 Let's do a little clean of the glasses. Our nice, hi everyone. This is Chicho. Welcome to my channel and welcome to another live stream. Today is May 24th, 2020. And we're doing our 10th drop in math tutoring session for the year 2020. And we're doing these on basically almost every set of live streams that we announce. We're doing a math drop-in session, tutoring session. Maybe at least every second one anyway. Aside from that, welcome. And this is an open discussion. So basically, mathematics comes first if anybody has any math questions. Lay it on us and we'll try to do our best to answer the questions. Hello, Spider-Man. How are you doing? Welcome, welcome. I hope you're having a nice chill Sunday. He's very chill here. The energy seems to be low energy and just relaxed and whatnot. I think everyone's trying to get a handle on how things are going to play out for the next little while, which is a good thing, which is a good thing. Slow people down. Mask of Raven. Hello, hello. How are you doing? I'm assuming notifications went out. Prez, how's life? Chicho, I hope you're doing good, brother. Doing well, man. Doing well. Thank you very much. Why would we not hope people roll in? I'm just going to do our little intro. I am up on Patreon. And if anybody wants to support this work, Patreon is a fantastic way to support this project. And you can follow the work and just get notifications of what we're sharing, what we're uploading, and stuff like this. And there's stuff going to be more than just the live streams taking place on there. This morning, I announced that the article that I wrote about anomalies, prisons, and geophysics, how governments use data, and how to stop them is now up on SoundCloud as well as BitShoot. OK. So Patreon is a fantastic way to follow this work, to support this work. We are live streaming this on Twitch, chicholive, twitch.com.tv, backslash chicholive. So if you want to participate in the discussion as it is happening, Twitch is where you want to be at. I do announce these live streams 30 minutes before we go live on Twitter, Gavs, Minds, VK, and Hello, as well as sharing other content. As I mentioned, we are uploading much of the audio to SoundCloud, a lot of catalog, a lot of videos. Elder God, how are you doing? A lot of videos that we've recorded the sound with the lapel mic to load on to SoundCloud. So I'm slowly going through that. And that's going to take at least until the end this year, if not longer, to get caught up. So there's going to be a fair bit of content coming on SoundCloud. And I'll be announcing them either in batches or solo as they get loaded on. It's fun doing it, really. It's super fun doing it. And we are uploading these videos to YouTube and Bichute. And if you are on YouTube, you do have the YouTube membership abilities by becoming a YouTube member is also a fantastic way to support this project. Hello, Feline Juice, how are you doing? I'm not sure how the math streams are going to go tell you the truth. There is, I've been working with YouTube and it's becoming more and more evil, it's crazy. You figure they figured it out and sort of do an about turn and say, OK, we don't want to go that dark because people are jumping ship. But no, full speed ahead, crazy. Lonely Peggy, how are you doing? Good to see you, Chichu. I like the shirt. Thanks. I got it as a gift from my aunt. It's a, what is it? The design is actually, oh, you know what? The design is actually like the each in. It's like the dashes and dots. So that's cool. X, how are you doing? Welcome to another live stream. And I'm very chill today. I don't know if you can tell or not. I might kick it up. I get excited, so math kicks up. But math kicks up my excitement levels and stuff like this. I am excited to do a live stream, but I'm like total chill mode. And by the way, I've Ozarks. I've been watching Ozarks. I'm just going to take these things down. I don't know if you guys are watching any programs or whatnot. I finished season two of Ozarks last night. I did a marathon on like three episodes. Darker colors are the only colors for me. Yeah, I like dark as well. I like light as well. Colorful stuff is beautiful, especially for spring and summer, right? My conspiracy channel has lost five uploads now. Oh, what, really? Oh, my God, you got a YouTube channel? I didn't even know this. What? Send me the link, brother. I had no idea. Dude, what? Am I subscribed to it? I don't think so. Yeah, they're zapping people mad. Really, as a company, as a business, they're committing harry-carry. Like, they're actually committing suicide on YouTube. They're like, if they keep this up within 10 years, YouTube will be irrelevant, which is a huge, like, what a disaster of a decision for a company that controls 95% of the video platform to do. Like, how could you go from 95%, possibly in 10 years, to being irrelevant? Unbelievable. Not mine. I'm a silent witness. Yeah, some of the videos, I noticed the videos that I was following and I had bookmarked and stuff from my articles that I wrote back in 2006. I used to embed a lot of videos into my articles, videos and hyperlink stuff and write text. A lot of the videos are done. They're dead. What are your thoughts on Joe Rogan moving to Spotify? I think it's fantastic. I think people need to really decentralize from YouTube and Google. And if you're only on Facebook, if the majority of your interaction online is on Facebook, your clueless has to what's really going on in the world. Like, I heard Facebook has banned Brighton video sharing platform. And it prevents, from what I understand, I don't know if it even allows BitShoot links to be posted. So I know there's still people on Facebook, but they've been caught by the political, economic turmoil of the world with this pandemic and all this stuff going on. They were blindsided because the information they were getting was completely censored. So they were clueless as to what was going on. I don't know, it's weird. But I think it's a good thing. I think people, big players on YouTube, them leaving YouTube, I think it's a fantastic thing. Fantastic. Galio, how are you doing? Hey, bro, how are you doing? Well, thank you very much. Enjoying my Sunday. As you can tell, my chill factor is decreasing and my energy level is going up as soon as we start talking about censorship and whatnot. I would like you to send that save to my graphite. No, brother. Sorry, no props to people, brother. Joe Rogan got a huge paycheck. Yeah, a hundred million, I think, if his stuff is to become completely exclusive. Yeah, I think he got, from one or something, he got a hundred million, which is fine, whatever, you know. They can pay people whatever they want, right? I'm here, but I'm going to be making a sandwich for a few minutes. Nice, enjoy your sandwich making ground. I love sandwiches. Are you shallow on Monk of mathematics? No, no. I would be the drunken master, maybe. From the Shaw brothers. I don't want to do harm to people, but I like sharing information. And yeah, I like the drunken master. By the way, if you ever want to watch an amazing Shaw brothers movie, it's called Come Drink With Me. As far as I'm concerned, it is one of their, for me, it's in my top five of Shaw brothers movies. Come drink with me. It is absolutely fantastic. Okay, if you can handle the Shaw brothers extremism and stuff like this, which is mythology, really, right? If you're a comic book fan, you should appreciate Shaw brothers movies. I have dump WhatsApp now. Telegraph is my new message app. Facebook is next to that. Nice, Seller God. I never use WhatsApp. I don't use TikTok. I only have a Facebook account to keep in touch with two, three people that I don't have access to talk to them. I don't surf my feet. I don't look at anyone's posts. I just go on there, message them, log out. And I don't stay on. I don't stay on for replies. I just message, log out. That's it. And hope that's frequency of that. I do that maybe check it maybe once every few days, like two seconds. See, you've seen a drunken come drink with me, Elder God? Fantastic. What an amazing movie. What an amazing movie. The depth of that movie is unbelievable. And the moral message and the societal message in that movie is amazing. Yeah, drunken master of mathematics slash froze. His friends on a different podcast said that's not the amount, but me that seemed like much, much more. So 100 mil is a fair estimate. Okay. Coincidence is big mathematicians also like, oh yeah. And from my university days, the math professors that I interacted with in the math department, and I belonged to the math club at UBC for a year when I went to university of British Columbia. And there was only like six of us, seven of us in the math club. It just formed, I think maybe eight of us. And they formed it when I was there. So we were the first batch of people that belonged to the math club and stuff like this. So we had a little space in the math building and saw a lot of the math profs. They're crazy. Half the math professors were alcoholics. A quarter of them were schizophrenic or something. I don't know, schizophrenic is the right word, but they're like, you talk to them and their mind is somewhere else. It's crazy. What a trippy place to be. What a trippy place to be. And they have one foot in, if they're lucky, they have one foot based in the present and another foot based in multiple dimensions in places, which is a brilliant interaction as well. Once you start talking with them and stuff like this, you realize the depth of connections that they're making. If you could plug into their mind and see the visuals that they must be trying to create to be able to process the information that they're thinking about, would be amazing, right? Would be amazing. Very chill place to be actually. If you ever wanna spend downtime at a university, just go to the math department, right? Take some math courses and just enjoy. Yes, and most of mathematicians, mathematics people sacrifice hair for math. Dude, slash. You belong to a math department and clothes and like raggedy clothes, they come in. And then there's the other side too. There were some people in the math department, the prof that were sort of celebrities and chess masters and stuff like this, which is cool. It's a very unique dynamic to be in. 13 pints last night. I feel great, please don't attempt this. No, that's not good. Well, if you feel great, that's fantastic. 13 pints, brother. I hope you reduce a little bit as you get older. But every now and then it's actually good to flush the system, right? It's actually okay to flush the system. As I said, I have no idea. Thanks to God, I'm not in math, but I have seen many people, yeah, slash, yeah. And the crazy thing about the math department is it sort of becomes a sort of a bubble. I think a lot of departments do, but math department is so, it's the same with the math department. My interaction with the math department and people who are really into mathematics and stuff like this is the same type of interaction, same type of mindset I've seen through the enthusion community, right? Because they're not just thinking about material possessions, material gains, celebrity them or whatever it is, they're esoteric, they're holistic, they're thinking about larger things about our universe. Good space to be in, right? I would love there to be a university where it's a mathematics enthusion faculty and see what we find out from that community. I really, like what I was gonna say regarding school and mathematics and stuff like this, half of my students, I won't get presented with, there are students right now that are working hard, trying to stay up to their classwork and trying to make sure they learn the material. I'll give you percentages. That percent is very few, okay? There's a certain percentage that are willing to learn as long as they get a little push, little push, little direction, right? Little interaction where it's fun and stuff like this. That percent is a little bit higher, okay? But the majority of kids in school right now are having a hard time trying to grasp how they're supposed to learn on their own or self-direction because they haven't been taught through our centralized education system that it is up to them to educate themselves. So they're trying to do an adjustment but it's very difficult for them and they don't have the resources available to them and they don't want to interact online. You know, unfortunately there's a lot of educators, a lot of people that don't know how to interact online, how to teach online. And nothing against them, it would be, for me as well, it would be virtually impossible to teach a classroom of 20 people, mathematics online. I wouldn't take it beyond five people personally if I was gonna do interaction online. So it's crazy. And the tools available to them, the educators is minimal, it's garbage. The bureaucracy involved in the tools is insane. Oh my God, what's the point of living if you don't feel alive? Yes, math as a subject is amazing. Like it never fails to blow my mind. Yeah, for me I'm not in depth in it anymore because I'm not in the university world anymore. So the mathematics I'm using is very rudimentary because it's mainly just high school stuff, right? At some point hopefully I'll get into more higher level probability statistics and whatnot. But when I was immersed in it, the problems of the world and the superficial fears and anxiety that people had about the world just seemed so irrelevant because you were sitting there trying to solve a problem that could only be solved through the realm of mathematics where you're taking in multiple variables and doing integrations and looking at different systems, trying to figure out what's going to happen, right? It's mind expanding. I tell people that it makes mathematics makes you smarter, period. I mean, almost anything you learn makes you smarter but mathematics takes it to another level. It really does. Graham, this might be a controversial opinion in here but I don't find math any more enlightening than other subjects. I love every subject and all subjects have opportunities for amazing things. I agree with you, Graham. However, math is different, okay? Physics is the only one that comes, actually engineering would as well. Structural engineering, just building things and stuff like this, what you're involved with, Graham. But mathematics is a world on its own because it's not concerned about what you can touch, what you can see, what you can feel. It is concerned about just specifically systems. Some of them might be imaginary systems and how they interact. It's basically really pure problem solving, pattern recognition and the pattern doesn't have to be real. It just has to have the possibility of existing, right? So I find mathematics the closest thing to science fiction, okay? That's why I think a lot of science fiction, people that I've met in my life have been avid math people and math people have been avid science fiction people. Mathematics is different because mathematics is its own language. Like if you're studying history, you're not studying a language, you're studying history, you're studying events, right? Biology is looking at just specifically one system and trying to figure out how these things work out. It doesn't, even though it's got its own words that you use, you know, there's languages that you have to learn, it's saying a little law or anything like this, right? But the structure of it is not from the base of mathematics, it's structure from the base up. It's built up the language, right? So it has its own nuances that I don't think anything else has. What did you work on at the university? Why did geophysics? So my stuff was very hands on, even though I got a math minor, for my stuff it was a lot of just taking data and just crunching data, processing data and that type of work. And then I did that for, you know, almost a decade doing geophysics. Greatest mathematicians that people don't really know about. Greatest, as far as I'm concerned, the most intelligent human being that, well, you know, we could say Galileo and all these people, but Tesla for me would be the one person, he's more known now if you get it. If you're older, if you're getting older and you've looked into the science and the conspiracy into the probabilities of what could be, you'll know about Tesla, but a lot of high school kids don't know about Tesla, right? So I would say Tesla is the greatest scientist that people don't really know about. There's a certain age group that does. I would say anywhere between 20 to 40, 45, they're aware of Tesla, but below that and above that, they're not really aware of Tesla, not too much. I want to ask that if someone is best at math, like he's regular, then does he get right to call other people dumb? No, no, because it makes you smarter relative to yourself when you learn math, right? So if you're at this level of intelligence, whatever that level might be, whatever the metric is you're measuring, you learn math, you're gonna kick up, right? You're gonna kick up a fair bit, okay? You learn anything you're gonna kick up, but math leaves some bounds, right? But just because someone doesn't know mathematics, you can't call them dumb because they might know a lot more, a lot of other things that you as a mathematician will not know about, right? As a friend of mine used to always say, two heads are better than one, right? There's always something someone else will know better than you or someone else will know something that you don't know. They should use their gift to help the others around them. Yeah, I agree, right? Is mathematics art or science? I think it's both. I think it's both. Mathematics is a language of science but mathematics is also the language of art that you can think about it that way as well. Mass covering, do the pure mathematics being abstractions? You can apply to a wide variety of things easily. I agree with masquerade, it's just mathematics you can apply anywhere. Like really, we apply to cooking, like food. Tesla, yes, I love his ideas. He reminds me a lot of Da Vinci in some ways, yeah. Like the closest comparison would be Da Vinci, right? For Tesla. Galileo Da Vinci. And as far as I see it, Tesla would have been above Newton. My personal opinion, okay. If extraordinary mathematicians don't call others dumb, then why the hell little math teachers in school call us dumb? F, f, f, f, f, f, f, f, f, f, f, f, f, f, f, f, f, f, f, f, f, f, because they're not really, they don't, most of the, there's a lot of people teaching mathematics in school that aren't, like for me, I don't consider myself a mathematician, not by a long shot, not even close. Like I've told people from the get go, and they tell my students I'm not a mathematician, I'm just someone that knows the language of mathematics through the ability that I need to, to be able to apply it in my life, right? There is other mathematics, higher level mathematics that I would love to learn to be able to apply in my life, but I have to take the time to learn and I don't have that time right now. At some point, I will make the time, right? And I've mentioned this from the beginning as well, right? But you have to appreciate that there's a lot of people teaching mathematics in school that have no math background. I know some of them, right? I've interacted with some of them. They've taken someone that has studied geology or some kind of science, right? That's their background. And they don't have a math teacher, so they assign this person to be the math teacher for grade eight and nine or grade 10 or 11 in their appropriate school, right? They're, just because someone's teaching mathematics, it doesn't make them knowledgeable in the language of mathematics. And as Mask of Raven says, because they're bad teachers, presumably, right? Grant, thank you for taking care of business. Wrangler is the highest certification in the world for mathematicians. Is it Wrangler? Wrangler? I don't know that. Definitely that was a math question. The art of science? Grant, Chico, I might have to disagree. If you were a historian, you might also say that history has its own language. History has its own patterns. But I don't agree that history has its own language, Grant. I think history has its own patterns. If we don't know our history, we're doomed to repeat it, blah, blah, blah, right? But I don't consider history to be a language. I consider law to have its own language as well, right? The words have different meanings based on, for example, if we say we understand in regular speak, then that means, oh, I get what you're saying. If you say you understand in Canada anyway, and I think it's the same in the United States, it means you agree with the person, right? So when the judge in a courtroom says, do you understand? The last thing you wanna do if you're being prosecuted and say, yes, I understand, it means that you agree with them. There, your future is sealed and you're gonna go to jail, right? So they do have their own languages that they use, but I don't think they are a language. Anyone want to help me solve this problem? Given close to x equals, find sine x, tan x, and so on, sure, let's do it. Miro, let's do mathematics, let's try this out. Good morning from Cali, good morning, Lark, how are you doing? You got to be there, emotes, sorted, save. Chicho, you seem to be good at strategies. Would you consider playing a video game called Civilization Six? Civilization is up to six now, right? Well, at some point I'm gonna get back into gaming, but right now I'm just, I have lots of my play plan that I'm enjoying, so on all the writing, grab chicho, what is your definition of language? Is a language not just a pattern of speaking and conveying? No, because that way the English language wouldn't just be English language, there's multiple dialects, right? I don't consider a language just whatever form we use in communicating. Language to me is you have to have the axioms, the syntax built up, and everything goes on top of that, right? Language is not just a way of communicating it. Well, I'm not saying that properly, but I don't think so. Hello, Chicho and Chad, good evening. Brett, how are you doing? I have dyslexia, how can I teach myself to do well with numbers? Too embarrassing being 26 and unable to count. We're gonna come to the trick question, by the way, Miro. Let me just answer this. First of all, you shouldn't be embarrassed. Okay, if you have dyslexia or you can't, you have a hard time counting and stuff like this, but you need to practice, right? I know it's hard, really. I work with students and I have worked with students that are on a spectrum, either autistic spectrum or have dyslexia and stuff like this. It takes hard work, really. And you have to be at peace with yourself. Appreciate that. It's gonna take a long time for you to be able to break through some of those boundaries, barriers, right? This Calculia, this Calculia. Oh, let me read the definition of this Calculia. Is difficulty in learning and comprehending arithmetic, such as difficulty in understanding numbers, learning how to manipulate numbers, performing mathematical calculations and learning facts and mathematics. Yeah, so I, this Calculia, this Calculia, I usually associate that with, I've had students that way that, I don't know if I'm putting in the right caliber, I just say usually spectrum, right? Either autistic or have dyslexia or stuff like this. But I've had students that have a really hard time, especially doing the counting. So first thing I do with them is make sure they're counting properly, right? And I don't hold them back because they can't count in a certain way, right? So for example, a lot of students that I've had have a hard time counting in the teens, right? That have, I'm not sure if they were diagnosed with this because I don't dig in to what the diagnosis has been, right? I just interact with them in a way where we can break through barriers. And I've had students where they have a hard time counting, especially going past the teens, right? Because the teens in English are difficult. If you're, because they don't follow the pattern, initially in the, you know, 15, 16, 17, stuff like this. But once you practice a little bit, you can let mistakes go by, right? And then you get into the 20s and you explain how the 20s work, 21, 22. And you get into the 30s, 40s, and then you get into the 100s. And once you get into the 20s, the rest of it should be easy because it's putting it together, right? But once you go a certain way, right? Then let's say you have, someone's having a hard time into the teens, right? Get into, correct a couple of them, but don't stay there too long. Go into the 20s, 30s, 40s, get into the 100, and then start correcting some of the mistakes previously. So you have to loop it when it comes to, that's the way I do it anyway. When I'm working with someone that's having a hard time, just with numeracy, really, with numbers, okay? After that is addition. And addition usually people deal with it okay, right? I tell people use your fingers. There's nothing wrong with using your fingers, right? If you have tools that you can use to be able to help you learn mathematics, it is 100% okay to use your fingers. Some people are embarrassed, they don't want to use their fingers. They clench their fists like this, like, what are you doing? Use your fingers. Why aren't you using your fingers, right? And then you get them comfortable with their discomfort of learning mathematics, right? As soon as you get into addition, multiplication should be the next step, not subtraction, because multiplication is an extension of addition, okay? So for me, I go into multiplication and multiplication is a big hurdle for people to surpass. Okay, I dropped down. Hello, Kyle, how are you doing? Let's make some numbers dance. Let's make some numbers dance, please. This Calculia is now a recognized learning difficulty. I can count, but I can't add, subtract or multiply or divide. I wasn't taught well in school because no one understood. I cannot count backwards. Backwards, I get into counting backwards when you get into subtraction. So I wouldn't worry about counting backwards, okay? Which please, okay. I wouldn't worry about counting backwards. I would go from counting to adding, so but I cannot add. So are you using, just because there's a difficulty here again, let me deal with this. Let's, Miro, are you okay holding off on the trig until we deal with this? If you're in a rush, we can deal with the trig and which please, are you okay waiting if we deal with trig? So one of you guys answers will deal with one or the other. Let me know, okay? Because if we're gonna get into this, I like to get people past their hurdle and both of these seem to be a hurdle. So let me know which one you guys will wanna deal with first. Okay, I'm quite hungover for today. So no worries, Kebuk. Trust me, there's a lot of math prof that are hungover when they're teaching mathematics. Okay. I have ginger and mint tea. So let me know, gang, which one you wanna deal with first? It's nice, I got, I'm very embarrassed. No, don't be embarrassed. Almonds and chocolate and a little bit of walnuts. Okay, don't be embarrassed. Let's deal with you first. Miro, I'm assuming you're okay with us waiting until we do the trig and I'm gonna write down the trig problem here. That way we're gonna deal with it. Cos 2x, cos 2x is equal to, three over five, three over five. I'm gonna wanna find sine and tan, right? Sinex and tanx. Sinex, tanx. I have trouble with multiplication in single digits. I can usually figure out the answer eventually, but it takes me way too long. Okay, Parker, my question to you is, what's multiplication? Multification is just multiple additions together. So always think of it that way. Don't be embarrassed. I'm totally okay. It's totally okay. We're all here to help and learn and we accept everyone, yeah. And here, which please? Let's deal with this right now, right? So you're okay with counting. It's been two minutes and I love it. Awesome, time to welcome to our stream. And by the way, thank you for the subs. Thank you for the follows gang. If I don't catch it, my apologies. My focus is on the mathematics, okay? But I very much do appreciate the support and the follows and the subscribes and all that jazz and the conversations of course, right? So I'm just gonna call you which please? Or I'm just gonna call you please. Let's assume you're okay with counting, right? Once you're okay with counting, let's deal with addition, okay? Because that's the key. You need to learn addition first, right? So if you're okay with counting, put yourself on a number line, okay? So draw a line, start at zero. And you know how to count, right? So you're gonna go one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16. Right? And what you're gonna do is say, okay, we're gonna do simple addition right now. We're gonna add single digits together, right? So let's assume we want to add, let's put it here, two plus five. So all you do when you're trying to add two plus five, you go to two, one, two, right? This is two. You put yourself here and you add five, which means you take five steps, right? So if you're here, you go one, two, three, four, five, and you're here, right? So you ask yourself, where are you? Because you just went five steps, right? And where you are now is one, two, three, four, five, six, seven, right? By the way, you can teach subtraction using the same method as well, right? So for me, I'm not gonna run you through, spend the time to do multiples of these, right? I'm just teaching you the process you need to do for yourself or with an educator where you have to learn or a method you can use to learn how to add, right? So what you can do now is say, okay, let's add multiple things together. Plus three, plus another five. So if you're gonna go plus three, plus another five, so from here, you go three, one, two, three, okay? So you were at seven, then you're at eight, nine, 10, right? So this is another three being added. You're here now after you add that guy, and then what you're gonna do, you're gonna add another five, one, two, three, four, five, right? So now you're at 15. So this is another five being added and now that you're here, okay? This seems simple, okay? But it's crucial to get a visual of what's really taking place. So you have to become comfortable with this. Now if you're adding large numbers, right? Happy Sunday, Chicho. You're having an awesome weekend. Thanks, Grand Prix. Having a good time. Hello, Chicho. I was gone. Don't know if you noticed, but I am back. Have you already solved the trick problem? No, Miro. What we did was say, we're gonna deal with this right now about adding, multiplying, subtracting, and dividing, and then we'll deal with your problem. I hope that's okay, okay? So just imagine you do this for a little bit of time. Okay, okay, got it. Okay, awesome. I hope you're okay with that, Miro. Now do this a little bit. Get a hang of it, get a feel for it, right? And then go, okay, let's add bigger numbers. Cool, okay? Let's add bigger numbers. Your source, I always am trying to memorize addition and subtraction of different numbers. So I know the answer immediately, but then I can't figure it out if I don't have it memorized. Here's the kicker parker, right? It's not about memorization, because if you do a lot, you automatically remember. The trick is to learn the process of it, okay? So learn the process, and then once you start doing something, your mind is magic. It can remember things, right? So don't try to put it into memory without understanding what's going on. Understand what's going on, and your mind automatically puts it into memory, okay? My general confusion is real good. I have, but I'm not sure why you provided domain. This is very informative, thank you so much. My pleasure. I'm feeling a little relieved. We're gonna continue with this, by the way, okay? Then Barbara Higio currently using a lot of logic to figure out some complex command blocks in Minecraft. Nice, that game is very useful for exercising small math and intense logic. Yeah, it is indeed. I have students that play Minecraft, and once you link it up with mathematics, they're like, wait a second, that's all mathematics. Now just imagine if we had bigger numbers to add, right? So instead of two, five, three, and five, let's assume we're adding 20, and I'm making the link very obvious, of course, right? But I'm gonna show you how this works, right? 20, 50 plus 30 plus 50, right? We just kicked it up one order of magnitude, right? So what you do is put your number line together again, right? Put your tick marks in there. One, two, three, four, five, six, seven, eight, nine, 10, 13, 14, 15, 16, 17, 18, whatever it is, right? Now what you're gonna do is, because these are bigger numbers, you're not gonna count these as one. You're gonna say, okay, you know what? Because I'm gone to another scale level, instead of making each one of these, one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, I'm gonna make each one of these tens. Each jump is now a 10, right? So zero, 10, 20, 30, 40, and so on, right? Then you do the same thing. Start off at 20, right? You're here, here's you, and you're gonna add 50. So each jump is a 10. So you're gonna go 10, 20, 30, 40, 50. You just added 50 to this person. He took 50 steps. Now you're at 70, okay? Then you're gonna add 30, one, two, three. Now you're at 100. Then you're gonna add 50, 10, 20, 30, 40, 50. Now you're at 150. Okay. So you're doing jumps of 10 now. You're okay with this, please? Minecraft is an incredible educational tool. I posted that is why it's popular, experiential learning, da, da, da, da. Love that. Lodge is a great part of math and it is user, da, da, da. I feel like an idiot being an adult and not knowing the answer to something simple like nine times six without taking like five. Here, Parker, anything times nine. I'll show you this trick right away. Anything times nine. Hold out your hands, right? Hold out your hands. So you're gonna go nine times five. Nine times six, what are we doing? Nine times six. You're gonna go one, two, three, four, five, six. What's nine times six? 50, four. What's nine times three? One, two, three. Hold this back. What's nine times three? 20, seven, right? So the nine multiplication trick with hands is easy. The other ones you have to sort of memorize, but the more you do, the more you'll know. We have a playlist, okay? We have a playlist. Early childhood education. Let me find it for you. Okay. Because I've gone through and I've put together some videos of how to teach adding and multiplying. And I'm gonna add subtraction and division to this, hopefully this summer. Okay. Here's the playlist game. If you wanna learn how to add, subtract, multiply and divide, check that out. But I'm gonna continue with this right now. I love the multiple of nines trick. I still use it when I'm draw blank. Yeah. And there's another trick as well, by the way, that you can multiply six, seven, eight, nine, 10 together. Right? So those are the multiplications that people have a hard time with. Okay. Cheecho, hello Felix, how are you doing? Okay. So the nine multiplication is just this. You count, you do. You know, seven times nine. One, two, three, four, five, six, seven. What's seven times nine? Six, 60, three. Right? Now, what if you had eight times nine? Usually I'm lost listening, but your voice is awesome. This is the old school tricks, old school tricks, right? Here's another multiplication where you can multiply six and nine, six all the way up to 10. So consider, start with the pinkies and each one is a six, six, seven, eight, nine, 10. Right? Let's say you want to do six times eight. Right? You get the six from here. You get the eight from this one. You go six, seven, eight. Touch them together. Okay. This is a little bit more confusing. So I'm going to do this. Right? I have a video out there showing how to do this too. Right? So six times eight. Right? All the fingers, including the touching ones that you went through already, they're tens. So 10, 20, 30, 40. Right? So these four fingers are 40 and then you multiply the two and the four. You got two and four together. Two times four is eight. So six times eight is 48. Okay. Sorry, did I, well six times eight, my bad. Six times eight is 48. Four times four times two is eight and these four are 40. Okay. I do have a video out there that shows this as well on my YouTube channel. It's not on Bitshoot yet. I did cum on back in the day, but was terrible about it and would rip out pages and copy out the answer book. It did give me the basics really well, though I'm thankful for it on that front. Here's the kicker, Gabu. I've had a lot of students that have gone through cum on that I've worked with. The problem with cum on is this, exactly what you just said. They give you pages upon pages of just multiplying, multiplying, dividing, multiplying, just do, do, do, do, do, do, like a machine, right? You learn multiplication well, right? You learn certain basic concepts well, but it takes the love out of mathematics, right? It leaves a hollow shell of human beings that consider mathematics to be memorization and they hate it, okay? I do not recommend cum on. I've had to deal with students that have come out of cum on where they're getting into higher level mathematics and they're having a hard time with it, right? Because they don't understand the concepts because they're just used to memorizing. They're not used to understanding, right? So cum on is great if you just want to learn multiplication, right? Because you're doing, if you do something for that long, that many pages, that many problems, you'll learn it no matter what, right? But I don't recommend it. It takes the love out of mathematics. You just blew my mind with that trick. I'm not being fictitious, fictitious, fictitious. Rosta, also, multiples of nine always have digits that add up to nine. Yeah, that's true too. A student might have pointed that out to me actually with the first number being one less than the multiple. So nine times eight is 72. Seven is one less than eight and seven plus two is nine. Nice. Nice, it's so fun and based on, sorry. Throwing up with math, gang. It's nice, I love that. Hey, Chichou, knowing that you are into math but are also open to conspiracies, what is your opinion on the ancient human feats of knowledge, strength, such as building the pyramids? Mathematics has been part of the human humanity forever. Some of the mathematics that we have known in the past has been incredibly strong, right? And we don't really know about human past civilizations that came before us, right? So there's major gaps in human history, right? For some reason, people believe that what we know now is the absolute truth which is not the case, right? What we knew 100 years ago, people say, oh, human beings only been around for 20,000 years. Now we go on and on. Human beings have been around for hundreds of thousands of years, right? The mathematics of ancients was powerful. They built astronomical grand structures that lined up with the eclipses and stuff like this. It's crazy. Oh my God, that was such an unexpected answer. That's exactly what I felt. Kumon was like a mental prison, mental prison indeed. As for the feat of strength, mass enslavement, unfortunately. Now, we're here right now, right? Right, please? So with the bigger numbers, all you have to do is just increase the increment, your tick marks. Instead of going up by ones, go up by tens. Then you ask yourself, okay, what happens if the numbers aren't exactly like this? You create another number line. Let's do, we're gonna do a simpler one, okay? Let's assume we're going 22 plus 53, right? Well, create a number line, okay? Now, we're into the tens again and you should be able to see that this doesn't go above 100, right? 20 plus 50, 22 plus 53. And I'm gonna give you a visual and then we're gonna do it algebraically. Algebraically is easier, okay? But I want you to see the visual as well. So if you see this, then what you do is you put your tick marks here and I'm gonna make the tick marks a little bit longer, right? So 10, 20, 30, 40, 50, 60, 70, 80, 90, 100. Right? Put yourself at 22. So here's 10, here's 20, and 22 would be here somewhere, right? So put a 22 there. Here, let me make this bigger so you see it. So we're gonna put 22 here, right? So that was 20. I'm gonna put 22 here, whoop, whoop. This is 22. Now you're gonna add 53 to this. So what you do is you do jumps of tens right now. So you're gonna go 10, 20, 30, 40, 50. If you were just adding 50 to this, you would be at, that's 22, 32, 42, 52, 62, 72. And then you just have to add the three to it. So you're gonna go one, two, three, 75. That's where you're at, okay? When you're adding this. This is just a visual. You're not gonna do it this way, okay? This is the way you're gonna add numbers together. And it's the old school method. Forget about anything new that they're teaching you, right? With the old school method, oh, I shouldn't have erased that, that was a visual, but oh well, we had 22 plus 53. And the beauty of mathematics is you do things in piecemeal, right? Mathematics is able to break things down into smaller segments where you can work from the smaller segments and build it up again, right? You take it apart, you build it up, take it apart, build it up, right? So what you do is you add the digits, the columns appropriately, and we're going by tens, right? So you have to understand the counting process, right? So if you understand the counting process, let's do this. These are the single digits, the tens, the hundreds. Put a little comma there. These are the thousands, 10,000s, 100,000s. Put a little comma there. And these are the millions, right? Each one of these goes from zero to nine, right? So there's 10 numbers there, zero, one, two, three, four, five, six, seven, eight, nine, right? Once you go to the 10, you move on to the next number, right? So over here, if you have 22 plus 53, you add these guys up. Two plus three is five. Two plus five is seven. So it becomes 75, right? Now let's assume we had a larger number. Let's assume we had two, two, eight, seven, four, plus 53, nine, five, seven. Nine, five, let's make this a two for now, right? So you're adding these two numbers together. Start from this side. You add these guys, four plus two, six. And then you add these guys, seven plus five is 12. And if you're having a hard time with this, put your number line together. Nothing's stopping you from creating visuals for yourself initially, right? Don't step away from the visuals. Create the visual for yourself if you need it, right? So let's put a visual here, right? Because each one of these, you're adding 10s, right? That's what you're concerned about. Just make a number from your, what do you call it? Your number line up to like 15 or 20 or something. Take it up to 20. So you're gonna go one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, right? The reason you're gonna take it up to 20 is because if you're only adding two rows, the most you could have is a nine and a nine. That takes you up to 18, right? So if you're gonna add this, seven plus five. So you're gonna go, this is zero, one, two, three, four, five, six, seven, plus five. One, two, three, four, five, right? So you're at seven, you went eight, nine, 10, 11, 12. So this is 12, right? So seven plus five is 12. Now seven plus five is 12, but you can't just put 12 here. What you do, you put the one, if this is 12, you put this guy here and you take the one and you put it up top here. So this is your 12, 12, okay? And then you add these guys. One plus eight is nine. Nine plus nine is 18. Now again, you can do it on a number line, right? Go to your nine, seven, eight, nine. This is your nine and then you add another nine. 10, so one, two, three, four, five, six, seven, eight, nine. Okay? So if this is 20, you know you're two back from 20, so this is 18. Now I'm going speedy Gonzales right now by the way. Okay, but I'm just showing you how you can teach yourself with this, right? So that becomes 18. And again, you put the eight here and you put the one here. So this is 18 and you do again. One plus two is three. Three plus three is six. Two plus five is seven. Okay? I hope that helps, please. You have to go slow. If you're having a hard time with it, just go slow, Matt. If you're learning mathematics, if you're learning anything, appreciate this. The school system is not the best way to learn it because once you're getting into this, if you're really into it, when you're learning something, there shouldn't be a bowel ringing saying, okay, stop thinking about this. Let's go learn history, right? If you're learning about this, spend two hours on this, three hours on this. When you spend a longer amount of time on something, you'll pick it up faster, okay? You might get frustrated, but you spent time with it, okay? I hope that helped. I hope that helped. Counter is running in the speakers, how the counter is running. Okay, let me see what I missed in the conversations. The trick problem was here. We're gonna deal with this right now, okay? Oh my God, that was such an unexpected thing. That was a trick problem. Another weird trick for nine is that if you take any number, multiply it by nine, and add up the digits, yeah, blah, blah, repeating the second step as many times as necessary, you will always end up with nine. Add up the digits of the products, repeating the second step as many times as you want, as necessary, you will always end up with nine. Ah, okay, cool. Ah, that's cool, Felix. I didn't know that. Do you think that there's some mathematical concept that are now lost for sure, Miro? I think so too. The chances that I feel are high. I mean, I wonder what kind of science math knowledge was inside the library of Alexandria, which was destroyed. One of the worst mistakes in human history in my opinion. Yeah, was it a mistake, Miro? I don't know. During the Crusades, much of the mathematics we had was destroyed, yeah. 10 is there for? A half. Okay, you did it, you gave me the answer. We're gonna do it right now. Thanks, Mask of Raven, by the way. There's a book called Abacus and the Cross that I've read about sort of the precrusaders, crusades math and scientists, monks of France, and the destruction of anything having to do with Arabia during the Crusades, yeah. Thanks, Mask. That was for you. Got it, Grant. Ba, ba, ba, wow, what's the conversation? Okay, I'm gonna do the, I'm gonna work on the trig gang. The trig problem is just simple algebra. Yeah. Many chapters of Euclid's elements, yeah. Okay, so let's do this trig problem. So, let me think a little bit. Yeah, think a little bit of water. Not water, ginger and mint tea. So, there's few different ways you can approach this. Okay, you want the sine of X and tan of X. So let's approach it, yeah, let's approach it this way first. Okay. First of all, draw a triangle if you want, right? So, we can draw a triangle if we can go like this. Just to get a visual for it. Now, I'm not sure if I'm gonna complete it this way, but at least it's gonna give us a visual, because you can get different types of problems with this, right? So, Sokoto, a sine, cosine and tangent work with right angle triangles, right? So, we're gonna put the angle, this is the angle, right? Two X, you can call it theta if you want. So, you could say let theta equal two X, right? So, we could do that, yeah. Because people are more comfortable with theta or A or B or whatever it is, right? So, we can say cos theta, cos theta, cos theta is equal to three over five, right? Agree? Okay. So, cosine, cos of an angle is adjacent over hypotenuse. So, adjacent is this and hypotenuse is this. So, adjacent, that's your ratio, right? Adjacent over hypotenuse. So, it's three and five. Okay, you're okay with that? I hope so. Yep, yep. Now, we're gonna use a calculator for this, by the way. We need to, okay? Yeah, I'm okay. Okay, cool. So, you can figure out what this is by using Pythagorean theorem, this side. Because Pythagorean theorem is A squared plus B squared is equal to C squared. So, you're gonna get three squared plus B squared, which is this guy, is equal to C squared, which is five squared. And C is the hypotenuse, right? So, you're gonna get B squared is equal to 25 minus nine. Minus nine. So, B squared is equal to 16 squared root both sides. So, B is equal to plus or minus four. The square root of anything is plus and minus, by the way, right? But for now, because we're drawing a triangle, it can't be negative length, so we're gonna make it a four. So, this guy is a four. This length is a four. Okay. And it's actually B round brackets, because it's an open subset. That's from something further on, right? Let's get right there. I don't think my answer was right. Uh-oh. Did it look quick? We'll check it out. So, if we're doing this, then we can figure out what sine of theta, sine of theta and tan of theta are easily, right? Because sine theta is opposite over hypotenuse. And for this situation, it would be sine of theta is equal to four over five. And tan of theta is opposite over adjacent. And in this situation, tan of theta, here, we don't need this part of it, because that's just becomes cluttering. So, tan of theta is gonna be four over three, right? Now, we weren't looking for sine of theta and tan of theta, or sine of two x and tan of two x. We were looking for sine of x and tan of x, right? But this is sort of a visual of what's taking place, the link between tan and cosine. So, whenever they give you a trig ratio, you can draw it, and these guys are just the sides, the length of the size that they've given you. Does that make sense? Is that okay? I hope so. Now, if that's the case, then what we've solved here for, I'm gonna erase this guy. Let's erase the part of that here. So, what we've solved for, yes, so what we've solved for here, really, is sine of two x is equal to four over five, and tan of two x is equal to four over three. Agree? Identities. Yeah, you could use the double cosine identities. Oh yeah, by the way, I should ask you this. Miro, is this question, are you guys doing the stuff using the identities? The sine and cos double angle identities and stuff? Or are you guys just using straight up algebra? If you're using the identities, we'll use the identities for this. Burning cannabis and learning mathematics. It's a wonderful Sunday. It's a wonderful Sunday, Grand Prix. So, which one is it, Miro? If you're using identities, we'll go identities. I'm not gonna go down this rabbit hole. I think I think you're using identities. Let's use identities. Okay, so this is just a relationship between the cosine and tan, if you wanna think about it that way, right? Now, from here, I'm just gonna do this quick, right? If you were gonna solve for x, because that's what you need, right? You need x, and then you can just do the reverse way, where you can do the identities. If you were just solving for x, you would just go, two x is equal to sine inverse of four over five, and two x is equal to tan inverse of four over three, okay? And then, whatever answer you get, you just divide by two, divide by two, right? And then you would have your x is equal to tan inverse of four over three over two, okay? Sine inverse of that equals to, but I also like this one. We'll use the identities. The identities make it look a little different, okay? So I'm gonna erase this down. This is, by the way, this is a good method to get a visual of the thing, of what's going on, because pre-two x, what they would give you is generally just cos of x is equal to this and five sine and tan, okay? So if you're using identities, check this out. We do, actually, we still do sort of, to a certain degree, need the triangle, but we'll leave that alone for now. So cos double angle is this, cos two x is equal to, I gotta get my identities, sine two, sine x, cos x. Hold on, let me do this. Trig identities, trig identities. Trig identities. As you can tell, I don't memorize the trig identities, okay? We need the double angle identity. Where's our double angle identity? No, there it is. So we've got three double angle identities for cos data, right? Cos squared a minus sine squared a, so cos squared x, this would be x. Cos squared x minus sine squared x. It's also equal to two cos squared x minus one, and it's also equal to one minus two sine squared x, one minus two sine squared x, okay? So if you're using your identities, this is what you would do, check this out. Boop, I'm here. You don't necessarily use, you don't need to use this one. I would use this one because you're trying to find sine, okay, sine of x. So what you do is this. You say, okay, cos two x, here I'm gonna write this so you see it, cos two x and cos two x, right? So what's cos two x equal to? Cos two x is equal to three over five, okay? Use identities with only sine and cos and that's easiest. Yeah, that's easiest, right? So we're gonna use this guy, right? And when you start using identities and formulas and stuff like this, consider it just when you were a kid, when you had, you know, if you watched little toddlers, they get little blocks in front of them, little things and there's holes like square holes, rectangular holes and they got blocks, they have to put them in and they go, oh, this doesn't fit here, this doesn't fit here, they're bang. And then they put one in the right place, they're like, oh, that fit in. They get all excited, they laugh, they clap and then they grab another one. Oh, this doesn't fit in there. They put it in the right place and quickly they figure out that the holes are just place holders for things you need to put in their place, right? Well, what's cos two x equal to? Cos two x is equal to three over five. So three over five is really cos two x. So you're just gonna go three over five is equal to one minus two sine squared x, right? That's what it is. If that's the case, then isolate sine x because you're trying to find out what sine of x is, right? Okay, grab the one, bring it over. So this becomes three over five minus one is equal to negative two sine squared x. Three over five minus one, common denominator is five so you're gonna go five. So this becomes negative two over five is equal to negative two sine squared x. Multiply everything by negative one over two or divide by negative two, right? So you're gonna divide by negative two because you're trying to get to sine x divide by negative two. So you got negative two over five divided by negative two which is negative two over five times negative one over two. Two kills two, negative becomes negative. So this is one over five, right? I'm just doing the speedy ones all this here that way we can just save space and write it down here. Okay. So negative two over five divided by negative two is just one over five, okay? I'll use these numbers in future. Other than mathematics, what is a very important school subject that is just as important as math? Okay, English, learn your natural language well, okay? So if you do this, you end up getting with one over five is equal to sine squared x. If that's the case, sine squared x just means sine x brackets all squared. So to isolate sine x, just square root both sides. So you square root both sides, okay? If you square both sides, you get sine x is equal to plus or minus one over square root of five because square root of one is just one, okay? Is that clear? I'm gonna erase, what am I gonna erase? I'm gonna erase the whole thing and I'm gonna write this up here, okay? So we have space. If you need to take a snapshot of this, take a snapshot of this, okay? Let's stop. Okay, awesome, me too. Hold on, go ahead. If you really want it, you could also derive the formula without memorization using linear algebra. Since cos two x can be thought of as two successive linear transformations, dice power that rotate our square by the angle. Oh dude, that becomes too complicated even for me, dice power. Yes, it's clear? Okay. Let's see if I pass college after this. Nice. Okay, I'm taking this down. So we got sine x is equal to plus or minus one over root five, right? So let's take all of these down. Sine x plus or minus one over root five. So sine x, sine x is equal to plus or minus one over square root of five. Right? Okay. So what are we gonna do now? We need to find tan of x, right? How are you gonna find tan of x? Do you know? There's multiple ways you could do it. Gosh, I never used one of the identities poop. There's multiple ways you could do it, right? You could look it up again. You could go back to your triangle to try to find out the tan of x. Should we do that? Let's do that, right? Here, here's a triangle. This is the easiest way to do it, by the way. Put your angle anywhere you want. That's your angle x, right? Dice power. Linear algebra was the key to me finally memorizing trig identities like the sine x plus identity for example. Was it masquerade even? I never memorized them. I always look it up. X, sine is opposite over hypotenuse, right? So opposite one over square root of five. Now we're only gonna use the positives because we're not gonna use the negatives, right? The answer for tan x, you're gonna have positive and negative as well, okay? But this is what we're gonna do right now. So tan, if you wanna find tan of x, you need opposite over adjacent. But we don't have the adjacent. So we need to figure out the adjacent. So we're gonna use Pythagorean theorem. A squared plus B squared is equal to C squared. Let's call this B, right? So one squared plus B squared is equal to square root of five squared, right? God, that writing looks horrendous. Square root of five squared, square root of five squared, right? So one squared is just one. Square root of five squared is just five. So B squared is equal to five minus one. So B squared is equal to four, square root both sides. So B is equal to plus or minus two, right? So this is equal to plus or minus two, but we're not gonna use the negative because we're gonna use the positive, right? We can't have negative length, right? So this is two. Well, that means tan of x is gonna be one over two. But because we have positive and negative, it's gonna be positive and negative. Okay, that's one way you could do it. It should be anyway positive and negative. Now, here's another way we could do it. We could use identities again. Okay, so let me erase those. What was the other identity we have? The other identity we have two cos squared x minus one. Let me just confirm it. Two cos squared x minus one, two cos squared x minus one, two cos squared x minus one, okay, cool. So we've got two cos squared x minus one, right? So the other identity we had was this. Cos two x is equal to three over five. Well, the double angle identity says this. Cos of two x is equal to two cos squared x minus one. Again, put your placeholders in. We're doing trig right now. Atomic, cryotomic, masquerade even. He gave it domain so we can get rid of the plus minus of it. Oh, really, he gave it domain. I didn't see the domain. Thanks, masquerade. Yeah, if you're given a domain, sort of a, I always like to call the range, but if you give it a sort of a range domain of where the answer could be, which is basically, you can think about as a unit circle, then you just eliminate whatever doesn't fit in there, right? For this, we're trying to get, we're gonna try to solve for cos x, because cos x is related to sine x tan x, right? The domain is, oh, okay, cool, cool. Three pi over two, let me write this down somewhere. Do, do, do, do, do, do. Okay, I'm gonna write it down here. The domain is three pi over two, three pi over two. Oh, two x is less than, okay, so two x greater than that and two pi, two pi, oh, two pi, which is really x has to be between three pi over four and pi, right? If that's the case, can you see that four down? Yeah, if that's the case, then you're gonna use, oh, I need the space here. So we'll deal with this afterwards, right? So again, you're gonna do the same thing. Cos two x is this, so this subs in here. So three over five is equal to two cos squared x minus one. Bring the one over, right? You're gonna get three over five plus one. We can do it on the side. Three over five plus one is the same thing as plus five over five, so that's eight over five, right? So this becomes eight over five is equal to two cos squared x divided by two becomes four over five is equal to cos squared x, square root both sides. So you're gonna get cos x is equal to plus and minus two over root five. You're okay with that? I hope so, does that make sense? I'm just square rooting both sides, square root of four is two, square root of five is just square root of five, okay? So what we have now is cos x is plus or minus two over root five. So I'm gonna erase this guy here. Let's put that guy up there. Cos x, cos x is equal to plus or minus two over square root of five. Okay, I only do game programming, my mind's been blown. I'm gonna erase these. Watch this. What's another definition of tan that we have? Tan is opposite over j-cent, tan x is opposite over j-cent. But it's also equal to sine over cos. Exactly, Miro, sine over cos. I just, I'm just amazed at how clean. Here, white keeps the water. It's, the trick is these guys, these things that they sell, these are garbage. Really, they're just brutal. Just get one of these rags that you get when cleaning cars. Fantastic. This one, I need to renew this, but it's still pretty good. So tan is also sine x over cos x. Well, we know what sine x is. Sine x is one over root five. What's cos x? We know what cos x is. Cos x is two over root five, ha-ha, right? You're amazed so you can buy a portable. So all you gotta do is sub this end for sine, sub this end for cos. Forget about the plus and minus for now, it's just gonna be plus or minus. Shop towels, is that what they're called? 10 bucks for 100, 10 bucks for 100 shop towels. That's amazing. The only reason I have this, by the way, the only reason I have this is because I had a salon with multiple, multiple markers and it was cheaper to buy one with the eraser than buy one without the eraser. So sine x is, I'm just gonna say one over square root of five divided by two over the square root of five. Well, when you're dividing a fraction in a fraction, we'll write this more clearly so it's not so messy. So you see it. One over square root of five divided by two over the square root of five. If you're doing a division fraction over fraction, just go sideways, square root of five divided by two over the square root of five and then you just flip it, right? So one over square root of five times square root of five over two, square root of five kills square root of five, you got one over two. So 10x is one over two. Hey, that's exactly what we got before. That's the same answer. Cool. If it wasn't, we were in deep trouble. G. Joe's mouth sucks. But it's not. You got one over two, one over two, perfect. So 10x is one over two plus or minus. Well, right now let's say plus and minus one over two. We're gonna look at the domain, right? I'll show you what the domain is all about. Wow, thanks, G. Joe. It's good to have someone like you doing these times. During these times, I appreciate it. My pleasure, man. Wow, I'm amazed. Chaos remains. Hello, hello. We actually do trigonometry at second year of high school where I am from. I have found the best way to remember the number is with the unit circle, unit circle. That's exactly what we're about to deal with. Right now, right? Let me show you the domain of this thing and the unit circle, 100%. Yeah, and by the way, I got a whole playlist of trigonometry. Let me give you guys a link for the trigonometry playlist. Trig, trig, trig, I love trig. And trigonometry is ridiculously important, right? So here's the trig playlist. And this was going to be the first module that I was gonna put out for mathematics. But I think it's the adding, subtracting one that we're gonna work on to bring that out. But the trig one I created, and I go through talking about the unit circle and it's like six hours worth of content there and I really get into the details of what it is that we're doing. But for now, let's deal with this, right? So we have the answers that we need, right? So I'm gonna erase all of this. I'm gonna erase this and I'm gonna do the unit circle here. Okay. Kill this, kill this, kill this, kill this. Kill this, kill this, kill this, kill this. Kill this, kill this, kill this. Plus or minus. Plus or minus one over two, right? So plus or minus one over two. It feels way better doing it here than doing this back in school in the classroom. I like this, good, good. Now take a look at this thing. The domain is this. Let me write down the domain here. Three pi over two, two x greater than three pi over two but less than two pi, right? Now we wanna find out what the domain is for x, right? Not two x. So all you gotta do is just divide everything by two. So really what you end up getting is three pi over four x and pi. Now what does that mean, right? That is your unit circle. Your unit circle, this is your x-axis, this is your y-axis. Well, that's gonna call it x and y because x we're using as the angle. So this coordinate here for unit circle is one and zero. This coordinate is zero and one. This coordinate is negative one and zero. This coordinate is, what am I doing, zero and negative one, right? So when they say you're going from, if it was this one, three over two pi and two pi, two pi is referring to this, the angle. So that's a full circle from there to three pi over two. Pi over two is 90 degrees. So you're going from here to here. So this is the region we're looking at, right? We're in the fourth quadrant. I'm not Sherlock. I only keep in my head, what is useful, but I might have to get a romantic understanding of this map and you might need what do you call him, his assistant, Watson. You need a Watson with you, our God. Exactly the same for me. If you know the best quarters numbers, then you know all the degrees. If you know the first, the first, yeah. If you know the numbers here, you know everything else, right? But they want the answer here, right? Actually, this is three pi over four. Three pi over four, so we're actually over here, right? Because pi over four is 45 degrees. So three of them, we're going boop, boop, boop. So we're actually talking about this range for X, okay? So you gotta figure out which quadrants you're in. If it was this case for two X, but the answer was supposed to be X, right? The unit circle is the most useful thing all the way through calculus. Yeah, agreed, okay? So what you gotta do is just say, okay, when here, everything's positive. In here, cos is negative. In here, sin is negative. Here, cos is negative, sin is negative. In here, what's negative? Tan is negative. Tan is negative, right? Agreed, agreed? No, sin is, no, what am I doing? I'm doing sin is positive, cos is tan. Oh my God, I got this backwards. I never remember this. I don't do it, I do it according to what's sin. I'm trying to do the, all students take calculus. I'm trying to do that, but I don't do that. I usually say the X axis is cos theta. The Y axis is sin theta. So sin is negative here, in here, cos is negative here, in here, right? And tan is positive here, positive here, negative here, negative here, right? So that's the way I do it. Cos and sin is negative on the third. Yeah, it's negative on the third. My apologies for that, by the way. I'm trying to do it the way they teach in school, but I get confused the way they teach it in school. So when you're doing this thing, what were we doing? We're looking, if you're looking for two X, then you're in this zone, right? If this was the domain, two X have to be within there. You're in this quadrant, okay? So you would take, the cos would have to be positive. So for this one, cos X would have to be positive. The answer for this would be cos X would be two over root five. The sin would be the negative one. Sin would be negative one over five. And the tan would be the negative one, which would be negative one over two. If you're in this quadrant, in this zone, then the sin, well, let's do the cos first. The cos X would be the negative, negative two over root five. The sin X would be the positive, which would be one over root five, and the tan would again be the negative. If I understood the question properly, anyway. But they shouldn't give you the domain for two X. They should say for X, right? Also, there's a tan axis, which is parallel to Y prime, and it passes through one zero. That's usual. My pleasure, Miro. I've never done the tan axis, actually. I probably did it at university, but I forget. I forget about it. Good question, good question. And Mask of Raven, thank you for answering, providing the answers for him, for Miro. I like, I like, good stuff. Mathematics, can't go wrong with mathematics, right? Great conversations. Very much related to much of our society, right? Very much related to much of our society. Good, we did one sort of simple mathematics, the basic stuff, adding, subtracting. We didn't do multiply. Oh, I was gonna do multiply to poop on the number line. I forgot the multiplication example. Oh, that's okay. We have the videos out there for it, so that's fine, right? So we did just the basic operations and one trig, which is good. By the way, Miro, what grade are you in that you're dealing with this? In my part of the world, this would be more, if you're lucky, you get in grade 11. You're not lucky, you get in grade 12. So, oh, you're in college. Okay, you're in the States then, yeah? States or Canada? So your college must be the exam time, must be now, I think. Pretty sure. Pretty sure it should be around now. I am from the US, okay? My teacher told me the coronavirus cases are going up like a logarithmic function. Possibly. Possibly. We'll see. They were initially exponential, right? So, if they're going up exponentially, and what does it mean by logarithmic function? Yeah, politics, thanks, Elder God. Oh, thank God. It's following logistic growth, actually. Logistic growth, I think logistic growth is this guy, isn't it? Isn't logistic growth this thing? Just basically the S? I'm gonna look it up. Logistic growth. Logistic growth, logistic growth. Logistic growth. Yeah, it's the S one, cool. Yeah, it's the S one, awesome. Logistic growth. It is, it is, yeah. It's S curve, right? Initially, many places were this, right? Hopefully it's going down, the growth rate anyway, right? And lockdowns are being released, right? We can interact more. Hopefully we don't see it going up less again. So hopefully we don't get this, right? Hopefully we get, maybe I'll do a little thing, but hopefully we get that. Hopefully it will be like logistic growth. It's looking more like exponential growth at the moment. Some places, some places, and that's the kicker, right? Like we have to, with any type of system, right? I'm trying to use my words well enough so we don't end all the realm of politics because we don't wanna be there, right? Depending on which system we're looking at, we're gonna see different things happening. All places I've seen have been completely the logistic curve. Might be a second bump, we'll see, might be, yeah. Yeah, from the looks of it, it's all, some people are a little delayed, right? Some places, obviously we've had this, but then if this is your timeline, right? Time, right? Some places didn't see the growth first, some places saw this, some places saw, boop, banged it right away, right? But it's all the same, basically. It's, and it's not necessarily this that was important, it's how the healthcare system within a society is able to handle the pressures being loaded on it, right? It's the load that matters, the abilities of the healthcare system to scale up, right? Any places that are running on bare bones, they weren't, any curve was gonna be devastating for them. Fun math, we did good math today. Good math, good math on a chill Sunday. Awesome, awesome, awesome, awesome, awesome. And tomorrow we're gonna do technology, I think. Yeah, I would say something here, but it would become a political discussion, so yeah, let's continue with math, let's continue with math, let's continue with math. I think we've done enough politics for a while. We're gonna, what are we doing? I'm just looking up our schedule. We've got two more, we've got stream tomorrow and next day as well, but I forgot, what are we doing? Oh, we're doing tomorrow, oh, tomorrow we're doing politics. Oops, okay, save the politics for tomorrow again. Tomorrow's 7 p.m. PDT, my time, we're doing politics and on Tuesday we're doing technology. I thought I skipped politics this session, but I didn't, I guess. So tomorrow, 7 p.m. to 9 p.m., we're doing politics and on Tuesday from 3 p.m. to 5.30 p.m. and all of a PST time, PDT time, PST time, my time, Pacific West Coast, Canada, United States, we're gonna do technology. Some tech talk tomorrow? No, tech talk is on Tuesday, my apologies. Tomorrow is economics. I wanna mainly focus on the economics. Economics is crucial right now, right? I have some pending math write-ups on Discord I've been trying to work on. Oh, did you, did you load those on? Spider-Man, so excited. I'll be there regardless. Nice, nice grand prix. Hi, professor. I wouldn't call myself a professor, no. Professor of comics? No, I wouldn't call myself a professor of comics. Professor, I'm well versed in certain things. So could you maybe show some examples of statistics and probability? I mean, that's huge. What examples will we be looking at? You can look at the dice, probably distribution of dice. I like dice, I got a video out there on dice. Let me show you the probability distribution of dice. That one's fun. Chichu dice. Let's see if it pops up. There you go. I gotta load this one on YouTube and it shoots as well. Here's the video for the probability distribution of dice. Yeah, that is the most common one. That would be cool. Okay, cool, let's do that. Not yet. Soon ones regarding logistic growth, goal and ratio, and maybe one more if I remember. Okay, cool. So here's dice, right? And we're talking about not one die, but we're talking about two dice, two dice, right? So the numbers that you can get on dice go from when you're rolling two dice, six-sided die, is two to 12, right? So I'm just gonna put the numbers here. Two, three, four, five, six, seven, eight, nine, 10, 11, 12. So three, four, five, six, seven, eight, nine, 10, 11, 12. Okay. Now, let's look at two. What's the probability of rolling a two? Well, if you're rolling two dice, right? Here's the two dice. To be able to roll two dice, is it like a bump in the middle? It's a bump in the middle, right? But you should look at it. Check this out. If you're rolling two dice, right? What's here? Let me draw this as if it's dice and then we're not gonna do that again, right? You need a one here and a one here to get a two, right? Well, what's the probability of rolling a one on the first die? It's one out of six, right? You need to roll a one, right? On the second die, you also need to roll a one. So it's one out of six. So the probability of rolling a two with two six-dided dice, you multiply them. One out of 36, not two out of 12, okay? The less you roll, the closer it gets to the normal distribution, yeah. So this becomes one out of 36, okay? So how many different ways can you roll two? One. This is, what do we call the y-axis? We call it, I love this math, I love this math, too. I did a unit once on the statistics of Dungeons and Dragons, great project. I'd like to see some of that. Oh, grand, that would be amazing, right? So there's only one way method. Let's call this method, method. So one way of getting two, right? You have to, it's one out of 36, right? The probability of rolling a three, there is, you need to get a one and a two. Now, we're not concerned about the second roll, right? On the first dice, you can get a one or you can roll a two. So you can roll a one out, one on the first die or two on the first die and still have the chance to get a three. So there's two ways, two out of six things you can roll on the first die and still make it, make a three. But if you roll a one on the first die, you only have one thing that you can roll on the second die to make it a three. It has to be a two. So there's only one out of six on the second die, right? So on the first die, you have two probabilities, two options to roll. But on the second die, you have to get that appropriate roll to make a three, right? So on the first die, you can get a one and then you have to get a two on the second die or on the first die, you can get a two but then you have to roll a one on the second die. So your choices for the second die are always gonna be one out of six because we're gonna count the choices to be on the first dice, right? On the second dice, it's one out of six. So the probability of this is two out of 36, okay? So there's two different ways you can roll a three. Two ways you can roll a three. The probability of rolling a four, right? You could get a one on the first die and then you have to get a three on the second die. You could get a two on the first die and you would have to get a two on the second die or you could get a three on the first die and you have to get a one on the second die. So the probability or the choices you have on the first die is three out of six, right? But on the second die, it's one out of six. So the probability of this is three out of 36. Probability of five, you got four choices, right? You could get a one, two, three or a four on the first die and then you have to get the, you have no choice. You have to match, not match but get whatever it is you need to make a five total. So there's only one out of six on this one. So there's four out of 36 for a five. Probability of a six, you can get a one, two, three, four, five on the first die. I've got a question for you, Chichu. You and I are going to roll dice, highest number wins. You have two choices, a 12-sided die or a 10-sided die. However, if you pick the 10-sided die, you win, you win ties. Which tie would you pick? You win ties. Oh, you win ties. Oh, I don't know. I would have to think about that. Oh, my God. Not Aligarh, Graham. And Aligarh, I once calculated the probability of me getting, oh my God, I stopped him for four days after this. I started laughing, I didn't finish reading it. I'm not just saying it, just speaking it out. So five out of six, right? And to get a six, there's five ways to make a six on the first die as long as you get the appropriate number of second die, right? So you have five choices on the first die and one choice on the second die. So there's five out of six. And the probability of seven, you can get any number on the first die. So six out of six, right? On the second die, you have to get whatever it is to make a seven. So if you get a one on the first die, you need a six on the second die. So your options are limited on the second die based on what you get on the first die, right? So this would be five and then six. So five, oops, and then six for seven. And then you're symmetrical. That's the beauty of dice. So you go step down. So eight is the same as six. Nine is the same as four. 10 is the same as, what do you call it? 10 is the same as four, nine is the same as five. 11 is the same as three and 12 is the same as two. That's a probability distribution of dice. Isn't it five out of 36 there? For which one? Oh, five out of 36, thank you very much. Thank you very much. If I make mistakes, please let me know. Okay, I appreciate it. Thanks, Mega. Yes, he missed the three. I missed the three. It's back. Not really, but I just realized my boots were made in the Dominican. I was wondering why they were so comfortable. Dominican cigars are good too, but Cubans are better. Okay, that's the probability distribution of two six sided die. As for Graham's question, you have two choices, a 12 sided die or a 10 sided die. However, if you pick the 10 sided die, you win ties. So where it gets the higher die? So if I pick the 10 sided die, you could still pick the 12, right? Good question. My instinct says I would pick the 12 sided die. One, 10, correct. I'll use what you don't pick. Same rules apply. I use what you don't pick. Okay, so one person here, let's check this out. Let's see what the answer is. So does the graph repeat for three, three dice, four and more? Does the graph, can you do radiance? Oh, we just did some trig. Skodos, here's my trigonometry playlist. Check this out. This is my trigonometry playlist. And I've put together an extensive stuff on trigonometry. Okay, and I deal with the radiance. If you know the preliminary stuff, you can skip over some of the initial stuff. I have an exam in a week. Dude, you wanna learn radiance? Check out the trig videos I put out in that playlist. The ASMR ones, okay. Here, let me find the radiance one. Radiance and degrees, how they're related. So fourth video down here. I'll give you the link to the specific video, but I think we talked about radiance a little earlier on, okay. But this playlist is fantastic. It's like, seriously, I'll toot my own horn, but it's the best explanation playlist course that is available to learn trigonometry. And I'm only halfway through, okay. I still haven't got to identities and graphing them in detail and looking at work problems. So, you know, there's still more work to be done, but there's like six hours of content there. It's nice and chill, and once you're finished that thing, the ASMR ones, you should have a pretty good understanding of what a unicircle is and what trigonometry is and what radiance are and all that jazz. And I show a few tricks of how to calculate things pretty easy. Not tricks, but how the cemetery works, okay. If you have questions, send me a message. It should help you out. I'm gonna take this down. Let's talk about the grams problem. Let's check it out. As for the question you asked, is it same for three dyes and four dyes? There will be cemetery there, for sure, but I don't know, I haven't grafted out. I don't know what it would be, right. So we have a 12-sided die here, and we've got a 10-sided die here, right. Question is, we're playing a game. Whoever gets the higher role wins, okay. Yeah, I learned about all that stuff in class, but isn't, it's in Dutch. Love the conspiracy theory of some of our fine-scram free. I wish I had good professors and teachers throughout my education, because I feel I could have been more interested in math a bit earlier. Yeah, mega, me too, right. I think everybody wishes that. We call the, circle over there. Oh, and what do you call it? The unit circle? In, in Henssegoel, man. Dutch is a hard language, right. And if you roll the 10-sided die, you always want to die when a tie. Yeah, and you win ties here. Tie, win, right. So we have 12. How will we calculate this? How will we calculate this? Maybe the three dice one applies for six times three, and the middle would be nine. Wild guess. Middle would be 20, 21, because all of them would be sixes, right? Three times six. Oh, sorry, three times. Yeah, it would be, the middle one would be, not 21. Oh, the middle one, what would the middle one be? The highest one would be 18. The middle would be nine, possibly. Think three dice and 11 have equal chances. I will take the dice. So how would we end up doing this? How would we do this? I think one of the first things we would have to calculate is, what are the probabilities of you getting the same roll? Right? That would have to come into play. Getting the same roll for this one would be, how will we go about this? This is all combinatorics permutations, and I'm horrendous at combinatorics permutations. This was an extra credit question I asked my sophomores. I had some figured out, I'm sure you can do it. Ha ha ha, pressure on, how much time do we got? In four minutes. If we pick 12 sided die, the probability of rolling two times, same number is two out of 12. Or no, two out of 24. Would there not be more chances to tie rather than landing on 11 or 12 and 12, on the 12 sided die? Possibly, that might be the best way to approach this actually. I got the answer. And the answer. And take the, the 12 sided, that's the one you take. You might have to extend your stream to do this once you try. Oh, love loba, how are you doing? Ha ha ha, awesome. How will we do this? I mean, this one has, I like, what do you call it? Pope's comment, what's the probability of landing on 11 or 12? And there's two of them there, right? So two out of 12, we're guaranteed a win because we get 11 or 12, right? Rule number 11 or rule number 12. The 10 sided die for me, thanks. That's what Elder God says. Kind of, he riskily, he riskily, he riskily though. And twice on Sunday, first find the chance of a tie up to 10. Yeah, what's the chance of a tie? The chance of a tie would be one out of 10, wouldn't it? Would that be it? Chance of a tie, one out of 10. No, what's the chance of a tie? What would the probability of a tie be? One out of 12, you get a one, one out of 10. Two out of, no, still one out of 12. So one out of 12, one out of 12, 12, 120. Okay, how do we calculate chance with 10% chance, is it? No, it's not, because this is 12. We gotta take into consideration rolling out 11 and a 12. Winner, winner, chicken dinner. Winner, winner, chicken dinner. I personally would pick the 12. However, actually one way you could do it this way as well, check this out. You could logically do it this way and this way you would pick the 10, right? You could say this, right? There is the number 11 and the number 12 give you an automatic win on this, right? So you have two chances of automatically winning on if you pick the 12-sided tie, right? However, there are 10 possibilities if you tie, you win with the 10-sided tie. So I would take the 10. I would take the 10. Assume D10 is N and go from there maybe, maybe. I'll give the answer if you want the industry. Oh, I always want the answer, Graham. You're asking the wrong guy. Just want to let you know that I really appreciate and respect you spending your time on helping others. Keep it up, we'll do. Thank you very much. Bob Ross, Bob Ross, totally real, Bob Ross, totally real. Thank you for popping onto our stream, right? I mean, the less side of the die, the more chances it ties, right? 10 for me. I would pick 10 because guaranteed win on this one is only two choices, right? Guaranteed win on this one, there's 10 of them, right? What's the question? You're rolling two die, right? You have a chance, you have a choice to pick the 12-sided die or 10-sided die, okay? Whoever gets the higher number wins, but if you pick the 10-sided die, if you tie, you win, right? Ready for that chicken dinner? Oh, wait, I didn't take into account that a tie results in a re-roll. Is it a re-roll? No, it's a win, mask of Raven. I think a tie is a win. Okay, spoiler warning, Graham, I want the answer. Anybody that doesn't want the answer, you should jump off the stream now. So I had a student work out every permutation. That's the kicker, that's what I was going for, but that's too much. Permutation resulted in figuring out the percentage chance of winning based on every permutation. You have two more chances to win if you pick the 12. Oh, really? Yeah, it should be a win. So the 12 is better. So is it just as simple as picking these two? Not really, but it's got to be the permutations. There's got to be a quicker way of doing this, Graham. It's simple math, actually. Oh, my God, hilarious. 12 is technically better, yeah. Those are the two chances right there on the board. So that's it, it's as simple as this, but a tie, you win with the 10. It's in the ties, it must be in the ties. Well, you do have two more chances to win, but isn't the chance of getting a tie in general lower? Yeah, I guess that's what the question would be. That would be an amazing way to do it, philotype. Figure out what the probability of getting a 11 or 12 out of 12 would be two out of 12, right? That's your probability, percentage, whatever that turns out to, right? And then you have to figure out what the probability is of getting a tie, right? That's it, and whichever one, so probability of getting a tie, tie, right? And whichever probability is more is the better chance, better die, no, you're free to promote, I don't want to pick up the permutations. Nevermind then, I'm right anyway. I'm right anyway, ah, Mask of Raven. If you roll only once, the 12 is the way to go. Gicho overtime, Gicho overtime, overtime. Okay, we call, we call. I'm horrible at math over Twitch, chat. I make too many slips, oh dude, Mask of Raven, I know how you feel. Pick 12 and think, if I roll one, I can win with nine different numbers, but if I pick 10, he rolls, I can win with one number. My second probability, it was a great question, Graham. Fantastic question, difficult, difficult, but great question. Okay, gang, let's call the stream. Thank you very much for being here. Super fun, fantastic to do, fantastic to do. I'm going to go roll sometimes, nice. If you like this work that we're doing, gang, I'm on Patreon. If you want to support this work, Patreon is a fantastic way to support this work. Okay, you can also follow, I don't put anything behind paywalls, and you can just follow what we're doing over time. And after a while, if you do feel like supporting this work, Patreon is a fantastic way to support this work. By the way, gang, on Twitch, thank you very much for the follows and the subs if you're following and subbing. And if you want to participate in the discussions here that we're having, because I'm going to be uploading this to YouTube and BitShoot, Twitch is where you want to be at. Okay, have a great rest of the day. Say you guys as well. Have a great day, everyone, for sure. I do announce these streams on Twitter, Gavs, Minds, VK, and Aloe 30 minutes before we go live. And I do announce other things that we are doing on those platforms as well, as well as Patreon, of course, right? I am uploading audio of the content that we're creating, a lot of the content that we're creating on SoundCloud now. Okay, I'm uploading the open discussions we're having on SoundCloud. I'm not doing the mathematics because mathematics, we need the visual, right? So anything that doesn't require visuals, we're going to upload the audios to SoundCloud. I'm also going to go through my previous library of 900 plus videos that we have on YouTube. At least 400 of those, 500 of those are with a lapel mic. 500, I don't know how many there are. 500 of those lapel mic. I've had requests to upload the audios because people just want to listen to the discussion and whatnot. I'm going to start uploading those audios to SoundCloud. It's going to take us at least until the end of this year to do it. Next few months, maybe longer. Okay, so if you want to get some audio of readings and discussions and other things, SoundCloud, you can join there as well. And I am uploading the videos to YouTube and BitShoot. Everything goes to BitShoot as long as the processing is done, no technical glitches. And most things going on to YouTube as long as it can go past the sensors, the filters, right? And if you are on YouTube, joining YouTube membership is a fantastic way to support this project as well. Okay, aside from that, I'll try to do this as well. Aside from that, how will they go, keep politics to politics? Aside from that, again, thank you very much for being here. Mauds, thank you for taking care of business. Thank you for helping people out if they had math questions. Thank you for coming here with your math questions. Thank you for participating in the discussions. And I hope you guys have a fantastic, fantastic Sunday. And we'll talk tomorrow. Economics, more economics related stuff really than politics and current events, but current events is economics. Okay, tomorrow night, 7 p.m. PDT. And on Tuesday, 3.30 p.m., I believe, we're gonna talk about technology. Nice, nice, nice. Bye everyone. Hope you guys have a fantastic rest of your weekend.