 make sure we're coming out live and we should be in this. Hi everyone, this is Chichu. Welcome to my channel and welcome to another live stream. Today, today is April 27, 2021, and we were doing our drop-in math during session number 73 or thereabouts. It's more than 73, I'm pretty sure, but we'll go with the official 73 number. And we're going to do a little bit of mathematics, high school mathematics specifically. And if we get the opportunity, you know, we can touch on preliminary stuff or post-secondary mathematics. And we've done a lot of these before, 73 minimum, and 15 years of creating math content online. And we'll see where the discussion takes us. And it is an open discussion. We can talk about almost anything you guys want. We'll probably reserve politics on politics, because we do want to load this up on a sensor tube as well. And sensor tube is not a free speech platform. So there are certain topics that we cannot discuss there as important as they are. So we'll try to make sure we'll keep that discussion on our current events, live streams, one of which we're doing tomorrow. That's the last one of this announced set. So if you want to talk about politics and stuff, it's going to be the current events live stream tomorrow. We'll talk about it. Aside from that, welcome, welcome, welcome. And while we wait for notifications to go out, I'm just going to do my little intro to what this is all about. If you want to follow this work, Patreon is a great way to do so. If you want to support this work, Patreon is a great way to do so. I don't put anything behind paywall. Everything's creative commons. Share, share, like. And my work is really layered on mathematics. This is the essence of what it is that we are doing. And this mathematics is really the reason that I started to have a video presence online 15 years ago or so, 14 years ago or so. Okay. Before that, I was blogging, writing about whatever that interested me at the time, but came out with a purpose where we wanted to teach mathematics to as many people as possible, make sure there are as many people as possible literate in the language of mathematics. And for selfish reasons, really for myself, because I believe personally that if there are more people that are literate in the language of mathematics, our world will be a much better place for all of us. Okay. And for those of you that are supporting this work on Patreon, gang, thank you for the support. It is a large part because of your support that we're able to do this. MC Mike, how are you doing? Good morning. Good morning. I hope you're doing well. And the chat that you see popping up here, there's going to be more of a popping up and little notifications that goes on there. That's on Twitch. We are live streaming on twitch.tv forward slash. CHO live CHYCHO. L I V E. Hello, Cheryl. How are you doing? Darryl Cooper. Hello, hello. I hope you guys are doing well. Gang, those of you who are supporting this work on Twitch, we're coming to these live streams. Good morning. Good afternoon from Texas. Kind of good afternoon freaking out. I got my vector calculus exam tomorrow. We can do a little bit of vector. I don't know about the calculus part, but we can do the vector stuff, which is fairly straightforward, breaking that into components, right? Which is really related to physics, right, vectors. Zack, the Ripper, how are you doing, brother? Long time no see. Good morning, CHYCHO and chat. Good morning. Good morning. How are you doing, brother? I hope you're doing well. M T L. Butte. Hello. Hello. Welcome. Welcome to the live stream or Bolinda. Hi, y'all. So glad to see you stream shows. So glad to be streaming mathematics. Thank you. I've seen like, oh, that would be cool. Let us know. I don't know if the calculus part, which part of the calculus part is just components, right? I'm back to going this way. It's like equilibrium problems, right? You break everything down. We could do one of those. I haven't done one for a while, but yeah, that'd be fun. This is a great things in you. I hope you're doing well, brother. Envious. How are you doing? Welcome. Welcome to the live stream. And for those of you that are watching this and other platforms after the fact, this is the conversation taking place right now. We have some regulars that come here. Thankfully, very much appreciate it. And gang, thank you for the support on Twitch and mods. As always, thank you for taking care of business. I do announce these live streams 30 minutes before we go live on Mines, VK, Gap and Parler. And we do have a Discord page where you can come to our Twitch channel. And anytime you want in the chat, type an exclamation mark social and all the links to Mines, Gap, VK, Parler will pop up, including our Discord link right there. And that Discord is slowly becoming nicely active and people are sharing a lot of information. We have close to about 800 people there now. And there's different roles there as well. So if you're on our Discord, you'll go to the roles folder or some of the top and you can specify, you know, what's topic. We have 10 different topics. I mean, we do a lot of stuff. You can say why you're on Discord if you want, right? It's cool to see the different reasons. You can pick all of them if you want. I'm there for all of them. Zach, the Ripper, Chicho, I'm doing well as I can be right now gearing up for back surgery next week. Dude, how are you, sir? I'm doing good. I've been working on the shoulder, brother. As you know, working on the shoulder. And I think in the next set of streams that we announced, I'll show you guys. We'll go, we'll do another meditation dodge Hellcat. Thank you very much for the follow. I think what we'll do in the next set of streams that I announced, we'll do another meditation exercise stream because I'm sort of doing different things now trying to improve this. Both of them really, just because being online so much and whatnot. And it's helping a lot. And I am seeing a couple of therapists as well that, you know, I've had access to. So I've been working with them, making sure because I tend to push a little too hard and injure myself or injure myself. So they're keeping me in check. So I'm doing things slow right? I hope the surgery goes well, Ripper. I hope the surgery goes well. Surgery takes time to recoup from. You've got to eat protein. You know the drill. I think you know the drill, brother. And via Cheryl. I will probably lurk on the sofa like most of the time. So I'm not typing a lot, but I'm happy you agree. As I saw in the chat, I'm doing fine, awesome. Awesome. Awesome. Awesome. Gang. For live streams, we don't have any visuals. We do upload the audio to soundcloud.com forward slash CHO, CHYCHO. And those podcasts should be available on your favorite podcasting platform, including Spotify and iTunes. And we will be uploading this live stream to SensorTube, to Bichu, to Rumble, and to Odyssey. Gang, regarding Odyssey. Okay. So two days ago, I synced Odyssey with SensorTube. Right? So this platform right there, I synced up with this platform right there. Now, SensorTube used to be called YouTube, where anybody could share anything they wanted to with any reason. Right? Life experiences, ideas, share their content. Right? It was a content independent content creator friendly platform. It is no longer an independent friendly content platform. And what I did, I synced up Odyssey with SensorTube. And 832 of the videos that we had on SensorTube were transferred over to Odyssey. Right? The videos that weren't transferred, when I did the sync, it told me that 1,000 of the most recent videos would be transferred. Now, we have 1,209 or 1,210 videos on SensorTube. So it only was going to grab the previous thousand. So there was 200 something, 210 that weren't going to be grabbed. And also, there was another specification saying that nothing more than 5 gigs was going to be uploaded. And nothing over two hours was going to be uploaded. So I'll have to upload those manually to Odyssey. Okay? Now, when I synced up the Odyssey channel with SensorTube, it created a new channel. I had to specify to create a new channel. I should have looked into this a little bit more intensely. Right? So I created a new channel and I called it Chicho's YouTube Sync. Now, five and Danny, 832 videos got transferred. Chicho was a happy, happy Chicho. Right? And then yesterday, I went up to upload a video to the channel that we originally created on Odyssey where we're uploading the new stuff. And I kept on loading it to the new channel that was created. So the link to our Odyssey channel has changed. Okay? Those of you who are subscribed on Odyssey, please subscribe to the new channel and the new channel link is this. Believe it or not, this is the crazy part. The first channel we created on Odyssey was odyssey.com backslash at Chicho double colon nine. This one is six. Okay? So if you're following the work on Odyssey, and I'm going to, you know, we're going to load everything on BitShoot Rumble on Odyssey. Not everything goes on SensorTube. So if you want to consume all the content that we're creating, you want to be on these three bottom platforms where you share platforms, not on SensorTube. Okay? Like, really? Because SensorTube is not really liking some of the stuff that we're uploading. Even though we already got our filters on, we're not even uploading everything. SensorTube is, we're in negative subscriber growth now. People are being unsubscribed. Right? Even though view counts are high, revenue is high. Revenue is 50% higher than last year. Views are higher than last year. View duration is higher than last year. Video platforms going up. Subscribers going up on the other platform. But subscribers are dropping on SensorTube. Being someone who has done geophysics, who did geophysics for 10 years, loving data. I have processed a tremendous amount of data in my life. Okay? And I know anomalies when I see them. The data is full of anomalies. Right? Which means, and they're not natural anomalies. They're external anomalies. Right? So, and this is something that a lot of other creators have experienced over the last few years. Right? So, it is what you're doing. Okay? So, just a heads up. If you're on Odyssey, please subscribe to the new channel. Odyssey.com. I hope that's not going to change again. That should not change again. That has 830 plus videos that were on SensorTube already on that platform. So, we already got a mirror going on. Which is a great thing as far as I'm concerned. Okay? I'm seeing Mike. Is a WikiLeaks Vault 7 video on Odyssey? I like that one. I haven't tracked yet. I just did it two days ago. I really actually don't know what's there. I know videos that are longer than two hours are not there. I know any videos files that were more than five gigs are not there. Okay? And I know the original 250 videos or so, let's say 210 videos are not there. Right? And the original 210 videos, those are the math content I have and the sound wave audio thing that I did and the martial arts videos that I uploaded. Right? So, I have the math stuff available as torn. So, I'm not worried about those. I'd like to upload the sound wave music festival that I went to or in 2007, 2008. I shot DJs in the forest, different venues playing music, electronic music. It was phenomenal. Okay? And the 2007 one was a 24-hour period that I just got there and I shot video for 24 hours. Different DJs, different times during the 24 hours. Right? I stayed awake more than that. Actually, it was like 36 hours, 40 hours. I stayed awake. But I shot for 24 hours and the 2008 one was over a three-day period where I basically slept for like two hours. Okay? And then, and all that jazz. But I'll check at some point. I'll check at some point. Okay? Hopefully, it's there. Do a little search on it. M.C. Mike. I haven't searched. If there's anything that you're looking for, do a search on it on Odyssey. See if the video is up there. Hopefully, it's up there. I hope it's up there. And if it's not, by the way, and if it's not, send me a message. I'll track it down. Restore it. Upload it. Okay? And good timing. Gang. Don't forget. Free Assange, Free Assange, Free Assange. Julian Assange is a publisher and journalist that has been crucified for trying to bring transparency and accountability of capitalist power to humanity. For more information, see WikiLeaks.org, defend.wikileaks.org, or our Julian Assange and WikiLeaks playlist on SensorTube for as long as it's there. Okay? Steel Lord of Iron. How are you doing? Hey, Chichou, first time here. Been watching on SensorTube for an ASMR video and I love your content. Thank you very much. And thank you for coming here. Thank you for coming here. MC Mike just started following you on Odyssey at that channel. This is cool. Plus, oh, I like the platform. The platform is great as well. I've been watching, starting to watch some videos on there as well. Like, really, we'll talk about this tomorrow regarding the ridiculousness of what's going on with the management of certain companies. They're killing the goose that laid the golden age. Felix, hey, Chichou, I recently dropped math in college. Nothing to do with the subject itself, just the teacher and the way it was taught. Yeah. Picking up something else next year. Happy to get my math fixed today from the stream. Awesome, Felix. And yeah, there are, I've had students that they get turned off of mathematics. And one of the first things I do with people that I start working with is to try to instill in a sense of excitement and joy into mathematics. Because in general, most students that I start working with, they really don't like math, mainly because of the way it's been taught, mainly because of the curriculum, the system, the teacher, the textbooks are horrendous. Okay. Let me take these guys down. And thank you, MC Mike for joining on Odyssey Gang. And thank you for those of you who are joining on the other platforms. I appreciate it very much. Chichou, good to see you. Good to see you, Ronnie. How are you doing? Love these math sessions. Me too, me too. Nicky, hecky, how are you doing? Hey, Chichou. I miss you, my brother. So much life going on these days. No time found to chill. No worries. I'll be here, man. This is my, I really enjoy this stuff, man. This is my social, and we can talk why in the politics world. Sunshine and the snow is melting. Hope you're well. I'd love to pop in for some Modern Valiant Reading piece. Got the split, split away, Nicky. And Modern Valiant, yeah, I need to get a Valiant Reading in there. Which one haven't we done yet? We did Harbinger 1. We've done X01. We've done Solar Man of the Atom number one. We've done Archer, our strong number zero would be an amazing read. Maybe we've done that. I don't think we've done that. We've done Fall of Harbinger number one. What else that we do, Modern Valiant? We haven't done too many Modern Valiants. We should do a Modern Valiant. What's up, Sundreel? How are you doing? Narnia, Narnia, Narnia, Narnia, Deathgate Cycle, Deathgate Cycle, Deathgate Cycle. I just found out there's two more books in the Deathgate Cycle that I didn't know about that came out 15 years later. Someone commented on our book recommendations when we went through this, right? And they said there were two more chapters in the Deathgate. Oh no, no, it wasn't the Deathgate Cycle. It was this one. The Well of Souls in the Well of Souls. So in the Well of Souls, Twilight, The Well of Souls, in this series, there are two more books that were introduced. It's a five-book series that I read long time ago, long, long time ago, right? I believe it ended in the 1980s and supposedly in the mid-1980s or early 1980s and in 2000 and 2001, they released two more books on this. I love this series, the five books, all the way up to four and a half. And then the last half of the last book, I really didn't enjoy. I thought they rushed it. So I wouldn't mind reading the other two books on this. Think, Bobber, hey, Chico, hope you're doing well. I heard a theory that Tesla is going to launch a coin and possibly route excess power from the solar panels to mining set coin. Only a theory at this point, but yeah. Possibly. Possibly. A lot of people are getting into the blockchain world, right? Fat, welcome. I am here to listen. Awesome. Omni fiat. Omni fiat. Omni o fast. Fiat. Fate. Omni o fate. And regarding Tesla, yeah, they might. What do you call it? Elon Musk is a meme, right? So he's staying up to the latest meme going around, because he wants to be in the spotlight and whatnot. And I really don't trust the intentions there for sure, as some people tend to do for some reason. I don't know why. Rummy kid in anonymity, in anatomy right now, but lurking in the background. Hope everyone is well. Awesome, awesome. Anatomy. Is that correct? He's steel lord of iron. Steel lord of iron. Ever read invincible comics a little bit? Are you watching the series? That's so good. The Amazon so stays pretty true. Yeah, very true. They took some of the events. I haven't read too much like I've read. Like just even the what I've read, like I read like three issues or something like this, right? Not much, but they're readjusting some of the time, bringing in something that occurred here, bringing in earlier and stuff like this, just from what I've read, right? But I like the series. So you've, have you read the whole series? Are you liking, is it, the art style is basically identical to the comic book. Where is I actually have the reprint of the number one here somewhere that I recently reread again. So it's fun. It's definitely fun. Think about it. Yeah. He boosts dodge, dodge, dogecoin with a single tweet. My friend theorized that he took the data from doge, doge block. I call it dogecoin. Like people say doge, dogecoin blockchain following his tweet and is going to use the data to help him launch his own coin. Yeah. I don't, I don't trust Alan. And I'll tell you why. I mean, this isn't, this is sort of touching on politics, but people will ask me why, what come, what come. This is how come when the CIA was conducting a coup in Bolivia, because Bolivia has minds that Alan Musk needs, right? To make the batteries for his test of products. And then people, people are skipped on saying, oh, Alan doesn't get his lithium and all that jazz from Bolivia. They get it from South Africa. Well, that's a source, right? So if that is blocked off, right? Then that means the price of lithium from wherever he's getting it is going to go up, right? And he would rather the price of resources don't go up so he can produce his products, right? So people don't think beyond the one dimension, which is crazy to me, which is why we do mathematics because mathematics takes it takes it down, right? You like once you link everything up, you're invincible, right? So and when the CIA conducted the coup in Bolivia, people asked Alan Musk what he thought about the coup and he said, he said, quote, we coup who we want, deal with it. That's what he said, quote. Pretty hundred percent sure that's what he said, quote, we coup who we want, deal with it, end quote, right? So I call Alan Musk, Alan, we coup who we want, Musk, right? And as far as I'm concerned, he can kiss my ass, right? Anatomy, human anatomy. Thank you very much, Ramekin. I might pronounce it sometimes I pronounce things too directly as word. I forget what it's called phonetically or something and exactly the way they're written, which is like I did a reading of rye number zero, right? And the Geomancer's name is Jeff, but it was written G E O P H. So I threw that whole reading, and I did that reading three times of having technical difficulties like crazy. I call them Jeff, Jeff, Jeff, you like to mouse something, I like math because it has no bullshit, no BS math. There is one answer and does not involve subjectivity indeed. That's why I was terrible literature classes that broken down literature, which can be interpreted in many ways and involve subjectivity. And there's a lot of things, a lot of literature that has been broken down by academics, right? And then you hear interviews or the people that wrote that literature, and they get questions, you know, people ask them questions. Oh, what do you think about this interpretation and this person's comments? And they're like, no, that's not, that's not what I had in mind. That was not my intention. They're just, they're academics, they're just talking BS, right? My intention was not what they're saying my intention was my intention was this, right? So, but, but as long as, by the way, and that is okay for people to interpret things differently, right? But when they, they become fanatical about their interpretation, no, this is what it means. There is no other version. This is exactly what it means. Then they're fanatics, right? They're, they're dictators. They're totalitarians, right? Iron. I love the show, but bought a compendium that has volume one to nine, so an omnibus. So you haven't read the whole thing yet. The show is fantastic. I'm watching it with my partner. It's like cartoony. And then all of a sudden something brutal happens. And it's not just the visual brutal, it's like the emotional brutality of it. And she's like, Oh my God, right? Basically, for anyone that's has watched the boys TV series, I don't know if that's on Netflix or what it's on, right? It's the animated version of the boys to a certain degree, right? So it's really cool. Ronnie writes, and yes, and yes, I'm working on a graphic designer, graphics designer. And oftentimes I have to explain ideas to clients. There's also so much space for interpretation. And oftentimes I make something up just to sound more professional. Ronnie, I work in a field where it utilizes the math. But due to randomness, I have to make best judgment. So I've come to peace with subjectivity. Yeah, for me too. And if you're if you're trading, if you're in any type of market, there's a mathematics part of it. But then there's the intuition part of it. There's the experience part of it. Right? That's why that's why automated trading will never, right? Will never, to a certain degree, will never beat a professional trader, right? There are like Martin Armstrong has a program where it analyzes a lot of data and talks about different trends that are going to take place, which are pretty damn accurate, like really phenomenal, right? However, when it comes to daily trading, right? A human being looking at that data, that interpretation from the AI will make better choices than the AI itself, right? Or machine learn itself. Just read about that quote, we will coo whoever we want, deal with it to it. He deleted it after two days, not spread. Did he delete it? Yeah. Sorry, Elon Musk, FU for thinking that you have the right to coo whoever you want. Those are human beings, their their lives are being destroyed. So he can kiss my ass. Felix Chichot, could you construct regular 2D shapes with ruler and compass, increasing in size by one inch, one each time? Okay, example, start with a triangle, then a square, then a pentagon, etc. I'm interested how far you can get. So could you construct the regular 2D, could you construct regular 2D shapes with ruler and compass, increasing in size by one each time? Yeah, so sure, why couldn't you? You mean like I'm just going to draw a general, right? So do a triangle, right? So let's assume this is 10 units, 10 units, 10 units, and then the next one would be 11 units, right? So I'm going to increase, so what I would do is increase each side here, like this length is 10, so this would be 11, but each side here, I would have increased by 0.5, 0.5. Is that what you mean? And I'm going to go through pens gang, a lot of these pens are dying slowly, so we're gonna junk them. I'm glad you like my, Kenny Roberts, how are you doing? I'm glad you like my Joker drawing. Yeah, it was really good, man. I'm very proud of that one. Yeah, that's the one you posted in Discord. Fantastic. Fantastic. That was really good. I would love to see a comic, full comic in that style. Creative product, Cheryl's ideas. Effectivity to non-creatives is a real skill, so if you need to make up your own jargon, do it, whatever works, whatever works. I agree with Cheryl as well, because it's very visual. Some people have a visual, like when you give them words, they visualize it, right? So you can amplify that visualization, whatever it is, visualization, then more power to you. I do it with mathematics, and then I have hardcore, some hardcore math people that look at my videos. You can't say that. I go, I say that to emphasize a point. I'm teaching like rudimentary mathematics, right? Ronnie 90. The reason why AI can't beat the market is because of one thing, and that is correlation does not equal causation. AI will use past data for making predictions, but we know there may be feature events, events different from those in the past. You can program AI to look into the future as well, to see what certain technologies coming from. But there is, there's one major problem with the AI, with automated trading, with all these programs is liquidity, right? Liquidity can throw out, destroy any system, right? Or lack there of liquidity, right? Once liquidity dries up, all of a sudden you'll see market changes go, right? And once supply dries up, you see the market go in the opposite direction. So those two things have huge effects on markets and they can come along instantly, right? One of the other problems with AI automated trading is everyone jumps into the same trade, right? So everyone's following the same wave, all of a sudden, if there is an anomaly, something that happens here, certain breakers are broken, all of a sudden you see, right? Or the other direction, right? Which is pretty cool. And gang, don't forget, free assange, free assange, free assange, Julian Assange is a 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 Julian Assange and Wikileaks playlist on censor to increase side by one. I think he meant increase side by side by one, increase side count. Oh, increase, increase side count. Oh, increase side count. Okay, okay, okay. So you're talking about this. You're talking about triangle and then square. So what about the length? Is there a limit on the length that you can increase? Or are you just fitting whatever shape you have tightly that the length you're going to go to is going to be tight enough to fit the shape that we have. And then you also have to specify your starting shape, right? This is like seed. Like for example, if we do a triangle like this, or a triangle like this, then the structure is going to look different, right? So this one, if we're going to make it tight, here, let's draw how we're going to make this tight. Here, we can just make it tight, go up here, right? Well, it won't be tight because if this length, actually, if this is a equilateral, then it won't be tight on the top. But if we drew this in a way where this length here was going to be long enough to fit this, right? So that means it would have to be, well, it won't be an equilateral, right? So this triangle is not going to be an equilateral, but this side can equal this side, right? And then you draw tight like this, and then you want five shapes. So one, two, three, four, five, right? So this one we could probably tighten up down, right? And then six sides, yeah, I don't know. For me, it's difficult to do these. And then this would look totally different, right? Well, you only want four sides, so it would be that and then the same thing. Padre, padre, padre, how are you doing? I was about to say intuition. What do you think that is? Unconscious pattern recognition? It's cool because for me, intuition is more of a gut feeling than that. I think intuition is very much padre linked up with experience. I think intuition is experience. And 90% of intuition is experience, in my opinion. Fiat. We need to look at the question of Felix. Felix, where to say Felix? I mean, it is a challenge. Using a ruler and compass, you can construct perfect regular shapes. And regular shapes means all the sides are the same, right? And I was wondering how many you could construct. Good question. I don't know. Has anyone tried it? Have you tried it, Felix? Slick, how are you doing? Math is a goal. Math is a goal. Repeat, maths is a goal. And should we do vectors again? I forgot who was that asked about vectors. MC Mike maybe? No, it was an MC Mike. Someone else. Padre, padre, padre. I've seen a video of a guy get kicked kind of far, but it seems like you need to know the math, to know how to do it. And even then, good rulers, good ruler skills. And if it's regular shapes, here's the formula for calculating the angles you need, right? Now check this out. Here, let's draw this. Actually, no, we'll take this out. Here. Okay, who wasn't that asked about vectors, Ronnie? If I had to memorize pages upon pages of dry materials like laws, regulations, what would be the best way you think I didn't get into it because I couldn't do it? I think it's, again, gets into experience. You have to immerse yourself in it. It's like trying to learn a language. Like laws and regulations and stuff is learning a language, right? So if you're trying to learn a language, then the best way to learn a language is to use a language, right? I would love to do vectors. Okay, Slick Mac, we'll do vectors after this. I personally have a tribe, but the highest I've seen is 17-sider regular polygon. Okay, I'll give you, I'll give you the formula for this. I missed a little bit of chat. But here, let me give you the formula for this. Take a look at this thing. And then we'll get into the vectors. Okay, Slick Mac, take a look at this thing. A triangle. Okay, doesn't make a difference what type of triangle. The sum of the angles in a triangle are 180 degrees. So this angle plus that angle plus that angle. Sum of angles in a triangle is equal to 180 degrees. Okay, that's the sum of the angles in a triangle. I need to start killing pens. I'm going to start killing pens. Okay, let me know if this is not coming out bright enough for you. Okay, I was going to go get some pens, but I didn't get a chance to do it. Okay, it's like my Odyssey channel. It's like my Odyssey channel. It's like a 69. Your device is always digging deeply, Ronnie. So some of the angles in a triangle is 180 degrees. Now, if these sides are the same, equal, then each one is x, x, x, which means all the angles are the same, right? So let's kill the x here. If all the sides are the same, then all the angles are x, x, x, right? Because all the angles control the size, right? So basically, x plus x plus x has to equal 180 degrees because they're all the same. So three x is equal to 180 degrees. And you divide by three. So x is equal to 60 degrees, right? Now, here's a four-sided shape. And we'll go up to a five-sided shape and I'll give you the low down on this, right? So whenever you want to find the sum of the angles in any polygon, break it down into triangles, right? So a four-sided polygon, if you break it into two triangles from one point, you break it into triangles, then this triangle, these angles added up are 180 and these angles added up are 180. So the sum of the angles in a quadrilateral is a four-sided triangle is 360 degrees because it's two triangles. So two times 180, right? What the hell is this? Complicated. Eighth grade. You're going to do this, by the way. You end up doing this in grade nine, okay? Pay attention here. You'll see it. All of a sudden, I'll just click and you go, oh, this is simple, right? Like you have two triangles here. One triangle, two triangle. What's the sum of the angles in this triangle? 180 degrees. What's the sum of the angles in this triangle? 180 degrees. What's 180 plus 180? 360, right? So the sum of the angles, some angles in a quadrilateral, in this, I'm just going to say, in this, is equal to two times 180 degrees, which is equal to 360 degrees, okay? Make sense? Okay, okay. Done deal. Watch this, seriously. You're going to, this comes up to you in grade, maybe even grade eight, right? Now let's try a five-sided and then we're going to come up with the equation for this. So five-sided polygon. Now it doesn't have to be a regular polygon. Remember, regular regular polygon means all sides are equal. They're all the same length, right? So let's assume they are there. We don't care if they are or they are right now, right? So we want to right now figure out what the sum of the angles in this pentagon is because this is a five-sided polygon, right? So we want to find out what this angle plus this angle plus this angle plus this angle plus this angle is equal to, okay? So what we do, we say, okay, let's break up this pentagon into triangles because we know the sum of angles in a triangle is 180 degrees, right? So I'm going to kill this so it's not as busy, right? So start up one node and make a triangle. So you can't make a triangle there. That's just a straight line. So there's one triangle and then you already used up this one. We want to here and then draw another line to there, right? And then that's all we can do. We can make three triangles, right? So one, two, three triangles. Well, what's the sum of the angles in this pentagon? Three times 180 because each one of these is 180, right? So three times 180 is basically 180 added to this because we just added one more 180 to a four-sided one, right? There was two here. One, two, now there's three, right? If we add these so we get zero, four, one goes up, so 540 degrees, right? That's what the angles in a pentagon look like. Okay, this is scary now because it looks complicated. He is helping me. I would have drawn five of fun. Now take a look at this thing. You would have drawn five. Yeah, you don't want to draw five. Now take a look at this thing. Let's figure out, okay, a possible formula for us to figure out what the sum of the angles in a higher-sided polygon is, like six-sided or seven-sided or eight-sided, right? So let's do, yeah, one, two, three, four, five, six. Question, what's the sum of the angles in a six-sided polygon, right? In a six-sided polygon. Okay, now take a look. This was a four-sided polygon and we had two times 180. This was a five-sided polygon and we had three times 180, right? This was a three-sided polygon and we had one times 180, right? So one triangle, two triangles, three triangles, right? Well, what's the pattern that you see? One triangle, how many sides did it have? It had three sides, right? Okay, quadrilateral has four sides, pentagon has five sides, right? Now take a look at this thing. Here is the formula to figure out what the sum of the angles in any polygon are, right? You go N, so you say let, let, and a let statement in mathematics is your friend. Let N, okay, equal number of sides in a polygon and a polygon is a shape like this that encloses, right? And it can't have jagged ends going in. Okay, now take a look. So let N equal number of sides in a polygon. So this has got three sides, this has got four sides, this has got five sides, right? Now the way we can come up with the formula is this, patre patre patre, geometry is fun as haldewa divot. It just looks complicated because you're new to it. Yeah, indeed, right? Once you get into it, it's easy. It can be easy. It could be very complicated. You could go into topology, which is just mind trip, right? How's tWitch explaining this better than my teacher? It's not tWitch, it's tWitch. Now take a look. The formula is this. Sometimes it's a guessing game. You massage a formula until it fits, right? For this one, you write it down as N minus 2 times 180. Okay, this is equal to the sum of the angles in a polygon equals sum of angles in N-sided polygon. This is the formula. Let me do this in red. You want to write this down if you're studying this. N minus 2 times 180 equals the sum of the angles in an N-sided polygon. Let's try it out for this. This is six sides, right? According to this formula, sum of the angles is equal to 6 minus 2 times 180, which is equal to 4 times 180, which is equal to 720 degrees. If that's the case, let's see if we can... It means we're going to have to be able to make four triangles, right? Four triangles in this thing. Well, let's try it out. One triangle, two triangles, three triangles, four triangles. One, two, three, four. See the pattern? A triangle has one triangle inside it. A quadrilateral has two triangles inside it. A pentagon, five-sided polygon has three triangles inside it. A six-sided polygon has four triangles inside it. Okay, what is a 12-sided polygon? What's the sum of the angles for 12-sided polygon? So, I don't even know how to draw a 12-sided polygon. One, two, three, four, five, six, seven, eight, nine, ten, eleven. Let's try that again. How do you just draw a 12-sided polygon? One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve. There you go. I know, it looks like a circle because it basically is, right? So, let's assume this is 12-sided. 12-sided. Well, the sum of the angles is equal to 12 minus 2 times 180, which is 10 times 180, which is equal to 1,800 degrees, right? How many triangles in a 12-sided polygon? Ten. Okay, with atoms, a circle with atoms, right? Dodge coin, it's dodge coin. Right? So, that's the formula. Easy, right? That's the formula to figure out the sum of the angles in any-sided polygon. Did that make sense? Divide? Divide? Divide? Divide? Is that okay? All right? Now, if I was you, if I was in grade eight or grade nine, I'd take a screenshot of this right now and have that as a note, right? Because it gives you what you need to be able to do a whole bunch of different types of problems. Now, there's one more level to this. Math, eighth grade math, eighth grade. Yes, I'm kind of getting it. Awesome. Now, watch this. She's about to get real for when you go to high school indeed. Now, watch this. I'm going to erase this, this, this. Okay, and this. And we'll just do the remaining work here. Now, a regular polygon. Okay, I will take a screenshot. And you can do it when you can re-watch the video and just freeze it at that moment, right? This is a timestamp of 28 minutes. No, when did we start? 11? Oh, wow, 58 minutes into the video. Watch this. Regular polygon. Here's a definition for you. Regular polygon. Regular polygon means all sides the same length. Okay? All sides are the same length. Okay? Now, if all the sides are the same length, okay, then what's each one of these angles, right? Because the way it works is if I draw you a shape, right? Let's say a triangle. If I say this is 60 degrees and I say this is 60 degrees, then this side has to equal that side, right? And if that's 60, that's 60. Some of the angles in a triangle is 180. 60 times 60. Yeah, 90, 45, 45 works too. Here, we'll do this. Here's 45. 45. Well, some of the angles in a triangle is 180. So 45 plus 45 is 90. 90 minus 180 is 90. So this one has to be 90 degrees, right? Okay? But an angle controls the opposite side. So this angle, if that's the same as that, then that length is the same as that. So if I say it's a regular polygon, right? It means all the sides are the same, which means all the angles are the same. And if all the angles are the same, and the total sum of the angles, for example, in a quadrilateral four-sided polygon is 360, then to find each one, you just take 360 divided by four. Five-sided polygon, you want to find out what each one of these angles is? You divide it by five. You got five sides. Six-sided, you divide it by six. So the way it works is you go regular polygon equals all sides, all sides the same length, right? Then all angles are equal. Okay? So once all angles are equal, it goes without saying that each angle, as Sunny Leo 98 is in, like Flynn throws us the equation, all you do, you divide the total, then all angles equal. Therefore, and this is mathematicians taking shortcuts, mathematicians are lazy, they shorten everything, right? So this is angles, right? Instead of writing angles, I draw an angle and put an S on it, right? Then total, then each angle, each, oops, that's not an each, that's equal, each angle is equal to the total divided by number of sides. Well, the total is this formula, and the number of sides is N, right? And as Sunny Leo 98 says, it's going to be the formula is N minus 2 times 180 divided by N. That's what each angle is going to be in a regular polygon. Okay? Is that clear? Does that make sense? And this is the way formulas are derived, right? You come up with one formula, you come up with one formula, and you build on that one formula based on different metrics you want to calculate, right? Remember, the mathematics we know, all of the mathematics we know, the mathematics that we've used to send people to the moon, right? To come up with technology where I, in west coast of Canada, can live stream a math tutoring session to you wherever you might be is based on five rules, five axioms, five rules, we try to explain the big bang. What? Wait, you write therefore like that. In Armenian Russian books, we had the boring, oh, you do that. Are you Armenian? So you use this? I write therefore like this. In Armenian Russian, you use this? Well, not the, you use that guy? Arrow? I didn't know that. This one's, this one's easier, and hence, hence is this way. Hence is this, upside down circles. Hence we write like this. To the moon, to the moon, to the moon. Formulas are great as shortcuts, but they make new learners lazy and don't study in depth the math that led to the four. Yeah, agreed, agreed. Yeah, cool. Equal and greater than. Yeah, equal and greater than that way too. Isn't there one for if and only if? Yeah, I don't, I can't, I don't use it, so I don't know it. Right? The three dots are for end of proof or QED. QED, yeah. It's Latin, stands for, I don't know what it stands for, QED. I don't use QED. End of proof, I put a checkmark. This is, this is Chichu's QED. I just go that. Done. Teachers didn't like it. When I was doing stuff, I wouldn't write QED, otherwise, they don't give you the marks. My coach had been, my approach had been calculus of corners and triangles into the middle. Example, in pentagram, all five are five triangles, only not that you subtract 360 degrees from center point. Oh, so you go and then you subtract 360, which is two triangles worth you're subtracting out. So you start off in the middle, draw five triangles, and then you take out two of the triangles. Quad erent demonstratum. That's actually easier than what I remember to be. If I learn this, I want to build a rocket. Awesome. MC Mike, if and only if is, oh it's a, if and only if is this? If and only if is that? Huh. I didn't know that. With two lines, I guess. Two lines. What is E? Where, where is it applicable as a number? E, you mean 2.7? It's a natural, you can be kicked into the natural logarithm, Hannah. I would have to dig into my math calculus more to remember. Quad. E is constant growth, but originally it represents compound interest. Great video on number file about it. Yeah. Euler's constant, right? Is it? I don't know. I can't remember. I can't remember. I'm pretty bad at Russian, but I know it because I'm from Latvia. Yeah, all Eastern Bloc people. Latin sounds so cool indeed. Yes, E is Euler's constant. Cool. Let's do vectors, gang. Let's do vectors. I hope that's okay. That was fun to go down. Why don't think we've done them? Ah, maybe we've done. No, we've done, I think, at some point in the last 15 years. Let's do vector. So, okay gang, let me ask you a question. Okay. E to the power of ln x equals x. Yeah, I remember that. That's fun. I love logs. Logs is super fun. They don't do a good job in teaching us, so a lot of people end up hating logs. By the way, gang, I got snacks. I'm going to do a little snack. Banana with dark organic chocolate chips. Okay. Very delicious. I mean, put chocolate chips on anything. It's delicious. Banana with chocolate chips. Dark chocolate chips. I hope you got good snacks. Banana is good because the chocolate chips stick to it. Cheryl's approximate symbol is the best math symbol ever. Approximately equal to. Wishing you well and have a nice dream. Thank you very much, Fiat. Thank you for popping in. Mathematics and snacks. And ln x is simply natural log with base 10, I believe. No, no, base base e, not base 10. Log is base 10. The triple contour integral. Like this. Slick Mac. Been waiting. Okay, vectors. Let me pop another one of these. This is like crazy delicious. You wouldn't have to be legalizing you guys in Canada, both medically and record. Don't know. Would you go into k direction? I don't know what k direction is. Okay, direction. You mean the third? 3D? Yeah, let's not go into 3D. Oh, that symbol. Smith, how are you doing? I don't even remember that symbol. This symbol. Is it a dot in the middle? That's a triple integral. This green doesn't come out too good. Let's put the green away. Let's see what else we got. I gotta kill some of these pens again. Let's do vectors because I'm going to need, nay, that's the single one. Oh, that's the single one. That looks like a tropical hurricane symbol. Well, it did actually. Vectors. Now look, gang. I'm going to ask you a question. How fast can you drive on the highways where you are? All right. How fast can you drive? Green's term. As in the 3D, yes, should have clarified, but probably better to stick to, yeah. 65 is the max in U.S. I think in the U.S. there's places where you can go 80 as well, no? Just for funsies. 100 kilometers per hour, yeah. Or 110 kilometers per hour. Here in Germany, unlimited indeed. The Autobahn, Lerking, Loris, 120 kilometers on the biggest ones. Cool. I can drive pretty fast. 70 miles per hour. Divide. 70 miles per hour. No. We have 70 in Pennsylvania. Yeah. I'm pretty sure there's places you can go 80 in this U.S. if I remember correctly. So that is a distance. That is a scalar quantity. How fast you can drive, right? Now, if you put a direction to that, that becomes a vector. Okay. So if you say I can travel 70 kilometers, let's make it, what do you guys want to do? Kilometers? The whole world does kilometers. The U.S. miles, but the majority of my audience in general is American. So things 120 in Ireland. By the way, can you do this kind of math? Because it looks crazy. Yeah, for sure. That's just the distribution. Should we do that one, speedy Gonzales style? Let's do vectors first and then we do that one, right? So take a look at this thing. Let's do simple 100 kilometers per hour. Let's say you can go 100 kilometers per hour, right? That's a scalar quantity. Okay. Montana is 80 now. Montana is 80. Cool. Yeah. Montana. I've driven through Montana. Nice try. Used to be reasonable and prudent. So this is scalar. Scalar, right? Which means there is no direction to it. But if I go 100 kilometers per hour north, oops, north. This is a vector quantity. This is a vector because it has direction. Okay. You're a good guy, man. Thanks. I tried to be, right? So that's as soon as you add direction to force, to motion, to anything, you end up with a vector, right? So there are two main types of vectors we look at. One is motion. The other one is forces, right? And when you're adding vectors together, so for example, let's assume we had this. We had, let's say we had 100 plus 30 plus 80 minus 60. Actually, that's not the at the minus. Let's keep it simple. This. If you're adding these together, then this is 120. Sorry, 120. 210, right? That's 110 plus 100 is 210. So that's 210, right? If this is apples, then it's 210 apples. If it's kilometers, then it's 210 kilometers, right? Makes sense? Okay. Now, if these things had direction associated with them, it becomes a vector. You can't just add it up that way. For example, let's assume this was 100 north plus 30 northwest plus 80 southeast, southeast, southeast. Let's say we wanted to do this, right? You can't just add the numbers because the way this looks is this. Take a look. Oh, algebra in college. I needed a waiver for it. I think my eyes just went across. Coach, hilarious. So take a look at this thing. Let's say we have 100 north. So 100 north would be here, right? Let's assume that's 100 north. And then we have 30 northwest. Here, let me draw this better. We'll tag onto it, right? 30 northwest. So you want 100 north, 100 north. And then when 30 northwest, so let's assume that's 45 degrees, right? So we want 30 northwest. Let's make the vectors proportional. If that's 100, right? Then a third of that would be 30. So 30 northwest. And then southeast, let's go southwest. That way we can draw it properly. Southwest. Okay. There's south and then west. And then you went this way. 80 this way. 80 southwest, right? This is where you end up. You start off here. This is where you end up. If you're going to add all those together, the total of those is going to be from there to there. That's what it adds up to, right? So this plus this plus this equals this. So because this is a vector, there is a magnitude involved here. Magnitude, magnitude plus direction. So it's got magnitude plus a direction. How do we figure this out? Looks complicated. If you have a ruler and a protractor, you could do it really accurately. Make centimeters represent, well that would be a meter. Make millimeters be one unit, right? And then draw it and have protractors going on and stuff like that. Well, to do this algebraically, we need to break this down into its components. And when it comes to components, we're talking about the Cartesian coordinate system. X and Y axes. X and Y axes. Why is that the case? Because if you're adding a vector that's going exactly in the same direction as another vector, then you can just add them straight up as if they were scalars because they're acting in the same plane, right? So if you had this, you had 100 North plus 30 North plus 80 North, then that would be 210 North. It's the same unit, right? It's just like 100 apples plus 30 apples plus 80 apples goes 210 apples. 100 North, 30 North plus 80 North is 210 North, right? But if they're all going in different directions, then what we need to do, we need to break them up into components, right? Let's do one. Let's do one. That's the intro to the vectors, right? And the best way to appreciate how this works, we need to do an example. And you need trigonometry. Now watch. We're going to draw this. Now we're going to draw this. I need to, I need, let's see what kind of pens we got here. Let's see what we got. I got a lot of pens out here right now. Hopefully I'm not going to drop them to make nasty noises. Oh, look at this. I got a ruler. Let's make a Cartesian coordinate system. Okay. Let's make it, no, let's make it up here. How's that coming out? Not bad. I wish they made dry erase pens that lasted longer. These things die off so fast. So once we got a Cartesian coordinate system, let's add what we had. Take a look. We had something that was going 100. So these are the measurements we had. We had, where should we put this? We'll just put it here. 100 North. We had 30 North West. And then we had 80 South West. South West. So let's do the 100 North first. So 100 North, lamb X, exit X, excite X, lamb excite X. Hello. What if you change the place of vectors in the sum? What if you change the place of vectors in the sum? It wouldn't matter. It wouldn't make a difference. You'll see. Take a look at this. So we're going to break this thing down to these components. So let's put them all originating from the zero. So we're going to go 100 North this year. So let's assume this is 100 North. So that's going to be 100. The next one is 30 South West. Oh, sorry. North West, right? 30 North West is going from here. That's North West like this. Let's make the 100 a little bit bigger. That way we can do the work 100. And this is 30 this way. Okay. And then the other one is 80 South West, Southwest. And 80 would be about this far, this far. So we're going to come here. Okay. So this is going to be 80. Now, if I say Northwest, I'm going to assume it's 45 degrees. So let's assume this is Northwest means 45 degrees. Okay. That means this angle here is 45 degrees. Five degrees. Okay. MC Mike. Okay. Makes sense now since the triples relate to volume. Yeah, for sure. For sure. And because I'm pretty sure you're doing integration, you're trying to figure out the volumes of things, right? Maybe MC Mike. And again, Southwest will assume this is 45 degrees. Now remember, this could be any degree. If you want here, let's make it, let's make this here. We'll redraw this. Let's assume it's this. Actually, let's do it this way. That way. And usually, usually, you want to do your measurement to the X axis, the angle. So let's assume this would be Southwest. If I say Southwest 60, then this is 30. Okay. Because this part would be 60. South 60 degrees West. There's different ways of saying this, right? I'm just writing like this. I'm explaining to you. There's different ways to represent this. I think they go South 60 West. But I don't want to use structure of saying things without it being accurate, right? I'm not going to assume this is the way they write it everywhere. Okay. So right now, because that's 60, I'm going to keep that as 30. Okay. Because I want to just do everything relative to the X axis. Okay. And this was 100. Remember, this was 100, right? This was 100. This was 100. And this was 80. So what you want to do is put them in the same direction to be able to add them, right? Because again, if this was 80 going down, then the total sum would be 100 minus 80 because it's going in the opposite direction, right? So what we end up doing is we take each one of these vectors and break them into XY components. So let's take the 30. Let's do it here. Let's take this guy. 30. And we're going to break it down into components in the X direction and the Y direction. Okay. So if that's 45 degrees, 45 degrees. Okay. So what we want to do now is figure out what this is and figure out what this is, right? But we're also going to do this with this. So I'm going to call this, what should we call this? X1 and Y1. Okay. Actually, let's call them X2 and Y2. X2 and Y2, because the 100 is really our first vector. Okay. So if we're going to do this, we need trigonometry, right? So if we're going to use trigonometry, we're going to use, let's see how dark this one is. So we're going to go, if you remember Sokotoa, Soka-toa. Sine of an angle is opposite over hypotenuse. Coast of an angle is Jason over hypotenuse. Tan of an angle is opposite over Jason. And we usually just end up, actually it comes out not too bright. I'm going to use black still. You're basically going to use sine and cosine because you're looking for X and Y. So check this out. If you're going to use that, let's use, let's try to figure out what X is. Okay. If you're going to look for this, that's adjacent to 45 degrees. So you're going to use this. So you're going to go coast of 45 is equal to adjacent, which is X2 over 30. So X2 is going to be equal to cross multiply up 30 coast of 45. If you want to find out the Y component, you're going to go sine of 45 is equal to Y2 over 30 cross multiply. So Y2 is equal to 30 coast of 45. Let me highlight this because these are the ones we're going to use. Right here. So we just broke this down into component here and here. That's what their links are. Right? Let's do the same for the 80. So 80 goes down and here is the X component goes in this direction and the Y component goes in this direction. So this is going to be 80 and this is 30 degrees. Right? And this is X3 and Y3. Now, if you want to keep track of your variables, you could call this X80 and Y80 referring to the 80 magnitude vector. And you could call this X30 and Y30. I'm just calling them two and three just because it's simple right now. We don't have too many variables I want to keep track of. Well, if you use Sokotoa again, then you have coast of 30 is equal to X3 adjacent over hypotenuse. Right? So X3 is equal to 80 coast of 30 and sine of 30, if you're going to use the Y, is going to be Y3 over 80. So Y3 is going to be equal to, what are we, 80 sine of 30. I hope that's clear. I'm sort of going through this, I'm assuming you know trigonometry in this. I'm assuming you know trigonometry. Now take a look at this thing. Okay, so we have the X part of this guy. Right? We have the X part of this guy too now, right there. We've got the Y part of this guy and we've got the Y part of this guy now. And we have the X part of the 100 because there is no X part, it's just going straight up. So the Y part of 100 is 100. So if we're going to add up these guys, right? If we're going to go this plus this plus this, right? Then we have to add the components, right? So the X part is going to be X total, let's call it, X total. Let's see if we're going to, should I do this in red? Let's do this in red. Red is coming out okay. X total, X total is going to be the X part of number one. So X part of number one plus the X part of number two, which is right here, X two plus the X part of the 80, right? Well the X part of number one is zero plus because it's not moving in the X direction, it's only moving straight up in the Y direction. X part of number two is this guy, 30 cos 45 plus the X part of the third part, which is 80 plus 80 cos 30. And what you can do is you can punch that into your calculator. Now if you know your special triangles, 30, not 30, actually we've got to do 30 anyway. So 45, 90, 45, 1, 1, root 2. And then the 30 triangle is 30, 60, 90, 1, squared of 3 and 2. So cos 45, cos 45 is 1 over root 2, okay? So this is going to be 30 times 1 over root 2, oops, squared of 2 plus 80 times, what's cos of 30 degrees is root 3 over 2. Root 3 over 2. So this is going to be equal to 30 over root 2 plus 2 goes into 80, 40 times 40 squared of 3. That's the X part of the total component. Now you wouldn't need to do it this way, you would just punch into your calculator, right? So let me move my pens here. So let's punch this in because we need the numbers. Let's do this. What do we got? I'm just going to punch decent, 30 cos 45, 30 times 45 trig cos equals, so this part is 21, 21, 21.21 plus 80 cos 30. 80 times 30 trig cos equals 69.28, 69.28 which equals, and you add these guys up, plus 21.21, 21.21 is equal to 90.49, 90.49. That's the X direction, okay, which makes sense. Take a look at this thing. This part added to this part will make it go this far, right? That's what really we're doing. Okay, does that make sense? 21.21 is this length here, 69.28 is this length here, and this one contributes zero in the Y direction, in the X direction. So if you add this and this, you get this, 90.49. Okay, now let's do the Y part. Okay, if we do the Y part, I'm going to erase this part. Let's do the Y part. Y total Y total is equal to Y1 total plus Y2, oops, 2 total plus Y3 total. Well, Y1 is 100. It's just straight up, right? 100. Okay, plus Y2 is 30 cos 45, 30 cos 45, plus Y3 is 80 sine 30, 80 sine 30. So this becomes, I'm just going to punch all this in, in one shot in the calculator, because we're limited with space, right? We're limited with space. So what do we got? 30 cos 45, 30 times 45 trig cos plus 80 sine 30. Well, 80 sine of 30 is just 1 over 2, but I'm going to punch it anyway, plus 80 times 30 second sine equals that and then plus 100. So plus 100 is going to be 100 and 161.2121. So that's the Y direction, right? Which makes sense to a certain degree. Oh, what a mistake, what a mistake. Look at this, look at this. This is going up, this is going up, but this is going down. In vectors, direction matters. So we're not adding 180 sine 30, we're subtracting 30 sine 80. Keep this in mind. Okay, so I'm going to punch this in again, right? How did I catch my own mistake? Well, I looked at this, I said, if that's 100 and that's going to be this much, how could we go 168, which would be over here if we're going in this direction, right? It wouldn't be. So let's punch that in. This is where people get burned big time. So we're going to go 30 times 45 cos equals 21. It's the same thing as this, 21.21. And then we're going to subtract sine of 30 is opposite over that. It's 0.5 times 80, which is 40. So we're going to subtract 40 minus 40. We get negative because if you were just doing this and this, the direction is down, right? But then we're going to add 100. We're going to go up. So plus 100 plus 100 equals 81.21, 81.21, 81.21. Cool. We have the X and Y components, right? Now, where are we going to draw this? Where are we going to draw this? Which part should I erase? Because we need more space. I can erase, I can erase. I'm going to take out these guys. Let's do this slowly. I'm going to take out these guys. So let's do the components on the original graph. Check this out. We had 90.49. Now, keep in mind, I went in this direction. So I called this positive, right? In physics, when you're doing vectors, it's up to you what you want to call positive, what you want to call negative. If you're going to stay with convention, I should have called this direction negative because that would have been positive. But I'm keeping track of it. It's the answer that matters, right? How I approach it is really up to me within reason. You can't break the rules of mathematics, but you can define what you mean with whatever variables and directions and stuff, right? It's your gain you're playing, right? So this is 90.49. So check this out. This was 80. So 90 would be like around here. So the total measurement is going to be this way. Here, it's going to be a little bit less than that length if we're going to stay proportional, right? 90.49. So this is 90.49. And then we've got 81.21. Now, remember, I called this down negative, up positive, and I subtracted this. So I know that's positive. So 80.21 is going to be here. I'm going to go all the way to here. So this is 80.21. So what you really have, you've got the legs, the components, the x and the y of your new vector, right? The total sum of all these three vectors added up. So what you can do is just take this guy and move it here to get a visual or take this guy and move it there. It's going to give you the same thing, right? So what I'm going to do is I'm going to draw this going up like this. So our total vector is going to look like this. So that's our total vector, right? There's two steps we need to do to finish this. We need to find the magnitude of this, and we need to find the angle of this. Well, the magnitude is easy, and the vector is easy. The magnitude is Pythagorean theorem. This is 80.21, 80.21, right? So all we're going to do, a squared plus b squared equals c squared. This is the total. So a squared plus b squared equals c squared. Where should we do this? Let's do it over here. I'm going to erase these guys, okay? So Pythagorean theorem says a squared plus b squared equals c squared. a squared plus b squared equals c squared. Where a is 90.49 squared plus 80.21 squared is equal to c squared. The total is c. Okay. We punch this in. And if you want to write this out, this becomes here 80.21. I'm going to write this out over here. We get more space. 80.21. So this becomes c squared is equal to, I'm just going to punch that in through the calculator. What's c squared? 90. 81.21 squared plus 90.49 squared. 90.49 squared equals 14,784. 14,784. Yep. And then to figure out what c is, you take the square root of bosa. So c is equal to square root of du stufiki. Square root of du stufiki is 121.599. So that's the magnitude here. Total is 121.59. Cool. We need to find the angle because we're doing vector. Vectors, right? We can't just give the scalar quantity because if we say, oh, the answer is 121.59, in which direction? We're talking vectors. So if we're going to do vectors, you go back to Sokotoa. Sokotoa, sine, cosine, and tangent. You have this length. You have this length. You have this length. You can use sine, cosine, or tan. Let's use tan. We use sine and cosine. Let's use tan. So tan of an angle, let's call this theta, tan of an angle, tan theta is equal to opposite, adjacent, what? Opposite over adjacent, right? Sokotoa, opposite over adjacent, opposite over adjacent, which is 80.21 over 90.49. Let's figure out what that is, right? 80.21, 80.21 divided by 90.49. Anyone want to guess what the angle is going to be? Let's see how accurate our drawing is. Check this out. I sometimes do this just for the fun of it. If this is 45 degrees, and if I drew this approximately proportionally, then this angle should be less than 45. So maybe it's around 38 degrees, 40 degrees. Let's check it out. So you get, we get this, tan theta is equal to 0.0.886464. So theta is equal to tan inverse of this duvaki, 0.8846. So theta is, let's do the inverse tan of it. 41.55 degrees, 41.55 degrees, and that's the angle. So this is 41.55 degrees, which is pretty good. Not bad. The accuracy was not bad. So your answer to this question would be the solution to this would be magnitude would be 121, oh we should have used blue from the beginning, 121.59. And we would say if we're going north and south, we could say 41.55 degrees north of west at 41.55 degrees north of west. Or we could say 121.59 at and figure out what this angle is and you subtract from 90. So minus 90 is 48.44 at northwest, staying with this convention, oh we erased it, northwest 48.45, 48.45. That's vectors. You have to be careful where. You have to be careful in adding, subtracting in your directions. If you're going to call this positive, then everything this way is negative. If you want to call that positive, everything down is negative. We call this positive and we call that positive because we're just working in that direction. I hope that helps. It's been a while since we did vectors and this comes into play in physics a lot, a lot, especially in problems involving equilibrium and forces and magnitude and whatnot. Fun, fun. That was great. Good math session. Good math session. And gang, I saw some follows and stuff flying through. I didn't cash the names, but thank you for the follows. Thank you for the support gang. Also, multiplication matters too since it's not necessarily cumulative in linear algebra. Yeah, yeah, yeah, multiply vector. It changes a lot. I haven't done multiplication of vectors for a while. I would have to look that stuff up, but adding and subtracting vectors, a lot. Bananas and chocolate chips. Hell, yes. I hope you have good snacks when you're doing mathematics. Not necessarily bananas and chocolates, but this is really something sweet. Gang, I hope you like the math session. We're going to do more of these. This year has been pretty wacky for a lot of my students that people have been working with. I don't know a lot. I know a lot of people are struggling there in school, which is unfortunate, but it is revealing the problems in our current educational system, which is a positive. It's very important for people to appreciate how, how horrendous our centralized education system is. Okay. I think it's been given a pass for too long and we can definitely see it playing out in negative ways, negative ways in our society. So decentralizing our education is extremely important as far as I'm concerned, and this is sort of my attempt at doing that, right? And I'm enjoying it very much. And from the feedback I've gotten, there's been a lot of people that have used this content to their benefit over the years. Yeah, university included. Not a fan anymore. No, university crap as well. Yeah, university, yeah. Yeah, crap. The whole thing's just completely collapsed in the Western world. Education. So, and as far as I'm concerned, that is by design, but that gets into politics, and we're doing a politics live stream tomorrow evening. So gang, thank you for being here. I hope you like this. We'll do more of these. Okay. I'll try my best to slip in as many as these as possible. We've got one more stream left in this set, and we're doing a politics stream tomorrow evening, I believe at 8 p.m. PDT Pacific Time, My Time, West Coast of Canada. So if you're into discussing politics, economics, personal finance, investing in all that jazz, tomorrow's stream might be a good place to pop into. Aside from that, gang, thank you for being here. Thank you for the follow-ups. Thank you for the subs. Thank you for the discussion, mods. Thank you for taking care of business. Share a review of rock, right? Gang, if you want to follow this work, I am on Patreon. Patreon.com forward slash chicho, C-H-Y-C-H-O. Why do I always join at the last minute? Oh, Blacklight 20. Y-O-Y-O-Y. We did great mathematics today. Really, super fun, man. Thanks, chicho padre. My pleasure, man. Real MC Mike. Thanks, chicho. Real cool math live stream. Yeah, super fun. Super fun. Cheryl, she got her wrench going on. Gang, thank you for supporting this work. I hope you guys have a fantastic day as well. If you want to know what this is all about, you can follow the work on Patreon. Patreon.com forward slash chicho, C-H-Y-C-H-O. I don't put anything behind paywall. Everything's creative, comments, share and share alike. And if you will follow this work, you know that everything's layered on mathematics for those of you that are supporting this work on Patreon. Gang, thank you for the support. It is in large part because of your support that we're able to do this. We are live streaming on Twitch, twitch.tv forward slash chicho live, C-H-Y-C-H-O-L-I-V-E. If you want to participate in these live streams, Twitch is where you want to be. Very cool channel. Thank you, bring math, methamac. Thank you. Do you also talk about statistics? Yeah, we've done some statistics as well. Not too much. I don't go too deep into it because they took it out of the curriculum in my part of the world like 15 years ago. So I don't get the opportunity to teach statistics too much. Thank you very much for the bits Will101. I don't get to teach statistics very much, but I love statistics. So we can definitely delve into, especially in normal distribution and stuff like that. And we will get into it a lot more. I do plan on creating a module to teach statistics and at some point we're going to delve heavy into it. Again, thank you for the support on Twitch and thank you for being here. I do announce these live streams 30 minutes before we go live on Mines, VK, Gap and Parler. And as Cheryl typed out, you can come to our chat anytime you want. I am in Twitch and type an exclamation mark social and all those links will pop up, including the Discord page that we have. And we do have a math folder in our Discord page as well. Discord servers as well, where there's people talking about everything, not just in the mathematics, but everywhere. Okay. For these live streams where we don't have any visuals, which we did today, for the job, that might not work, Cheryl. It's good for people to know, right? You can, we do upload the audios to SoundCloud.com forward slash Chico, CHYCHO is a podcast and those podcasts should be available on your favorite podcasting platform, including Spotify and iTunes. And we will be uploading this live stream to SensorTube, to BitShoot, to Rumble and to Odyssey. And for those of you that are following this work on Odyssey, I hope they're also catching live streams and paying attention to what's going on, Patreon page. I haven't announced the change, the channel change on Patreon yet. I haven't let that go because I'm going to upload one more, make sure everything's flowing smoothly. Before I let people know, our Odyssey channel changed. It's audisi.com forward slash at CHYCHO colon six. Okay. Used to, if you go Odyssey by forward slash at CHYCHO, it'll take you to the original channel I created. But once I synced up the channel with SensorTube, and 800 plus videos got transferred over, a new channel was created. So it seems to be only uploading to that channel right now. So I'm going to stick with that and just continue to upload. And the odds are I'm going to do a test run. The next video, I'm going to load it on SensorTube and see if it loads it on Odyssey or not automatically. For videos that we're not going to be loading on SensorTube, I'm going to load them up manually onto Odyssey. So Odyssey, Rumble, and BitShoot get everything. SensorTube gets select material, mathematics, 100%. Aside from that gang, I hope you have a fantastic day. And if you can make it tomorrow evening at 8pm, I believe we're going to do current events. A lot to talk about. Bye everyone. Bye, Cheryl. Thank you.