stages of a unit circle. Length of Pi, given the length of Pi. Pi appears in this, but we're going to keep the radius simple because if you give this the length of Pi, then you're going to have more Pi's appearing in your circumference. Right? Shh. Don't tell people froggy, man. Oh, first time chat. Some fun. So we give the length of the circle a unit of one.  More Pi is fun also. Thank you for the follow, froggy. So we give the radius of one a unit of one. So you know what, this is going to be our standard circle that we're going to scale and try to understand every other circle and why we try to understand circles because we're trying to understand cyclic functions. Right? Oh, my God. Hong Kong. Right? So what we do is we say, you know what, a circle with a radius of one, we're going to call it a unit circle. Unit circle. Unit circle. Right? Okay. I never actually understood how is Pi connected to circles and the significance of it. We'll talk about it, baby. Nice. We're going to get to it. Okay. So now that we've created a unit circle, we want to understand this unit circle better. So what we do, we break things into pieces. So the ideal thing, the simplest thing to do to break this thing into pieces is we're going to go through the center of the circle horizontally. We're going to go through the center of the circle vertically. So all of a sudden we cut our circle into four different quadrants. And guess what? Now, we don't have to understand the full circle. All we have to understand is what happens in this quadrant and then we can just mirror it and we understand what's happening in the whole circle. We just made this problem a quarter easier. Right? But that doesn't sound on topic. But who knows? That, that appears, that message appears all the time for on our channel because it's very important for humanity to free us so much. Right? Now, we're trying to understand the circle. We do that, right? And since we've broken this up horizontally this way and vertically this way, well, we have something that we use that's similar to this.  We're going to call this the x-axis. We're going to call this the y-axis. Right? That's the x-axis and that's the y-axis. And if you want to find out where you are on a circle, right? Well, you can just talk about the coordinates x and y. Right?  Oops, your y. Right? That's your x and that's your y. Right? And what you end up having is a right angle triangle and Elder God, our froggy, as Elder God says, Junissons is central to our philosophy here, which is free speech for all and sharing information. Right? Fundamental, fundamental, aside from transparency and accountability of capitalist power. And if you remember, so what we've done right now is connected up a triangle to a unit circle. Right? And if you remember your Pythagorean theorem, there's a formula for a triangle. There's a formula for a right angle triangle which is called Pythagorean theorem which is a squared plus b squared. Let's make this a small b. It usually appears as a small b. b squared is equal to c squared and for this right angle triangle you would have x squared plus y squared is equal to one squared and one squared is just one. So right now we've got x squared plus y squared equals one. Right? Froggy, I'm a fan, but yeah, know a lot of your friends in college went the other way. Yeah. All right. So x squared plus y squared equals one. That's one of the formulas we can get from this. Right? So if we have a radius of one here and if anywhere we're on the circle, we can derive the coordinates of this thing. Right? You saw the NSA recruiter in the math department. You know, listen to William Beanie, William Benny, Benny, Benny, the guy who came up with the NSA system. He quit them. He quit them and he became a whistleblower against them. William Beanie, that might be pronouncing his last name incorrectly. Right? So this is the fundamental principle of a unit circle. Right? Now one thing that happens is for a right angle triangle, we have theta here and theta is in standard position is usually, well it is, the angle that we're moving around the circle relative to the positive x axis. Right? So I could also tell you to go to this point by telling you the angle that you're going to go on the circle. Right? Froggy, did you see the British guy online asking a viewer if they even knew the path? No, I didn't see. Crazy. Oh my god, my company recently introduced a math quiz for all possible new recruits. Oh, the things I have seen. Oh man, I can't even imagine. Oh my god. I can't even imagine. Right? So what we can do is talk about an angle. Right? In degrees usually. But another thing we can talk about is eliminating, again math petitions are, what is this saying? Pierce Morgan. And then his co-host called her out and he said the question was 3.147 or something. Crazy. And Pierce Morgan, well, isn't he the guy that doesn't believe in bodily autonomy? You can kiss my right? So what you can do, mathematicians come along. This is where pi is related and say, you don't want, forget about degrees. Right? Forget about degrees. No for, no for any, I have embarrassing math literacy. So they're really cool. Much needed refresher. Awesome. Awesome. Now take a look. Mathematicians in general, I tell all my students, mathematicians are lazy creatures. Right? Because they like to simplify things as much as possible. Okay? Simplify to a level where they can actually easily solve a problem and then extrapolate all the everything else that they need to extrapolate. So mathematicians end up looking at this and saying, you know what? We've got too many variables here for the circle. We, you know, we've got an R to find out where you are on here. And theta and degrees. Right? You don't want to forget about degrees. Mathematician came along and said, you know what? We're going to take the variable R and theta and merge them together. And we're just going to really eliminate the theta in degrees. We're going to start coming out with a new unit called theta in radians. And theta in radians is this. If you have a circle, right, and you're going to travel one, oops, that should be a one. Let's erase it with the finger. One. If you're going to travel one radian, is that too small? That's too small. Let's make it bigger. If you're going to travel one rad, here's this. If you're going to travel one rad radian around the circle, that means that should be more. If this is the radius, right? If this is R, one rad, the angle traveling around the circle is the same distance as you travel R around the arc length of the circle. Right? So if your radius here was 10, and if you travel 10 meters on the circumference of the circle, we're going to call that one radian. One radian, the angle that you've traveled around the circle. Right? So they just eliminated degrees. They just eliminated degrees from the unit circle. Right? It's still there. You can use degrees, but they simplify the matter and call it radians. And this is where pi comes into place. No matter the size of a circle, doesn't make a difference what size a circle is. Right? If you travel half the circle, the radius along the circumference of a circle, right? If you travel along the circle halfway around the circle, then you've traveled pi radians. You've traveled 3.1415. I'm just going to write down pi. Pi times R, whatever the radius is here. Radius. Right? So if I give you a circle, let's say the radius is 10, then how far, what's the distance halfway around the circle? It's 10 times pi. 10 pi. Right? If the radius is 20, then what's half the circle? 20 times pi. No matter what size circle. And that's where pi comes into play. It's very cool. This goes a lot deeper as well. I just try to sort of define what a unit circle is and give you a little bit more on it. But we've done a lot of videos on this. If you do Chicho Trigonometry playlist, I have a full playlist on... Here, let me find it for you. Full playlist on Trigonometry. It's basically the first ASMR math videos I started putting together because it's so important, so important, so crucial. Let's see if it's going to pop up. Trig. There we go. Take a look at this. I'm proud of this playlist. These videos here, you want to understand Trigonometry? These videos will do the trick for you. Really, if you're patient enough to sit through them, these videos will do the trick for you. I'll have the link in the description of the video once it's been uploaded to our platforms. Okay. I'm just going to get caught up with the chat here. I saw that clip. You saw it for a good year. Even recently, he wasn't given the correct information. Yeah. He's garbage, Pierce Morgan. Tyrants hiding behind mathematics. Lowly piggy, before I started watching Chicho, math and simplifying things could have never made sense together for me hilarious. Lowly piggy, funny. Every time you say circle, I get, Mr. Miagai vibes. Awesome. What do you call it? On off? Put on? Put off? What's it called? I got to watch Karate Kid again, man. This is one of the best feel good movies there is. Base pie. Is this room appropriate for children? It depends on the mental capacity, the mental capacity of anyone, right? I've talked with 14 year olds, 12 year olds, they're way smarter than some 30 year olds I've interacted with. So it's not about age, it's about intellect, the way I see it. But six year olds know. But in the past, we've had people that come to our live stream and they say, hey, I'm watching your video live stream. Is it a comic book reading or whatever it is or math with my six year old child, a kid or eight year old kid? And we really tone it down to that level, right? The information is still there, but I refrain from using certain words, right? So if you're going to watch it with your child, our live streams, if they're not political politics, we can't help it, we've got to go hard. But if it's math, comic book readings, cooking streams or anything like this, if you let us know ahead of time, you're watching it with your child or an underage person and stuff like this, we'll definitely keep it clean. We'll definitely keep it clean. First time chat, Kav Kazip. Free Nelson Menda. I think I freed a while ago. Joe Chicho. Why did you stop uploading to your 420 math and math and real life chat? Just because it was at that time, I lost someone hacked into our website, the Drupal site that we had for Chicho, and I couldn't access it. So I lost my website, my main Chicho website. That's why we're on Blogspot. So I transferred everything over to Blogspot. So I got really overwhelmed with doing a lot of things, trying to make sure I stay up to date with everything. And I started creating a lot of other content. And I just couldn't keep up with uploading everything to math and real life and 420 math channels and websites. And the 420 math, basically prohibition was ending. So I knew from that end, that job, and I'm against all prohibitions. So I'll maybe kick that up again. But I saw that the moment of kicking up on that front. So I didn't feel as much as a need to get the information across. But at some point, we're going to totally pivot into full blown mathematics when I start doing some of the writings, which I have. I just have to start putting it together. Just a matter of time and energy and resources, really. Thank you very much for the cheers, Thomas, live. Salute, salute. Slayer dart, sort of in and out. Clearing up my computer, awesome. Suraman, the white teaching math. Ha ha. Hong Kong, thank you very much for to follow, Thomas. Appreciate it. Fragment, make your junior high kids watch this guy. Uh-huh. Gooply. Math books are full of problems. Ha ha. Chuckle, chuckle. Fragment, the joke was derivative. Gooply. Of course, mate. Awesome, Thomas. Awesome. And gang, do not forget, do not forget. Free Assange, free Assange, free Assange. Julian Assange, publisher and journalist that has been crucified for trying to bring transparency and accountability of capital as power to humanity. For more information, see Wikileaks.org, defend.wikileaks.org, or multiple resources online. Thomas, thank you very much for Twitch Prime, sub, Hong Kong, salute. And welcome to our live streams. Gang, I think we're coming to the end. We're coming to the end. Nice chill math, Sasha. Fantastic. Fantastic. We do a lot more this year. We do a lot more this year. They'll be watching frequently, maybe. Awesome. I hope you like all different types of contents. We go all the way to place, Thomas. So if you see some stuff that you're not interested in, don't watch, especially the politics. If you want to avoid politics, don't watch our current events live streams. Okay, gang. This is a sort of suggestion I made to people a long time ago. Stay with us for the math, for the comic books, for the cooking streams, and stuff. Okay. All gone. I'm ready for yearly auction. Let's advertise ahead of time. Yeah, indeed. And gang, not next weekend, but most likely the following weekend, which will be, let's check it out, which will most likely be, well, at the end of November, we're going to do it. So most likely the weekend of November 26th and 27th, we're going to do our yearly Twitch points auction, because when you're watching, if you subscribe, if you do stuff when you're watching Twitch, what happens is you accumulate points and you can use those points for something. Now, instead of just using them randomly to do online stuff, we decided three years ago as a third auction we're doing now to auction off some stuff that I put up for auction, right? So it could be jams that we've made. It could be honey that I've jarred. It could be we've auctioned off a lot of these things. Drug war trading cards from late 1980s, early 1990s, from Eclipse Comics, we auctioned off a lot of major history here, tons of history here, right? Most likely in two weekends, we're going to do it, okay? Get on our, you can follow the work on our Patreon, substack or subscribe star, right? If you follow the work there, you don't have to subscribe. An important thing to do on paywall, you'll get notification when I set up the live stream for that, okay? So heads up, probably within two weeks we're going to do the auction, maybe three, maybe three.  Salute. This is a little bit of soda at the end with a little bit of blackberry. Look here. Super yummy, super yummy. Refreshing. Randall says happy birthday to Cheryl, awesome. Great chill session, perfect to keep me moving through report prep. Oh yeah, yeah. Slayered earth. To be honest, I'm only straying away from the current affairs streams for now because I'm standing to take math and physics at A level as a private candidate. Awesome. Yeah, I don't, I don't recommend our current events live streams to people. Yeah. Unless you really want to talk about what's going on in the world, okay? Oh my god, 27th November is great. Okay, maybe we do on the 27th. That's on a Sunday I believe. I think so. I think that should work. Let's hit it up on our gilded server and bring up the question and see if everybody's cool with that, right? Slayered earth. So I think I would be best served by focusing on those right now. Indeed. Focus on anything else on the current events, unless, unless the thing interests you and you know what's going on, or you want to know what's going on. Panic New One, how do you maintain any sort of positivity or not fall into depression knowing while constantly reading and knowing how up everything is? Because there's a lot of positives going on in the world. Panic, for example, I couldn't do this 10 years ago. Livestream math tutoring sessions to people to try to help people learn mathematics could not be done. We can do it now. We've been doing it for three years, four years, right? There's a lot of positives happening in the world, information being shared. Those who control a lot of capital resources, they don't want to share. And they're putting up blockers for people. But we're sharing. So that's huge positive. Bink US Gamer. Thank you very much for the follow. Salut salut. How can welcome to our Livestreams see that I can't wait for the auction. One of these years I'll want a jar of chicho jam. Awesome. I have some jars this year as well. Cav. Made my own pomegranate blueberry liqueur. Awesome. Delicious. Super delicious. I have trump cards. The cards. You have the trump card? I have. I have some too. That is same day as Canada football game. It's the same day as Canada football game. We've got to make sure we don't overlap the time. Maybe we do. Live updates. Remember the Iraq war criminal card list? Yeah. Yeah. We've got to read those as well. And we've got to finish off the JFK cards. I got to get back into the card readings. Indeed. Cheryl, current events is even more gore. Card gore than packing a car for vacation stuff. Hard core. Oh, hard. Not going. Hard core than packing a car for vacation stuff. Cheryl says. Later in the day chicho for Cheryl. Maybe evening chicho time. Maybe. Maybe. We decide on gilded game. We'll decide on gilded. Plenty of innovation and betterment of mankind. Indeed. First time chat. Bink US gamer. Hey, I am 12 years old and I'm trying to figure out how to use Pi. Could you explain? Oh, we just use Pi. Pi is, what is it? I just know what I think to four numbers. It's just 3.1415 and repeating. So just think of Pi as a number. That's it. Pi is this. Right? It's like, if you say you don't know how to use Pi, it's like saying you don't know how to use number two or the number three or the number 10. You do exactly what you do with this as you would do with any other number. So if I go five Pi and number in front of Pi means multiply. So this means five times Pi. What's Pi? Pi is 3.1415. We just say 3.14. You just multiply them together. That's it. That's it. Pixel camp. Hello. Hello. Welcome. Welcome. First time chat. Fragment. I do.  Oh, yeah. Don't let your wife just tell her it's an investment. Joe Chicho. The other day I was reading a study where they asked children in the US and China what their aspiration was for their future. The most common aspiration in China was to become an astronaut while among the US children was to be a social media influencer. If you played those two societies out over the upcoming decades, what is the result of that? I don't want to do the math for that man. That's depressing math. Thomas, next mass stream. Can you do circle, uh, thrums? I got my, uh, circles? Yeah, for sure we're going to do trick. For sure we're going to do trick. Uh, but I don't know what thrums are. Oh my god. No worries. It's 8am your time for the Croatia versus Canada game. Okay, awesome. That's good. That's good. Pixel draws the meaning of life. Mathematics is the meaning of life. That's it. If you know math, you know the meaning of life. Gord, hardcore, hardcore, even more hardcore. Padre, Padre goes guard core. Even more hardcore than hard core. Hilarious. Look it up real fast on the pie. Hilarious. You know Pfizer pie? Hilarious. Pops my, can you do circle, thrums? I got my, I don't know what thrums are. What are thrums, brother? Thomas, go to our guild server. Tell us what thrums are. If it's just circles, talking about circles, yeah, we can do trick. But I don't know what thrums are. What would the application be of base pie math? Never seen it. I don't know actually. I don't know. Maybe it's got to be related to waves somehow. It's got to be related to waves. Panic, man. I've always sucked at circles.  Oh man. Watch this. Okay. I think that's my playlist. Panic. That's my playlist for trigonometry right here. Okay, right here. It's a grade 12 trigonometry I teach in this playlist. The first eight videos or something anyway. There's best videos you'll find online to learn trigonometry and you'll have an appreciation for circles. Okay. Oh, Thomas. Circle theorem. Circle theorem. Which, what's this? There's so many theorems involving a circle. I'll have to look into it. I'll have to, I'll have to look into it. No, I'm not a Croatia froggy. I'm in Canada. Guard Corps does sound interesting as Guard Corps. Dude, he's Guard Corps. Fies or pie. Dude, he's Guard Corps. G-S-C-E ones. Would that be like stuff like this? Yeah, let me erase some of this. So it'd be stuff related to like stuff like this. The relationship that this has with, you know, oops, this, right? So the angle here versus the angle here, A and B. So the angle at B is twice angle A. So B is actually to A. Stuff like this, I'm assuming, right? And there's a lot of things like this. Ivanka, thank you very much for the follow, right? And we can do that. I just have to bring out some of the rules and stuff. And you can do, you know, if you have this and if you have a tangent line going like this, how's this work? There, there, there. And if it goes like this, then that's 90 degrees. If that's not a tangent line and whatnot. Yeah, yeah, that's it. Yeah. This stuff is super fun. For sure. You know what? Thomas, go to our Guild server, server, and we have a mass section. And I think we have a request section there. If there isn't, I'll create a folder there, go to general and say, Hey, can you do this in a next math livestream? And we'll do it. But provide me a link as to if you have any resources. If not, I'll just have to look it up and find out some of the rules. And we need questions, problems to do, right? It's super fun stuff. I'll stop. Stay good guys. Be indeed, indeed, Gilded. Bink, US gamer, I know pie. I used for circumferences in area. I don't know how though. Yeah, yeah, that's all it is. It's all related to radiance. We just talked about it, actually. We just talked about it. It's basically the link.  And if you want to find out how long, how far you've traveled, right? Well, if this is your radius, then the relationship for any size circle doesn't matter.  The distance halfway around the circle is your radius times pi. That's where pi comes in, right? It's related to radiance. That means the angle here in radiance is pi and you traveled pi radiance around the circle, right? Halfway around the circle. Super cool. How far does your math knowledge go? High school, university, masters, not masters. I have a bachelor's in mathematics, uh, panic. A major in physics, geophysics and bachelor's in mathematics, but I forgot a lot on the math I did in university. I can do basic introductory calculus and then what do you call it? And introductory probably statistics. Yeah. I used to teach more hardcore, but the demand wasn't there as much, so I didn't get enough practicing. Froggy, have you noticed anecdotal evidence of diminished math capacity in human right now, right after they recover from? No, I've noticed the diminished math capacity of human beings because of centralized education. In my area, anyway, they've got at the math curriculum. They teach about 30% less mathematics in high school right now than they did 10 years ago. And that's by design. Can't have too many people having critical thought in society now, can we? Joe Chichot, I think I've asked you this before, but do you like computer programming? When I took it, it was Pascal and Fortran and man, those are horrendous languages. I seem to remember you saying you didn't like it. If that's the case, is there something specific you don't like? Something that always surprised me when I was at university was that most math students who I spoke to found programming really hard, which is something I could never understand. What people have to study in their final year in a math degree is way harder than anything in programming, in my opinion. Joe, it was the monotonous nature of the programming when I was taking it. Running the program, trying to deal with all the errors and stuff like this, that's what I didn't like about it and the language at the time. I'd never gotten to C or C++. I took Pascal one course and Fortran another course and I think we had a little bit of basic and stuff like that. It was just so monotonous and I didn't want to sit behind the computer just trying to debug something. That was the only reason, really. So how do I find circumference of a circle? What is the formula? The formula is 2 pi r. If half a circle is the radius times pi, then a full circle is 2 pi r. Twice that. Right? Twice that. Math in real life is the best mathematics in my opinion. All the guy says, me too. I agree, I agree. We do signal math for my kiddos. I don't know signal math. I found that programming helped me understand certain mathematical concepts. That cost us better. Froggy, I did C++ in college. Boring, boring. Gang, let's call this stream. Thank you very much for being here. For those of you that are supporting this work on Patreon, on Twitch, on Substack, on other platforms. Gang, thank you very much for the support. It is in large part because of your support that we're able to do. What it is that we are doing and thank you very much for that support. I hope you're enjoying the content. And mods, mods, mods. Gang, salut to the mods. Salut to the mods on Twitch and on Gilded. Without them, we wouldn't be able to do all this work. So I thank them. And again, happy birthday, Cheryl. Happy birthday, Cheryl. Gang, I do announce these last streams 30 minutes, 45 minutes before we go live. On Get Our Minds, we kick out Parler and BitCloud. We'll see where the platforms we go on, but they've got to be free speech platforms, gang. They've got to be free speech platforms. For live streams where we don't have any visuals, we do upload the live streams to soundcloud.com.fo slash chichou as a podcast. And those podcasts should be available in your favorite podcasting platforms, including Spotify, iTunes, and Google Play. Joe, chichou, I think a great way to test if you understand something in math is to try and implement it. I agree. I agree, Joe, for sure. And man, I wish, I wish. I highly recommend it. If you, if you can take a program in course in school, learn how to program. I wish I knew how to program, but I don't. I don't. And all the guys say, chichou, send us the word. Where should we send you? What room are you sending us to? I don't know. You guys tell me where we should go. We'll send people to a room and gang. We will be uploading this full live stream to SensorTube, to pitch you to rumble and to Odyssey. And of course, if you want to join our little community, we've got a little community on Gilded where people are sharing a lot of information. So you're definitely welcome to join us there. I know how to program. I have pretty solid math knowledge. Random. How do we do random? I do random. I don't know how to do that. I just wish I had attained higher grades back in school. Happy birthday, Cheryl. Padreses. Our own dancing in a tub sent us here. Just hilarious. How do we do raid? What is it? Raid random? Do we do raid random? Shout out the channel, what to provide, username, commands, and I don't know how to do random. Raid. Let's check it out. Chichou, Joe, I think the best way to learn programming is to learn. It does something you like. If you like video games, then take a course which teaches you by creating games. Yeah, it would be. It would be. Pascal made me insane. Raid someone with 0-1 views and let's all go create. But how do I find them? We could go to Yang. He's a what? He's in Vancouver too. Okay, we're going to raid this guy. Grow a forest. Let's go. Random name, I mean. We're doing this guy. Ready? I hope this works. Okay, gang. If it works, I'll see you guys over there just for a quickie. Okay, otherwise we're out. Let's go. Let's see if this work. Raid has been created. We're going. Ready to raid. Raid now, raid now. 31 weirs. Ready to raid. Raid now. We're going. Oh, comedy stuff. Oh my god. That's hilarious. Raid.