I'm Zor. Welcome to Unizor Education. I'd like to present the problem on the topic of complex numbers. It will be problem number two, actually. Here it is. It's related to graphical, geometrical representation of complex numbers on the plane. So let's consider you have a unit circle and a complex number on it. a plus vi, and it's on the unit circle. It means that a squared plus b squared is equal to one. This is a squared. This is a, and this is b. So a squared plus b squared is equal to one. So that's what it means that it's on the unit circle. Now, let's assume I'm considering a square of this number. The problem which I would like to present is the following. The square of this number is also on the unit circle, and these two angles are exactly the same. So basically to square the number which has a representation sitting on the unit circle, you just have to basically use the same angle which it has with an x-axis and just double it basically. So the angle between this radius and the x-circle is exactly double from the angle between this radius and the x-circle. So this point is a plus vi squared. So that's the problem. Two parts begin. One part is that the square belongs to the same unit circle. Second part is that the angle doubles. Alright, let's prove the first part. That's the easy. Since the distance between two different points which represent complex numbers is basically a modular of their difference. Well, this is zero, so it's a modular of the number itself. Let's find what's the modular of a plus vi. Obviously, we'll use the fact that a squared plus b squared is equal to one. So what's the modular of a plus vi? A plus vi squared. We need to know the modular of this number. Well, let's just do the calculations. Square is a squared plus b squared i squared and i squared is minus one. So it's minus b squared according to the rules of multiplication of complex numbers. So this is the real part of our new complex number. And our imaginary part will be ab to abi. Okay? What's the modular of this? The modular is the square of the real part plus the square of the imaginary part. Right? Well, this is not the modular. This is actually a square of the modular. So if I will prove that the square of the modular is the same one, that's the same as modular is equal to one. But now, what is this expression? Well, that's very easy. It's a to the fourth minus two a squared b squared plus b to the fourth plus four a squared b squared which is equal to a to the fourth minus two a squared b squared plus four a squared b squared. So it's plus two a squared b squared plus b to the fourth. And obviously you have recognized that this is a squared plus b squared which is equal to one because a squared plus b squared is equal to one. That's the condition, initial condition that we were using our initial point. So proof that the square of our complex number which belongs to the unit circle also belongs to the unit circle. That's easy. Okay? That's the first part. I want to explicitly ask you to press the pause button before I start solving, proving this particular thing. Well, I forgot actually. Now you can press it because if you want, the most important part of this problem is number two actually, that the angle is doubled. So before I start this continuation of this problem, solving this problem, those of you who would like to try their own and I do suggest you do that, press the pause button and think about this yourself. But I will continue now with proving the second part of this problem that the angle doubles when I'm squaring a complex number. This is a little bit more involved but anyway, here it goes. I hope you did press the pause button. Okay. Let's consider these two segments. This, by the way, is one because it's a unit circle. This is also one. Now, obviously, since we are on the unit circle, so all these right radias are exactly the same and equal to one, if I will prove that this segment has the same length as this segment, that will prove that my angles are the same. So the total angle from x-axis to my new square complex number is double. So the only thing which I would like to prove is that this distance is equal to this distance. Now, as you remember, the distance between two points on the plane can be actually solved using called algebraic methods of complex numbers. That's the beauty of it. So I will use the complex number which represents this point, this point, and this point. I'll take their complex numbers difference and the lengths of the corresponding segments will be a modular of differences. All right. So the only thing which I have to do is basically just do a bunch of tedious calculations and I do have to tell that this is a little bit lengthy and tedious. It's simple. It's just plain multiplication and addition and subtraction of numbers, but well, you've got to do it and that would prove our problem, our theorem. All right. So first of all, let me express this a plus bi square as a more traditional complex number, which basically I was using before. It's a square minus b square. That's the real part and complex and a imaginary part is this. That's exactly what I was using to prove that this segment is equal to one. I just took the module of this and turned out to be a square plus b square squared, which is one. Okay. So this is traditional notation for this particular point. Now, at this point, we already have this notation a plus bi. How about this point? Well, this point obviously is real part is one. Imaginary part is zero. That's what we have for this point. So the distance from this to this should be equal to distance from this to this using a square plus b square is equal to one as a condition. Well, let's just put all these four conditions again on the board so I will have some free space. So a square plus b square is equal to one. That's one of the conditions. Now, my three points are point number one is a square minus b square plus two a bi. My second point is a plus bi. And my third point is one plus zero. From this time on, we do not really need any geometry. We will just use pure algebra. Okay. Now, let's frame this as a condition. Now, the distance from this to this. Well, you have to basically make this difference which is a square minus b square minus a as a real part. And plus two a bi minus b as imaginary part. That's one number. That's the difference between these guys. Now, the difference between these guys is a minus one and b minus zero i. So it's a minus one. That's the real part. And b minus zero. Well, that's just a b. Now, the parentheses i. That's the difference between these points. So what do I have to prove? That the module of this guy is equal to the module of this guy. Right. Okay. Now, we will wipe out again what we don't really need. With that, we need this condition. And all we need to do right now is what's the module of this calculated by square of this plus square of this? What's the module of this? Square of this plus square of this. And compare them, they should be exactly the same. All right. So this is my a, and this is my b. Two complex numbers. Module of a, I'll use two vertical bars just to signify the module. It's equal to, I will probably put this b somewhere here. Module of a, square of this plus square of this. Yeah, that's tedious, but anyway. a square minus b square minus a times a square minus b square minus a. That's the square of this guy. Now, square of that is, well, I can do it right now. It's four a square b square minus four a b square plus b square. Square of this number, which is this, minus double this times this, which is this, and plus this. Okay. Equal. Now, we have to multiply these. All right. Let's first multiply a square by each of those guys. We will have a to the fourth minus a square b square minus a cube.  And the third one is minus a. So it's minus a cube plus a b square plus a square.  Okay. That's my overall expression. Well, it's a little long, but, well, what can you do? Just to make things simpler, we can do the following. Look at this. a to the fourth plus four a square b square plus b to the fourth. This obviously is a square plus b square square. But a square plus b square is one. So the combination of this, this and this gives me one because it's a one square, which is one. Again, a square plus b square square is a to the fourth plus four a square b square plus, well, actually, I'm sorry, that's not exactly true. That should include this as well. Minus two a square b square and minus, because minus a b square a square b square and minus a square b square and plus four a a square b square. All together is two plus two a square b square. And that's what gives me one. Because a square plus b square square will be a to the fourth plus two a square b square, which is this, this and this. Minus one minus one plus four. So it's two a square b square and b to the fourth. So that's one. Okay. I told you it's a little tedious and not very interesting. Anyway, what else do we have here? Okay. Okay. What can we do here? All right. So minus a cube remains. The last thing we can do about this. Now a b square. Oh, there's another minus a cube. Okay. So we will put two a cube here, two a cube. So we covered this guy and this guy. Okay. Great.  So it's minus two a b square. So we covered this, we covered this, and we covered this. What's remaining? a square and b square, which are together again equal to one. So we have another one. So instead of that, I will put two here. That's what we have, right? Now this can be simplified even further. So this is two minus two a and in parentheses a square plus b square. Right? If I a, bring it outside of the parentheses minus a cube and minus two a b square, which is equal to, again, as we know, a square plus b square is one. So it's two minus two a. So you see, such a very big and complex, complex in terms of complexity, not complex numbers.  So that's my module of the difference between square of the complex number and complex number itself, original. Okay. So let's just put it somewhere here. I don't need this. I can just write the answer. Two minus two a. Very nice, very simple, etc. Okay, great. Now b, what's the module of the difference between our original complex number and the point on the circle which lies on the x-axis. Remember? So this is a and this is b. So this is the length which I am trying to establish right now, which is modular of the number b, which is square of this plus square of this, a square minus two a plus one plus b square equals, again, we all know that a square plus b square is one and another one, so it's two minus two a. As you see, they are equal, which basically proves the point. Whenever you square this number, which is represented by a point on the unit circle, you just have to double the angle from this number to the x-axis. So this is two alpha. That proves the point. Thank you very much.


Hi everyone, Joe for jaspyscasebreaks.com, coming at you with 2022 Panini Capstone Baseball. One box, random team number 56 with eight diamond dozen spots being given away. The last filler is up. Once we do that, we can unlock that diamond dozen break. This break also part of the promo that ends on Tuesday night. Check out the details on jaspyscasebreaks.com. Big thanks to this group right here for making it happen, appreciate you. All teams are in, let's roll it, randomized names and teams, snake eyes, two times different dice roll for the giveaway part. One and two, and then snake eyes for the teams. One and two, easy. All right, there's the no trade windows, but here's the first half of the list. All right there, second half of the list right over here. Let's alphabetize print and rip. All right, here's the print out, hot off the presses. Thanks everyone for making this break happen, appreciate you. And at the end we'll re-randomize everybody's names, see who ends up in the diamond dozen. And there it is, New Jersey advances. They win the game seven beating New York Rangers. Let's go to Sun's Nuggets, how's it going there? Yeah, Denver, up by two, seven, 50 left in the first half. We've got a Julio Rodriguez rookie card for Seattle. That's gonna go to Scott. We've got a Shohei Otani two-color dual relic. Nice, that'll be for Chad and the Angels. Oh, I wish I saw your comment just now, Mike, but unfortunately Alexi Lafreniere did not have the stage of one-man comeback for the Rangers, which would most likely improve his stock greatly. Hobby-wise, we'll have to try again next year. There's Matt Veerling to 35. This is an artist-proof card for the Phillies, who are actually playing my Dodgers tonight. And you have to switch between this Nuggets game and the Dodgers game. Looks like Dodgers are up for nothing. And the top of the third is Ryan Vallad. For the Rockies, that's 18 out of 25. Tristan with Colorado. Another Julio Rodriguez, that's Redfoyle this time. We've got a blue steel, Vlad Guerrero Jr. That might be a shorter printed insert, maybe. Another Julio goes to Scott. This goes to Denny and the Blue Jays. Here's a Christian Pashé, it's like an autograph. It is. A's edition, going to Tristan. You got Seth Beer, dual relic for Denny and the Diamondbacks. Mmm, beer. And that, my friends, is that. All right, not a bad break. Now, let's see who's gonna get into, what are we giving away here? Oh, Diamond Dozen spot. So let's flip back over to this list. Let's gather everybody's names one through 30. New dice, new list. And it will be the top eight after eight, two and a six. Good luck. One, two, three, four, five, six, seven, and eighth and final time. So from nine on down, it's gonna be sad times for the moment. Sad times for Chad, very close, but just not quite. Nine through 30, thank you very much for giving it a shot, appreciate you. Top eight, you're in the Diamond Doesn't Break. Chad, you're in. Dennis, you're in. So as Nick, Dennis again, Darren, Chad, Dennis, and James. Congrats to the top eight after eight. We'll see you next time for the next one.


What's going on everybody Ryan Williams here from fan duel here to talk about the week nine DFS studs in the Weekly edition of the fan duel hurry up got three plays for you that we can target for our Sunday main slate lineups Without further ado, let's get into it Starting off at the quarterback position as we always do got to talk about Lamar Jackson this week He's eighty three hundred dollars and when you're talking about the quarterbacks that are priced around him Hopefully his ownership doesn't come in that high. We're looking at you know, Patrick with Holmes who's been struggling Josh Allen who is in a great matchup against Jacksonville But maybe you're hoping that they put this game out of reach and and Josh Allen doesn't get there You also got Aaron Rogers popping up on the COVID list Kyler Murray dealing with an injury. So not a lot inspiring at the top of the pool. So let's just go with the Safe option here. I think a lot of people might think of Lamar for a floor The game before the buy was very disappointing against the Chargers and we expected fireworks to be having that game We didn't get them But now he's coming off the buy and he does get a Minnesota defense where the numbers have been good against the opposing quarterbacks But you're looking at the past four quarterbacks They face Cooper Rush Sam Darnold Jared Goff and Baker Mayfield that doesn't leave much to be desired there So I think the Lamar Jackson sets up in a prime spot here You love that he is passing the ball Very well, he's leading the leading the league in a dot as it comes to it He's top five in yards per attempt in passing having one of his best career Years as far as passing goes with yards per attempt and this Minnesota defense does give up some big chunk plays Now they do like to get pressure on the quarterback and we know Lamar is not good When he's faced with pressure or faced with the Blitz But they are going to be missing Daniel Hunter on the Minnesota defense So that should maybe help alleviate some of those concerns and I really like again Just the floor that you're getting with Lamar here But I do think he's got upside here as Minnesota does tend to give up some chunk plays and we know that Lamar Jackson's not not afraid to either take it himself or throw it deep You also love here too just a little tidbit that Lamar Jackson versus the NFC has been pretty successful in his career He's 11 and oh against the NFC conference in his career and the Ravens are averaging 28 points per game in those 11 games as well too So that's that's also something to keep in mind when you're targeting Lamar Jackson this week moving over to the running back position I'm going to talk about Austin Eckler here now. He comes in at a $9,000 price tag For the fan dual slate, which doesn't make you Doesn't make you feel good to pay that price for Austin Eckler, but we love what we're seeing out of him I mean just last week we saw 75 percent Seize a share 75 percent of the share of the backfield and that was with him dealing with a hip injury last week Pretty much all week. We weren't even sure if he was going to play until late late on saturday there with the news breaking You love that This eagles defense has given up a ton of points to opposing backs They're allowing the sixth most rushing yards and the fifth most rushing touchdowns to opposing backs This is a favorable game total and this might you know with the price tag being high And you're thinking about last week with Deandre Swift and what should have been a smash spot He didn't get there that game was kind of put out of reach with the eagles running up the score So if this is you know, again now we get a good game environment here If this game is close, Austin Eckler is definitely going to be involved And I definitely love getting him into my lineups this week. Finally, let's talk about wide receiver here And it's going to be tie re kill for me. This is the second time I believe that tie re kill has made it into the fan dual dfs studs video And and we got to go back to the well again You absolutely love his target share that he is seeing on the team right now Not sure what's going on with travis kelsey if he's got some ailments or or something there But it's tie re kill or bust and for the past five games tie re kill has seen 12 or more targets The yards haven't been there. He hasn't gotten 100 yards. I believe in in quite some time Over the past couple weeks, but he's just been so explosive and you're looking at a green bay team That's not going to have air and rogers on the other side. They're going to have jordan love. Maybe that helps keep tie re uh hills ownership percent down if people are kind of getting off that game We've already seen a huge decrease in that game total It opened up at I believe 55 points and now it's already dropped down to 48 48 and a half on the fan dual sports book, so This is a game where I think people are going to be a little bit wary on and and I want to get explosive plays in my dfs lineup You're looking at wide receivers that have faced this green bay team and terry mclauren won for 70 122 and one chase went for Six 159 and one deontay johnson 992 and one and then deandre hopkins last week before he got hurt. He saw two for 62 or 66 So there's a lot of room for tie re kill to just explode in this game Get right spot for the chief's thief or for the chief's offense here Against this green bay defense at home. You got to love that if it wasn't for cooper cup We'd definitely be talking more about tie re kill absolutely love this play here love all the plays this week And uh, these are the guys who i'm going to be getting into my lineups. That's going to do it for week Nines dfs studs here on the fan dual hurry up again ryan williams You can follow me on twitter at ryan alexander underscore w make sure you guys are subscribing To our youtube channel for all of the fan dual content that we got to bring and you give us a thumbs up on the videos We we much appreciate that see you guys next week for the week 10 dfs studs until then get that money


I had planned to record other videos this weekend and do other projects but I saw something yesterday that I wanted to stop and tell you about. I watched Under the Skin, a 2013 science fiction movie starring Scarlett Johansson, which I had heard about in passing a couple of times. A few weeks ago I downloaded a handful of these films that I had been reading about and Under the Skin was among them and last night I sat down to watch the first few minutes of it to see what it was about, see if it would be something that I would want to sit through and I ended up sitting through the whole thing. I couldn't take my eyes off of it. I'll tell you before I go any further that I am recommending this film as strongly as I can. I'll also tell you that it's not going to be for everybody. There are people who are going to find it too disturbing. It is a horror film. It is a real horror film. It is not a splatter film or a startle film like we've come to think of horror films today. Every scene in this film is disturbing in one way or another and they're disturbing in different ways. I'll also say before I go any further that if you're taking my recommendation seriously, don't read anything about the film first. Don't even read the Wikipedia description and certainly don't read about the novel. It is based on a novel. Just go get the film and sit down and watch it. This movie is unlike anything I've seen recently. It is actual cinema. It is actually the art of film. It is a very carefully crafted visual and audio experience. The first line of dialogue in the film happens 14 minutes in. I was watching the clock. And even then what little dialogue is happening is just another part of the audio-visual scenery. I noticed at about half an hour into the film that I had not heard one single sentence of plot advancing dialogue. There was not a single conversation that actually advanced the story or the plot. Everything was about watching the film. This was not just a radio play in which the director filmed the actors having their conversations, which is what most movies are. You can actually watch most movies without actually looking at the TV or at the movie screen. You can work while you're watching movies and experience them just fine. This film, you have to shut up and glue your eyes to the screen and watch the movie. The only thing I'll tell you is that Scarlett Johansson is killing men. That's clear from the very first scene. That's what she does. It's clear what she's doing. It is not clear why she's doing it and it's not clear how she's doing it. It's left up to you to watch the film and in some ways just decide for yourself what you're actually seeing. There aren't any questions that are answered for you. I don't like it when people compare films to 2001 and Space Odyssey, but I'm going to do it here.  Earlier that same day I had actually watched some of 2001 and Space Odyssey and if you're familiar with that film and with much of Kubrick's work, there's a great deal of silence in his films in which it's left up to you to watch the screen and absorb what's happening rather than have things explained to you. That's what's happening in this film. In fact, the entire film is that way. You need to watch the film and abandon any need to have everything explained to you and just experience the awfulness. I feel like this film had a lot to say about the experience of being human, in particular about the experience of being a human woman. People who have been victims of assault, particularly victims of rape, may not be able to stand sitting through this film and I would certainly understand that. For those of us who have not had those kinds of unfortunate experiences, I think we could learn from watching this. I feel like I saw something important, something that I could learn from, not just a film. Having said that, I don't believe I'll be watching this film again. I could see myself showing it to someone else and watching it with them, but sitting down myself, no. Although I do think there's a great deal to learn about filmmaking from watching this, especially how to tell a story without having your actors just gabbing the whole time. After seeing the film, I went onto Wikipedia and read a synopsis of the novel and just the first sentence of the synopsis told me more detail about what was happening than I could have imagined for myself from the film. So this was a proper cinematic interpretation of a novel. It doesn't try to reproduce the novel. So if you haven't figured it out yet, I recommend Under the Skin. I recommend that you get a copy of it, that you not learn anything about it before watching it, and that you sit down in a quiet place and a quiet time and absorb this film. And if you have trouble tolerating it, don't feel guilty, just stop. Maybe come back to it later. At the very least, I guarantee you've not seen anything like this before. And that by itself is always worth something.


Have you ever pondered over what the future holds for cryptocurrencies or more specifically the potential of SUI? If you haven't, it's about time you did. The world of finance is rapidly evolving and cryptocurrencies are taking center stage in this revolution. Among the myriad of digital coins available, SUI stands out for its unique features and promising prospects. SUI, a cryptocurrency operating on a smart contract platform, is maintained by a permissionless group of validators. Its native token, SUI, is not only a means of payment for gas fees, but can also be staked for potential rewards. One of SUI's remarkable traits is its ability to achieve parallel agreement on independent transactions, thus enhancing scalability. SUI has made significant strides in the decentralized finance, or DeFi space, surpassing $300 million in total value locked and bridging over $100 million in USDC. This success is a testament to its scalability and transaction processing speed, attracting leading protocols to its platform. In the next few minutes, we will delve into the world of SUI, its unique features and its potential in the crypto market. So what exactly is SUI and how does it stand out among the vast sea of cryptocurrencies? To begin, SUI is a member of the ever-expanding family of digital currencies, known as cryptocurrencies. But it's not just another run-of-the-mill digital coin. SUI is a unique cryptocurrency that operates on a smart contract platform.  Imagine a traditional contract, but without the need for intermediaries. Smart contracts are self-executing contracts with the terms of the agreement directly written into code. The SUI platform is maintained by a permissionless group of validators, meaning anyone who meets certain criteria can participate in the network's maintenance. This decentralized approach to network management is a fundamental principle of blockchain technology and cryptocurrencies, ensuring that no single entity has control over the entire network. But what role does the SUI token play in all this? While SUI serves as a means of payment for gas fees, gas fees are essentially the cost of executing a transaction or a contract on a blockchain network. They ensure that the network continues to function smoothly by incentivizing validators to process transactions. Moreover, SUI tokens can be staked, which is a process where users participate in the network's operations by locking up their tokens for a certain period. In return, they can potentially earn rewards adding another layer of utility and incentive for holding SUI tokens. Another notable feature of SUI is its scalability. Scalability in the context of blockchain refers to the ability of the network to handle a large number of transactions. SUI achieves this by reaching parallel agreement on independent transactions, a feature that sets it apart from many other cryptocurrencies. In essence, SUI presents a robust and scalable platform in the crypto market. But what truly sets it apart is its unique features. What makes SUI a game changer in the crypto market? A compelling question indeed and the answer lies in its unique and innovative features. One of the most distinctive features of SUI is its ability to achieve parallel agreement on independent transactions. But what does that mean in layman's terms? Well, it simply means SUI can process multiple transactions simultaneously, independent of each other. This is a significant departure from the traditional sequential method of processing transactions which often leads to bottlenecks and delays. This is where the magic happens. By leveraging this parallel agreement feature, SUI achieves enhanced scalability. In the fast paced world of crypto, scalability is key. It allows for a higher volume of transactions to be processed in less time, making the entire system more efficient and reliable. Think about it this way. If each transaction were a car on a highway, traditional crypto platforms are akin to single lane roads where each car must wait for the one in front to move before it can proceed. On the other hand, SUI is like a multi-lane highway where multiple cars can move forward at the same time. The result? A smoother, faster journey for all. This parallel agreement feature isn't just a fancy buzzword, it has a real tangible impact on the performance of the SUI platform. It increases transaction speed, reduces congestion, and ultimately leads to a better user experience. SUI's unique feature set doesn't stop there. The platform has also demonstrated its versatility by attracting leading protocols and has even ventured into the world of Web3 gaming through a partnership with Space and Time. This highlights SUI's commitment to staying at the forefront of the crypto space, continually innovating and adapting to the needs of its users. With such remarkable features, it's no surprise that SUI is making waves in the crypto market. But what does the future hold for this cryptocurrency? Given its unique features and market position, what could be the potential future of SUI? SUI has been making waves in the decentralized finance, or DeFi space, achieving some notable milestones that position it well for the future. The platform has surpassed $300 million in total value locked or TVL and bridged over $100 million in USDC. This is a testament to the trust and confidence that users have in the SUI platform. But SUI is not just about achieving milestones, it's also about creating partnerships that drive growth and expand its ecosystem. One of these partnerships is with Web3 security firms. By teaming up with these firms, SUI is ensuring the security of its platform a critical factor in the world of DeFi. This not only gives users peace of mind but also reinforces the credibility and reliability of the SUI platform. In addition to partnering with security firms, SUI has also launched a grants initiative. This initiative is designed to support and encourage the growth of its DeFi ecosystem. It's a strategic move that signals SUI's commitment to nurturing innovative projects and ideas within its platform and lets not overlook SUI's partnership with Space and Time, a move that opens up new avenues for SUI in the realm of Web3 gaming. By providing advanced tools for Web3 gaming, SUI is expanding its reach beyond just finance, tapping into the exciting and rapidly growing world of blockchain gaming. So as we look to the future, it's clear that SUI is not resting on its laurels. It's forging ahead, making strategic moves and positioning itself as a versatile player in the DeFi and Web3 space. It's this dynamism coupled with its unique features like parallel agreement on independent transactions for enhanced scalability that makes the future seem bright for SUI. The future seems bright for SUI with its continuous growth, strategic partnerships, and potential for scalability. So to sum it all up, we've dived into the intriguing world of SUI, a cryptocurrency that operates on a smart contract platform maintained by a permissionless group of validators. We've explored its unique features, such as its ability to achieve parallel agreement on independent transactions, leading to enhanced scalability. This cryptocurrency, with its native token SUI, serves as a means of payment for gas fees and can be staked for potential rewards. We've seen how SUI has reached significant milestones in the DeFi space, surpassing $300 million in total value, locked and bridging over $100 million in USDC. SUI's partnerships with Web3 security firms and its launch of a grants initiative to support the growth of its DeFi ecosystem highlight its commitment to innovation and security. Moreover, its collaboration with Space and Time to provide advanced tools for Web3 gaming underscores SUI's forward thinking approach. With its current standing and future potential, SUI is showing signs of being a strong contender in the cryptocurrency market. As we continue to navigate the ever-evolving world of cryptocurrencies, SUI certainly stands as a beacon of potential and innovation.


If the Prophet Muhammad ﷺ plagiarized the Bible, which is the standard Qur'anic, the standard Afwan, the standard Orientalist trope that he plagiarized the Bible in the Qur'an, then they say this even to this day. Why didn't he copy these problems? How did he know to make this adjustment to the narrative? How did the Prophet ﷺ in quotes know that the rulers of Egypt at the time of use of alaihi salam were called muluk? They were called kings, not pharaohs. The ruler at the time of Musa alaihi salam was called Fir'an, was called Pharaoh. The Qur'an is correct historically. The book of Genesis gets it wrong. Why didn't the Prophet ﷺ call the ruler? Why didn't the Prophet again in quotes call the ruler of Egypt at the time of use of alaihi salam a pharaoh like the Bible did? How did he know to make this adjustment to the narrative? How did he know to avoid this anachronism? It's called anachronism. There are linguistic subtleties in the Qur'an that the Prophet ﷺ could not have known. Allah ﷻ says The name Zatariya in Hebrew means the mention of the Lord. This is what his name Zatariya in Hebrew means the mention of the Lord. So this verse is a play on words. The mention of the mercy of your Lord to his servant, the mention of the Lord. There's this beautiful subtle symmetry in this one ayah. The author of this ayah, new Hebrew. There's no doubt about it. If a Jew living in the Hijaz heard this verse, his ears would perk up. He would notice the subtlety. Another example. The wife of Ibrahim ﷺ, she laughed and then we gave her glad tidings of Isaac. Isaac means laughter. And then it says And then following Isaac, Jacob. The name Isaac means laughter in Hebrew. The name Jacob means to follow or to come after. This is a type of word play that adds to the eloquence and brilliance of the Qur'an. Whoever composed this verse, new Hebrew. Of course we know this is a revelation from Allah ﷻ. I'll give you another example. There's hundreds and hundreds, if not thousands of these types of examples. Now Yahya is John, John the Baptist. These be upon him, most probably. The Qur'an calls him Yahya. Meaning he lives because he was martyred. And the martyrs are alive. They're alive with their Lord, receiving sustenance from their Lord. But the Hebrew name of John is Yohanan, which is related to This is the only occurrence of this word in the entire Qur'an. And it's describing Yahya ﷺ because it actually relates to his historical name. These are subtleties that go over the head of 99% of the Qur'an's readers. The author of the Qur'an is playing with these languages in a masterful way. Now we also believe in miracles. Musa, alaihi salam, performed many miracles. The idnillah and secular historians do not consider miracles when determining what happened in history. That's part of our iman bil ghayb, right? Because the past is ghayb. We don't have access to it. We can't reproduce these things. Our belief in miracles is not irrational, nor is it falsifiable. It is based upon our belief in Allah swt. And we can argue rationally that this universe had a designer and a creator. And that this creator is personal. This is why there is something rather than nothing. This is a big philosophical conundrum for these philosophers. Why is there something rather than nothing? This creator who brought this universe into existence from nothing has power over every atom in the universe. Miracles are easy for him. But this is a philosophical argument. This is a theological argument. But from a standpoint of history, the Qur'an's narratives avoid the historical pitfalls of the biblical narrative.


In the Christian Bible, Malachi is the last of the prophets in the final book of the first Testament.  The temple has been rebuilt, but there are still lots of problems. There is still poverty, a foreign ruler, drought, poor harvest and locus. They feel frustrated. They feel abandoned. Slowly their worship becomes half-hearted at best. What have we believed in, they wonder? And when they thought they were forgotten, God answered back. A messenger is coming. Restoration is happening.


Spring actually is still coming. It'll be here in a couple of weeks. But in the meantime, we have weather like this, and the roads really are dangerous. The House and the Senate sent everybody home at 11 o'clock this morning. I'm sending everybody home three hours early in the executive branch. But there's one group of people who are gonna be out working throughout the day and throughout the night, and that's these folks. And I just think we don't give them enough credit for what they do for us to keep our streets and roads as free of snow as possible. They're really doing a lot of work. And as you know, this has been a rough winter.


Welcome back to our lecture series Math 3130, Modern Geometries for Students at Southern Utah University. As usual, I'll be your professor today, Dr. Andrew Mistledine. At the end of lecture seven, which just as a reminder in lecture seven, we introduced the three parallel alternatives, the elliptic parallel postulate, the Euclidean parallel postulate, and the hyperbolic parallel postulate. The most famous of all of those three is certainly Euclidean parallel postulate. At the end of lecture seven, we define the idea of an affine geometry, which the definition is now here on the screen. An affine geometry was defined to be an incidence geometry which satisfies the Euclidean parallel postulate. So to be an incidence geometry, you satisfy the four axioms of incidence. We have line determination, which means for any pair of points, there exists a unique line determined by that pair. C can't see, which guarantees that every line has at least two distinct points on it. Point existence, which says there's at least three points in the geometry. Non-colinearity, which tells us that not all points lie on the same line. Again, those four axioms give us an incidence geometry. And then if we equip to the incidence axioms, one parallel axiom, particularly the Euclidean parallel postulate, this creates for us the idea of an affine geometry, which reminder, the Euclidean parallel postulate gives us the uniqueness of parallel lines. For any line, L, and any point P that's not on the line, there exists exactly one line parallel to L, which contains the point P right here. And so in this lecture I should say, because there'll be more than one video, we're gonna formalize the idea of affine geometry into an axiomatic system. And we're gonna see that the affine geometry's theorems that we'll do in this video in the next will generalize that of young geometry. Because we've seen affine geometries before, our so-called four-point geometry we introduced earlier in this lecture series is really the four-point affine geometry. And young geometry is really the nine-point affine geometry. And so many of the theorems we've proved about four-point and young geometry will be identical and some will generalize it, of course. So the first one here, we saw this when we studied young geometry here. We called it Proclus Lema. And I gave it a name then because really this was a general theorem for all of affine geometry. And I wanna make mention that affine geometry is a very important study of geometries. It's a very broad setting. After all, Euclidean geometry R2 is an affine geometry. Clearly there's more structure to Euclidean geometry than just the affine structure, incidence, and parallelism. But it's very important when we study Euclidean geometry we understand its affine structure. In fact, if one goes to linear algebra, linear algebra has tons of affine geometry all over the place. You use words like affine a lot. And when you talk about linear algebra, affine transformations, affine spans, affine combinations. Because honestly, if you take any field, which of course a field for those who might not have the abstract algebra background, this is a collection of numbers for which we can add to track multiple and divide. And those operations follow the usual rules such as associativity, commutivity, distributive laws. We have identities, we have inverses, all that stuff. So if you have a field, if you take the square of a field you can actually make an affine plane with it. And so essentially every two dimensional vector space is an affine plane and in higher dimensions as well are affine geometries as well. But of course in this lecture series we'll look only at planar geometry. And so in particular, if your field is a finite field you can get finite affine geometries. Our four point geometry is a result by taking the field of two elements and squaring it. Young's geometry can actually be given a coordinate system by taking the field of three elements and squaring that as well. So again, just want you to be aware that this affine geometry can be found everywhere. So back to Proclas Lima. I'll restate it because there's a good chance we don't remember it when we studied Young's geometry here but this is a theorem of any affine geometry. Suppose we have lines L, M and N and let's suppose that L is parallel to M and that M intersects in. Then we claim that L intersects in right here. And so we need to prove we're gonna prove this one right here. That is, if these two lines are parallel and those two lines intersect then we guarantee that these two lines intersect. And this is gonna lead directly to our transitivity parallelism which we're gonna do in just a second. So this proof is gonna be identical. I want you to compare it. Maybe you have notes on this but this is gonna be identical to our proof we did for Proclas Lima in Young's geometry. There is no part of the proof that we have to change because essentially the proof only comes from really Euclidean parallel posh. So there is of course one important exception here but let's start the proof here. Let P be the point of intersection between M and N. So of course we know by assumption that M and N intersect each other. So let me draw a sketch of that. So we have our two lines M, M, M and N. Excuse me, we're gonna label them. We'll call this one M, we'll call this one N and by assumption they intersect each other. So let's call that point P. We claim that this point of intersection is unique. This is a theorem of incidence geometry but now that I've written it I wonder do we even need uniqueness there? We'll see it in just a moment. Well, we know that in an M are parallel to, or intersect each other, excuse me. We know that L and M are parallel. That's what I of course was trying to say. So let's add L to our diagram right here. Let's label it L. So we know that L and M are parallel but N and M intersect at the point P. So we need to prove that L and N intersect each other. So we're gonna do this by proof by contradiction. Let's suppose that L is parallel to N. And so that's what we're gonna do here by way of contradiction. We're gonna assume that L is parallel to N, right? Why is that a problem here? Well, notice here that we have the line L like so. And we have the point P, which we know that P is not on L. How do we know that? Well, P is on M and L and M are parallel. So P can't be on L. So we have a line and we have a point not on the line by the Euclidean parallel postulate. I want you to be aware of that. Then there should be a unique line parallel to L that passes through P. But we have them count them one and two. That's a violation of the Euclidean parallel postulate. So we get a contradiction there, which then means we must get the opposite of what we assumed. So we're gonna get that L is not parallel to N, which means L and N intersect each other. So this theorem follows really just from the Euclidean parallel postulate. Like I said, why we do have uniqueness in the intersection, we never actually needed that. It was a theorem of instance geometry. We mentioned it also for Young's geometry, but really it's a superfluous fact. All that matters here is the Euclidean parallel postulate. If the assumptions of Proclus lima were satisfied but the conclusion was not, then we would have multiple parallel lines, which is in violation of the Euclidean parallel postulate. So this is a theorem for any affine geometry because it really just needs the Euclidean parallel postulate, which Young geometry satisfied, four point geometry satisfied and thus general affine geometry satisfies Proclus lima. In fact, I'm not gonna prove this in this video. You can actually prove that N incidence geometry, Proclus lima is logically equivalent to the Euclidean parallel postulate, although EPP is what we will assume as the axiom and we prove Proclus lima from it. Related to this is the transitivity of parallelism that I referenced earlier, right? This is something we explicitly proved for Young geometry, but the proof there is transferable immediately to affine geometry. We don't have to change the proof whatsoever because this is a generalization of Young geometry. This is generalization of four point geometry just affine geometry. We have the four incidence axioms, we have Euclidean parallel postulate, that's all we need. Now transitivity of parallelism, remember this tells us that if two lines are parallel to the same line, they're parallel to each other. So we're trying to prove something like the following. If L is parallel to M and if let's say L is parallel to N, then we have that M is parallel to N. Now to write transitivity, we typically have to write this a little bit differently. We might say something like this, let's swap these elements right there. So we'd say that M is parallel to L and then L is parallel to N, then M is parallel to N. That's how transitivity of the relation is typically written. Now because parallelism is a symmetric relationship always you can swap the order of that, no big deal. And also by construction, parallelism is a reflexive relation. So if a parallelism is a, if it's a equivalence relation depends entirely on whether it's transitive and it turns out it'll be transitive only in affine geometry. Transitivity of parallelism is also something logically equivalent to the Euclidean parallel postulate inside of incidence geometry. We will prove it as a consequence of Proclus lima. Now, how do we do that? Well, let's take the assumptions here. Let's assume that M and N are both parallel to the line L like we have assumed right here. And then let's suppose the contradiction there approved by contradiction, we'll say not M parallel to N. So let's say they intersect each other. So let's draw our picture. Well, our picture is gonna look exactly like we saw a moment ago. Since M and N intersect each other, they would cross like that. L is parallel to both of them like so. And so what's happening here? We have our M, we have our N, we have our L. We see that because L and M are parallel and because M and N intersect each other then Proclus lima applies which with our numbering system that was 148 that then gives us that L and M must intersect which then contradicts the assumption here. So if we didn't have transitivity of parallelism we would contradict Proclus lima which is already been established. So therefore M and M have to be parallel to each other. That's an important consequence here. So look at these theorems here, the Proclus lima, transitivity of parallelism. These are the exact same proofs we used with Young's geometry because it was really a theorem affine geometry. We didn't have to change the proof whatsoever. Now in some situations, well basically this, everything that's true about affine geometry must be true for Young's geometry. It must be true for four point geometry because those are affine geometries. But there are some theorems that will be more, will be more specific to those geometries. Like for example, Young's geometry only has nine points. Every line in Young geometry has three points. Now that theorem won't be true for every affine geometry because in four point geometry lines only had two points. But what we can do is generalize those theorems to any affine geometry. So like we observed, four point geometry, every line had two points. For Young geometry, every line had three points. In general affine geometry, we can generalize that principle to the following. All lines contain the same number of points, which of course in four point geometry that number was always two. In Young geometry, that number was always three. This happens in general. And this is actually a very beautiful proof. One of the most important proofs I'd say for affine geometry, that all lines contain the same number of points. All right, so what we're gonna do to prove this is we have to take two arbitrary lines. So we're gonna take two lines, L and M. And what we're gonna then do is then prove, since these two lines were chosen arbitrarily, we're gonna prove that these lines have the exact same number of points. We can do that by establishing a bijection between the points on L with the points on M. A bijection is gonna be a one-to-one onto map, an injective and surjective map. This will establish a one-to-one correspondence between the points of L and M, which then will say that the set of points on L, compared to the set of points on M is the same number. This will even apply if we have an infinite number of points. So if one line has a cannibly many points, then the other line has to also have cannably many and one line has uncannable many points, then the other one also has to be uncannable. This even applies to infinite sets as well. So how are we gonna do this? Well, we have to take a starter point. So the line L has some point on it, we're gonna call that point P. It doesn't matter which point you choose, but by secance theme we know it has at least one point. Likewise, there has to be a point on M. And I should also mention that this point P is not on M, okay? Because it could be possible that L and M actually intersect each other. We don't claim that they're parallel lines, right? It could be that they intersect each other, but intersections and incidence geometry are unique. So there's only one point of intersection between the two lines if there's even one. Maybe they are parallel lines. But by secance theme there's a second point, then that second point can't be on both lines. So we do know we have a point on L that's not on M. And likewise, there has to be a point Q on M that's not on P by the same reasoning. So we have a point on one line, but not the other and on one line out the other. So we have these two points P and Q. So so far, of course, how we've done this, we've used secance to get two points online. We use line determination to guarantee that the intersection of lines is unique. We're gonna use line determination again, because we're going to form the line that connects P and Q. Now let me draw that again. Connect the lines P and Q.  Like so, it's the line uniquely determined by P and Q. Then for each point on L, and I'm gonna write this as an X right at the moment, because I want you to think of this as a variable, right? Because for every point on L, it's called X, and we don't know how many points there could be on L here. Like in four point jumps there's only two points and young there's three. But in Euclidean geometry, we're gonna have uncountably many points. These are all affine geometries, doesn't matter. Just take, consider any other point on L. By the Euclidean parallel postulate, there exists a unique line that's parallel to n that passes through X. And so consider that line for a moment here. The unique parallel line that contains X that is parallel to n. Let me make it look a little bit more parallel, at least parallel in the Euclidean sense. So we get something like that. We're gonna call this line n sub X. This is a line parallel to n, but passes through the point X, all right? Such a line is guaranteed as, by the Euclidean parallel postulate, it's the only one there is. And I should mention that it will, the line nX will intersect L, but that intersection will be unique. And so the only point that's shared between nX and L is gonna be this point X, okay? So now when you look at this over here, my diagram seems to suggest that the line nX should intersect M. But how do we know that? The thing is we're not drawing a picture of Euclidean geometry, although my diagram looks Euclidean at the moment. How do I know this intersection actually exists? Because when we draw a four point geometry, after all, we draw it like this and we have four points, one, two, three, four. And while there's an intersection in the diagram, that intersection actually has no point there. How do we not know we have the similar thing going on here? It's just, it's a misinformation from the diagram or something like that. Well, we have to have an argument here. There is in fact a point of intersection here and this follows by Proclus lima because notice what we have here. Whoops. We have that the lines nX and n are parallel to each other. We have that n and L intersect each other. Excuse me, that's not the one we wanna do. We have that n and m intersect each other. The direction I was going would show that L and nX intersect, but you already know that. But let's see, nX and n are parallel, but n and m intersect. Then by Proclus lima, we have to then have that nX intersects M somewhere. We are gonna call that point Y sub X like so. So there's some point of intersection and again as intersections are unique, there's only one point on nX and on M. And so we can in an unambiguous manner identify this point as YX. And notice we gave it the subscript Y sub X. And the reason we're doing that is we're connecting a point on L to this point Y sub X right there. So there's an identification going on. In all reality, this is going to be a function relationship. So we've established a function from the points on L to the points on M and it follows the rule that X is going to map to Y sub X by this construction. I'll note of course that if you take F of P, this is identified with the point Q because there's a unique line parallel to n that passes through P and that's n itself because n is considered parallel to itself. So just you're aware Q is the point Y sub P. I've always continued to call it Q right here. So we have this identification and I want you to be aware this is a well-defined map because given any point here, there's only one point on M it's gonna be identified to. And likewise, it's also going to be a one to one map. If you take any two points over here, there's only one X, I guess what I'm trying to say, if you take different Y coordinates, you're gonna have two different lines parallel to n associated to it. And so just give you two different X coordinates. It's gonna be a one to one map. It's also onto, how do I know it's onto? Well, we can kind of work the other way around, right? If we take the line n and we take any point on M then by EPP there's a line parallel to n that contains that point. By Proclas Lima, that point will intersect here somewhere on L and then that point will map to the starter point. So this map is in fact, bijective. You can also construct the inverse of this map by working backwards. Notice we started with points on X. We could have started points on M, excuse me, we started points X on L. We could have started with points on M and worked backwards. It has an inverse, that also proves it's a bijection. So that's the important thing here. This map, F, is in fact a bijection. It's one to one and onto. Which means that the cardinality of the domain is equal to the cardinality of the co-domain. For which what do I mean by the cardinality of a line here? I'm talking about the points on the line. And so this establishes that the number of points on L is equal to the number of points on M. It's a nice, cute little argument but this is one of the most fundamental arguments for affine geometry. All lines have the exact same number of points. Young's geometry had three points per line. Four point geometry had two points per line. And we're gonna see in the next video what are the consequences of this very important observation.


Alright guys, welcome back. Let's get this ball bounce animation finished So if you've been sticking with this exercise so far what we've got is a ball that Starts in the air bounces down has a few bounces. It's got squash and stretch. It's got a nice weighty look to it So far so good, but to add a little bit more realism We're going to try and move this from one side of the screen to the other have a little bounce and then Roll to a nice stop. So we're going to put that on in place Right now what I'm going to do is I'm going to select this controller here Which is the one that's controlling the position of the ball and what I want to do is add another layer of animation to it Now there are different ways I could go about this, but my personal favorite, which I found quite neat It's to put it into a group and then animate the group and what that means is that I'm putting animation Onto something clean. So it's kind of like an an empty vessel that I can put keyframes into So I'm going to select this controller. I'm going to hit control and G on my keyboard And I'm just going to call this movement Just so that I can find it in my outliner if I ever need to And what that will allow me to do you can see there are no keyframes on here now But I can move the ball side to side kind of on a fresh timeline, which is How I prefer to work so Let's get this animation set up. So I'm going to go back into my side view And I want the ball to start currently where it is. So on frame one. I'm going to press Yes, and then a little bit later. Let's just expand the timeline a little bit. Let's go to about frame 30 I want it to be in the air actually About frame 33 I'm going to move the ball. I've got about 12 units to the right Now I'm going to set that keyframe and then I'm going to bounce it back. So I'm going to go Think in this case to about frame 60. So well after it stopped bouncing so it gives it time to roll I'm going to move it back not all of the way to about there. So now I'm about four units away from where I started Okay, so that's the base of the movement. Let's have a look how that is looking Okay, not bad, but it's picking up and losing speed at the wrong times And that again as it was with the bouncing is down to the way that the curves are working in the graph editor So let's sort that out So I'm going to go a window animation editors graph editor I'm then gonna just scale this bad boy up a little bit.  So this is that the problem When it hits the wall, which is here. It's this keyframe The line should be straight because it's hitting a solid surface So I'm gonna slap this keyframe and make the lid linear tendons there I'm also Gonna make this one linear to because I want to start off at constant speed and Then I just want to come to a more gradual halt than it currently is doing So I'm gonna start this keyframe here again. I'm gonna break me tangents Break those bad boys And then I'm just gonna smooth The curve out like that Now as you can see that's had a bit of a weird effect because now it's going to bounce off the wall faster um Than it originally came off the wall.  I'm just going to drag And then That'll allow me to just come to a more gradual stop and match the speed that I had before Okay, so hopefully that's going to look how I want it to look. So let's um Rewind that and have a look That's not bad. It is still bouncing off the wall a little quicker than I would perhaps have liked it to But overall I'm fairly happy with it um Yeah, I think I'm just going to remove this keyframe Because I don't know what it's doing and then just check that again Yeah, so I just think on this keyframe. I'm just going to move it back a bit I'm going to reset that See what we get Yeah, and we've got a nice little rollback animation as well so The reason we get that rollback animation Is a happy accident and it's because My curve has gone past the the original spot But that's kind of what you're looking for in a ball balance animation anyway So we're basically finished The one last thing I'm going to do you can follow me in this step if you want to or not I'm just going to put in Um a bit of geometry So that it looks like the ball's bouncing off it. So I'm just going to create a cube and move it over here And then I'm going to scale it up and it's just going to kind of represent a wall And there we go. I just need to now go into this view because it's not going to be thick enough in this direction There we go And then I'm just going to put it into edge mode Slap this bottom edge. I'm going to press control and E to extrude it Then I'm going to go straight into my move tool I'm going to pull that edge along just to make a bit of a flaw And put it back into object mode Okay, and now it'll look like it bounces off A wall. Hooray! Amazing.  I'm just going to make sure that is Connecting with the wall Isn't quite so I'm just going to reposition that That's pretty nice And there we go a ball bounce animation So hopefully that has given you everything you need to know It's a very sort of basic introduction to character animations So it introduces timing it introduces squash and stretch Introduces giving weight to a character in this case a ball And it also covers some useful tools in Maya such as the graph editor So that brings this exercise to an end Make sure that you subscribe if you want more exercises like this one And please like this video and any of the other steps that have helped you out If you've got any questions or you need any help then you can either email me or you can drop a comment below the video And the final thing I'd like to do in this video is thank you for watching and I'll see you in the next one


Welcome to the Welluck Way. I'm Jessica and today's video is our August Amazon haul. So today is the day when I share with you guys everything we purchased in the month of August. Let's get started with books. So the first book series that I grabbed were these rescue princess books. There are I have no clue how many in the series. I bought the first nine because there was like a package deal and I thought they were adorable because they are princesses and animals. And one of the princesses, I think it's this little redheaded one, is actually named Emily. So they were like perfect for Emily. So these will be independent reads for her. Next up we have Greta Eskridge's new book Adventuring Together. You guys, I pre-ordered this. I was so excited for it because I love Greta. Spoiler alert, I've already read it. And if you are a mama who wants to adventure together with your family and make family memories, I highly recommend grabbing this because it is amazing. I also picked up the Kingdom Keeper's books 1, 2, and 3. We are really missing Disney, like really missing Disney. So I don't know if we're gonna be doing these real lots yet. I'm gonna read the first one and see what I think. See if I think they're too advanced for Emily or too dark for her. But if they're not, we are definitely going to be reading these aloud and I'm really excited about it. The other book that I pre-ordered for myself this month is Awakening Wonder by Sally Clarkson. I have not had the chance to rip into this one yet, although I will soon. But if it is anything like Sally's other books, I know it is going to be amazing. In the last book I picked up in the month of August was the Home Learning Year by Year. This is the new updated and revised version. Actually, one of you guys let me know that there was a new updated and revised version, which I of course immediately added to cart because this is a book that I love. I plan with it every year. It is hands down one of my home school favorites. If you want to see more about how I use it for planning, you can do that right here. Now, I don't know if you guys remember or not, but in August there was a deal of the day that was on games and certain games were 48% off. So all of the games that I have purchased for the most part were part of that deal. So the first one we have is Word Waffle. This is a vocabulary game by Edgiprest. They actually have different grade levels. So this specific one is grade three. Mystic Market, EmuTep Dual. You guys know I'm always looking for great two-player games. Me and Emily often play games by ourselves. So when I saw that EmuTep Dual was on the sale, it was the first one I added to cart. I love two-player games that still give us that great game quality. This is Dungeon Drop. I have no idea anything about it. I just looked at it and it looked really, really fun and like something that our family would really enjoy. So I grabbed this for us to play. And then the last game I got was this Rock Me Archimedes. So it kind of looks to me like a kilter, mancala type thing. And we love those like critical thinking two-player games. So I thought me and Emily would really, really like this. I also grabbed these Learning Resource Angle Legs. These are actually really, really cool. Emily's already dug into them and then using them and she really enjoys them. They come with like this protractor type thing and then all of these little leg pieces that you can build different angles with. And in the Learning Resource fashion, they come with activity cards as well. So Emily has already been looking forward to Christmas and talking about what she wanted to like make because we make gifts for or she makes gifts for families and friends. And she mentioned that she wanted to make like bath bombs and bath salts and soaps and stuff. So I grabbed her this Thames and Cosmos cosmetic kit that does soaps, bath bombs, salt scrubs and more so that she can just kind of get a little bit of an idea of what it's like if she enjoys it and if it really is something that she wants to make on a larger scale for gifts. If you follow me on social media, you probably saw that over the past week, we've entered down to Clearwater to the Clearwater Marine Aquarium. Don't worry, a video about that is coming soon. But to prepare Emily for the trip and kind of let her know that we were heading there and to surprise her and to give her a little bit of education beforehand, I picked up the Winter's Tale book which is the true story of Winter's Tale. She is the Dolphin from the movie Dolphin Tale. And then the book Hope for Winter which is the Dolphin Tale 2. Dolphin and again this is the true story and I also got her the 4D vision model of the Dolphin Anatomy. We love these. I know they have mixed reviews. If you look at them on Amazon, Emily is eight. She's been doing them since she was seven. She loves them. There's been like one time that she got frustrated and I had to help her but other than that she does them completely independently. This is actually on Amazon. They were surprisingly a pack of three which was perfect for us. I bought two packs just in case we lost one that they are like really really thick soft cloth so that they're comfortable to wear on your face.  I also purchased myself a set of two. You guys the other one's already at my computer. Blue light glasses. So my prescription glasses when I purchased them does not have blue light on them and so as much work as I was doing at the computer and on screens it was really starting to bother my eyes so I just purchased a set of two blue light glasses because luckily my prescription and my vision is actually for far away so I can see at the computer pretty well. Like right now I just can't see like you know the camera screen over there if I didn't have my glasses on. So this was if you have kids or you yourself are doing a ton of work on screens I highly recommend them. I've noticed that my eyes have gotten a lot less tired than when I was wearing even just my prescription glasses that don't have that blue light block. The next three things I have to show you are technically homeschool but they were purchased for our first day of homeschool so I had to wait until Emily was like in another room so she couldn't hear me. So we have always done a first day of school gift for her and so this will be her first day of school gift from us. She will get this Harry Potter game called Spellcasters game. I thought it was super cute. It just has like these little spell cards and you use the wand to try to like draw the spell action in the air and then the other players have to guess what spell it is so it's just the kind of like charades Harry Potter style. So if you have not heard what my plan is for the next few years to slow the books down a little bit we are going to do one book and one unit from all of Wizards and Wands to start our school year every year to kind of kick it off. So this year we are starting well we're kind of restarting the book that we stopped with when COVID hit was Prisoner of Azkaban so we're going to pick that back up and kind of back up and start it over. Since we're doing Prisoner of Azkaban I went ahead and got her the Lego Knight Buzz as well as the Expecto Petronum Lego. So these both kind of go with that movie slash book and I thought it would be really fun for her to be able to build these while I was reading a lab and then have them to add to her set. And since there are some for each book we'll probably get her the remaining Legos as we do each book in future years. All right guys the very last thing I have you probably already saw over in the community tab and it is my brand new camera. I can't show you anything other than the box because I'm actually filming on it right now and I'm exterminating so please be patient with me as my videos are coming out over the next few weeks as I learn and tweak new things. But I did get the Canon 90D. It is kind of like the perfect photography camera and video camera at least I'm hoping so. So this was my big purchase for the month of August. All right you guys that's it for the August Amazon haul. Let me know in the comments down below what your biggest most frivolous or most interesting purchase was from Amazon in the month of August.


I'm a professor of infrastructure reliability and management at the Cyprus University of Technology. Structure and health monitoring is an important tool for the design and also for a proactive and smart approach to integrity management of structures and systems. This particular course section is significant in promoting the fusion of ideas, design, development and standardization as well as the uptake by practice of these techniques with significant potential benefits for industry.


Happiness always looks small while you hold it in your hands but let it go and you learn at once how big and precious it is. Maxim Gorky Happiness seems to elude us many times and we wonder what to do. If one could find a way to package and sell happiness in little bottles, such a person will make a lot of money. However, the person will also need to use the product as happiness is rare. If ever, stable in one's life, things come and go, the sun rises and sets, the years come and go, people are born and people die. And in all these, we find happiness, sorrow, joy, sadness and sometimes a mix of them all. To remain happy, there has to be a change of mindset and a shift from the practices which have promoted sadness in the past. Happiness is a state of mind which depends totally on the individual who seeks it. In the pursuit of happiness, one must look within and make deliberate decisions to be happy and then protect the newly found happiness with all they've got. In the ideal world, once happiness is found, the finder remains in that state perpetually, simply because it can't be lost but we live in a real world where everything tries to steal our joy. The question then is, how do we remain happy no matter the circumstances? How do we protect our happiness? There is no one right answer to these questions but there are tips on how you can work at it and below are 5 such tips. 1. Stop Trying Hard Edith Watten said, If only would stop trying to be happy, we would have a pretty good life. Some too many people are looking forward to being happy. They try to catch happiness and so they allow it elude them until they get to the point where they recognize it based on their definition. The truth about happiness is that you can find it wherever you are no matter what situation you find yourself. By trying too hard to be happy, by chasing all those things you think would make you happy, you miss out on being happy right now. Some people are chasing more money and so they miss out on watching their children grow or they miss out on having a loving relationship. Some are chasing fame and they miss out on the necessary genuine human connection which makes the world go round. Stop trying too hard to be happy. Chasing happiness won't make you happy, start living happily instead. 2. Stop Seeking the Next High One of the many reasons people get addicted to hard drugs is their search for euphoria. They yearn for the states where everything looks great and they are oblivious to the troubles in their lives. When the effect wears off, they take another dose if possible a higher one. The cycle continues and they are addicted. However, some people are addicted to getting high on other things which are not hard drugs in search of the same euphoria. For some, it is a new job. The novelty trail and challenge that comes with a new job makes these people be in the market for a new job continually. To some others, it is a relationship. They believe that a relationship will solve all your problems so they jump at every opportunity to be in a relationship no matter how abusive, premature, inappropriate or unnecessary it may be. Stop looking for the next thing to make you high on happiness but be grateful with what you have and make the best of it. Remember your happiness depends on you. 3. Stay in Control Each time you blame something, a situation or someone for your unhappiness, you hand over the reins of your life to the thing, the situation or the person. That is no way to leave. Assume responsibility, avoid the blame game and take charge of your life. Your life is yours to leave. It would be best if you didn't make a mess of it but it is yours all the same.  If you don't like a situation, get out of it. If you don't like something, do away with it. If you don't like the way you are being treated by someone, speak up and if they refuse to change, avoid them. The plan is to protect your happiness and preserve it. It is your life. Do not leave its happiness in the hands of others or any other thing. Decide to be happy and stay happy. 4. Take Action This tip is a follow up from Staying in Control. If you discover that something robs you of your happiness, you can complain about it or you can avoid it but none of these will make it go away and that means that you will remain in a state of unhappiness. If you know that there is something you can do to regain, maintain or preserve your happiness, get to it. Many times our unhappiness about a situation comes from a feeling of helplessness. If you can do something, you can change the story. If you can change the story, then you can make it a happy one. If you can make your story a happy one, why are you still unhappy?  Start jogging and start eating healthily. Does your lack of confidence make you miserable? Attempt to do daring things. The more you attempt, the more confidence you will feel. Preserve your happiness. Do that thing whatever it is. 5. Expect Nothing Immediately One of the sad realities of life is that nothing is guaranteed. Hard work and diligence give rewards in one way or the other but the rewards might not come to the athlete in the form of him winning the race. There are a lot of factors that come to play in our desired results and it is wise to expect nothing especially immediately. Do not jog for 5 days straight and expect that you would become a size 0 bikini model in that time frame. Everything has a timetable and some things never happen as we hope. To avoid getting disappointed and discouraged, find many other things to encourage you in your journey of self-development. Exercise because you feel more energetic and better about yourself when you do. Eat right because you are taking charge of your health and laying the right examples for your children. Do not smile at people because you expect them to smile back. They might not. Smile because you want to smile. Happiness means many things to many people. For some, it is seeing others smile. For others, it is being self-reliant. For another group of people, it is in having their own space. Whatever your definition of happiness is, a time comes in life when it will come under threat. Life is full of up and downs and nothing in life is guaranteed. The wise way to live is to stay prepared in mind. Using the above listed tips, you may not always be ecstatic but you will forever remain in a state of gratitude. You must stay grateful because if you can be thankful for what you have, you will always find a reason to be happy. If you look to others for fulfillment, you will never be fulfilled. If your happiness depends on money, you will never be happy with yourself. Be content with what you have. Rejoice in the way things are. When you realize nothing is lacking, the world belongs to you. Lao Zou


Welcome back to the channel, everybody. For those of you who are new around here, my name is Michael, aka Dr. Cellini, and I'm a board certified diagnostic and interventional radiologist in New Jersey. On today's video, we're going to be talking about what I've experienced in the first six months out of training as a completely finished attending physician in New Jersey. And it's been quite a whirlwind, and I wanted to talk to you all about it because A, it may give you a little motivation going forward if you're like in a rut and menstrual residency and all that stuff. And you're like, how I will never be at the end. Maybe this video will help you out because it's so, so much brighter on the other side. I promise. And I wanted to touch on a few things that I liked about being an attending physician in the first six months so far. So let's get into it. So I'll just be right into it here. So one of the biggest things I've noticed being in practice for a whopping six months now is that as an attending physician, you have complete autonomy.  I would hope you would have autonomy. However, this is like super delayed autonomy because we go through our entire med school of four years training six years for me. And you never completely have full autonomy or the final say in anything. But now you do. I have the ability to decide and make the final decisions as the physician. I can put my foot down and see if something is medically necessary or say no to something that isn't medically necessary. And I have that autonomy to do so because I'm a board certified physician. It's hard for me to really put into words, but this is just something I've been waiting for so long. However, it comes with great responsibility because as you can imagine, having that kind of autonomy is very stressful. And that's something I wasn't prepared for. Well, I was sort of prepared for it, but you never really know what it's gonna be like until you're in the driver's seat and you're experiencing it firsthand. People always told me, it's gonna be stressful being the autonomous one and having the final say in everything, but it's a blessing and a curse. It's great because you can do everything you've learned to do and be an autonomous practicing physician because you're trained to do so, but it's also terrifying at the same time. But you like slowly get used to it over time. I can't really describe it any other way. So besides autonomy, the next thing I love so far as I'm attending is the respect you get from your colleagues. Now I'm not saying like, oh, there's some big bad doctor walking around and we should respect him.  Now, you don't immediately get it and I most definitely don't have it from every physician in my hospital. You do have to earn it somewhat, but the thing is once you do earn it, you have the respect of everybody else, your peers and everybody you work with, and it's awesome because you don't get that in training. No one really trusts your clinical acumen because you're not a board certified specialist in your field, but once you are, people do respect that and they value your opinion. They come to you with questions about their patients, how to manage them, how to treat them, what kind of procedures can you offer them and they trust you and they have respect for your crafts and your field and your clinical judgment and your medical knowledge and your clinical acumen and your procedural skills. And it's something we're used to people just not having respect for us in training, but once you're finally there, it's not really something I seek out, but it's nice to know that your colleagues kind of trust you and have respect for you. The next thing I love so far, this may be one of my top things I love so far and that is you get to kind of customize your practice into whatever you wanna do. And what I mean by that is, if you don't wanna do a certain type of procedure or you wanna do a certain type of procedure, guess what, you can. You can just be like, oh, I don't do those or I don't wanna do those or I don't wanna develop that practice, but I do wanna do this. Like, I don't wanna do, you know, I like ports, but say someone didn't like to do chemo ports, I could be like, oh, I don't do ports or whatever, I send those to someone else, but on the same token, I could be like, oh, I really wanna do fibroid embolization and I could do that. Your ability to kind of customize your practice into whatever you want. And again, I keep comparing it back to training where you just have to deal with whatever comes through the door and you have to do it with whatever the physician you're working with wants to do. You're just kind of there doing whatever they wanna do. You're never working or thinking for yourself and doing whatever you wanna do, you're just doing whatever someone else wants to do. So now that you're finally in practice, you can do what you wanna do and it's so nice, you can kind of make your own schedule, do whatever procedure or whatever things you like as long as the hospital and your practice are okay with it and it's nice for once. One of my favorite things I've noticed so far as I'm attending for six months now is that you get to develop close, awesome relationships with your staff. And honestly, I built relationships with my staff, especially in residency because I was there for four years and I also built relationship with my staff during fellowship, but it was only one year and you're rotating in and out of multiple rooms and it's hard to really get to know people in that short period of time. However, now this is our practice. We all work together as a team and we get to know each other like a team and I've had a great time so far getting to know all of my texts, getting to know all my nurses, getting to know all the ancillary staff and even getting to know other physicians around the hospital.  I don't know. I like meeting people and I like to get to know people and when you're working with people for so long and so close together for so many hours every single day, it's nice to become friends with everybody. I've always enjoyed working in kind of like a family environment and that's ultimately what I was seeking in residency and founded at UNC, which is why I'm next there and that's what I was looking for in a job as well because you want somewhere where everybody's on the same page, everybody has each other's back and you're a team. All right, so what kind of financial medical person would I be if I didn't mention one of the best things about finally being done with training and that is finally having a decent salary. It's been very tough living on no salary for four years and then a smaller salary with a lot of training behind your name and a degree behind your name and you're not getting paid your worth for many, many years but now you finally can and it's not just having money. It's just, it's a little easier now, right? You always have a student loan debt but you now have a little more wiggle room and a little more freedom and ultimately what that does is allow for a little less stress in your life because we all know we worked in a very stressful career and everything that we've gone through up to this point has been very stressful but now at least we can offer it a little bit of less stress with a little higher paycheck and it makes going to work hurt a little less. It's always a little better going to work knowing that you're compensated what you're actually worth rather than being not compensated what you're worth in residency. And yes, I don't care what anybody says. Obviously we have the student loans but it's pretty nice having a better salary and being paid what you're worth. I wanna reiterate that. It's not having a high salary, it's just the fact that you're paid what you're worth because we go through all this training and ultimately we're just like, is this even worth it? But eventually it is and it's nice. For those of you who are wondering if it's going to be nicer on the other side, it is. All right, so besides that, what is my absolute favorite part of being a completely done board certified physician so far? And that is, drumo please, the vacation. Obviously I like to pay but the vacation is everything for me because you know I like to travel. So the reason it's so nice and I love it so much is because I spent so many years not being able to go to so many different functions. I missed out on all of my friends' events, multiple weddings, multiple birthday parties, christenings, showers, baby showers, all this stuff, graduation. I missed out on so many things during my late 20s and early 30s. I'm trying to like make up for lost time. So now that I have the ability to, A, take time off and B, go on vacations. I go somewhere all the time in multiple times a year. I did a lot of vacation, probably more than most physicians but I spend that time now kind of compensating for all the stuff I missed out on. I'm going to every baby shower or whatever I possibly can right now and hanging out with friends as much as possible because I wasn't able to do that. And I'm traveling as you know, I usually have a vacation, give or take once every month or so and I'm trying to travel as much as possible to make up for lost time.  And that's what we've been doing, obviously you've seen my Italy travel blog, you've seen my Paris travel blog and that's just in the last few months and we were going to go somewhere this month but we ultimately decided not to because Pandy Wendy is picking up in certain parts of the world and the last thing I wanted to do was get stuck somewhere and get the illness somewhere and not be able to come back to the United States because that's the most stressful part of traveling right now. But nonetheless, the vacation is like, I have been waiting for this moment for so long and it's finally come true and I can't really explain it.  So that pretty much sums up this entire video about my first six months as an attending physician, diagnostic and interventional radiologist and in private practice and hope you all enjoyed it. Let me know in the comments below if you have any questions, make sure you join my channel, become a member, you get some pretty cool perks and otherwise smash that subscribe button as usual, follow me on Instagram and TikTok and I'll see you all on the next video. Bye.


Hi in this short e-lecture I would like to discuss one central question of referencing objects the question of local reference or in other words I would like to discuss how we reference an object in space. In fact there are several options of defining the position of an object in space or the position of an object with regard to another one. These ways are referred to as local reference. Here are some examples. You would probably agree with me that this situation can be described as the ball is under the chair and this here is clearly a situation where you would all say the ball is on the chair. What about this one here? We possibly all agree that we can say the ball is to the right of the chair but couldn't we also say the ball is to the left of the chair seen from the position of the chair and what about this situation here? Would we still agree that the ball is under the chair? Well depending on the definition of the reference point and the position of the addressing we can distinguish several types of local reference. Let's define them on the basis of my position the position of the board behind me well I already said behind me and your position which for me is symbolized by the camera and for you by your position in front of your computer screen. The first situation I would like to mention is referred to as primary dyk-tick reference and here I would say the board is behind me. The primary dyk-tick definition of an object in space uses the speaker that is me in this case as a reference point and also as the origin of the coordinate system and relates all other objects to the speaker's position so I am the reference point and the origin here. In saying the ball the board sorry the board is on the wall I have a case of secondary dyk-tick reference. Now the secondary dyk-tick definition of an object in space uses the speaker as the origin of the coordinate system but the reference point is another object here the wall. So seen from my position the board is on the wall and then there is the intrinsic reference.  The intrinsic definition of an object in space uses an external address C as the origin of the coordinate system in this case U. The reference point is any other object so the origin is thus your position and the reference point is the board. So this is from your point of view and you are somehow behind the camera as I said earlier on. These are another principles contribute to the organization of conversation considerably. Well so much for the principles of referencing objects in space. In fact there is much more to say about this issue for example how we relate objects to one another why we prefer for example the water is in the bucket instead of the bucket is around the water or why we think the tree is in front of the building is more adequate than the building is behind the tree. These are another cases of referencing and other principles of conceptualization are normally attributed to psycholinguistics or to studies into language and cognition. So thanks for now see you again.