So, welcome to Didier Abou. He will talk about from Smaki to Kolobat, a history of software in Switzerland. Didier is a devian developer since some years and also a member of the DevCon team and he was quite involved in organizing here the whole event and he will tell you the rest. And yeah, come on. Thanks. So, as Gartens said, I will try to tell you a little about a partial history of software in Switzerland because most of you probably have never heard about anything that happened here and everyone thinks that Windows is the only and one solution. So, introduction, early days of computing, a little about EPSI tech and then Kolobat. About me, so I'm 27 years old, I was basically grown up with computers. I think I could use a computer when I was three. It was not a Windows, it was not a Mac, it was a Swiss computer, one of the 300 Swiss computers at that time. And now I'm working at Leap on e-learning. Towards Debian, I'm using GNU Linux since 2005. I haven't been maintaining packages since 2009. I'm now a developer since 2011 and as Gartens told, I co-organized this step conf and some of the packages you can see. So, as a first disclaimer, this talk intends you to show you a piece of our history that you probably haven't heard of, but it's also definitely non-exhaustive, focused, perhaps fun and definitely biased. So, I will tell you a little about the Laboratoire de Microinformatique, then from electric wires to computers and then from computers to humans. The main actor of all that was Jean-Daniel Nicou. He got a master in physics at EPFL in 1963 and then grew an interest in logic systems. And he became a professor in 1973 and was the founder of the Laboratoire de Microinformatique, which has been between 1970 and roughly 1990, the beating heart of computing in Switzerland, or as I haven't heard of many Swiss-German computing, at least in the French-speaking part of Switzerland. So, that was Informatics in 1967. And that was basically one calculator to do additions and subtractions.  I don't know if they were wearing black and white, but they were black and white. That is a decimal calculator. So, you could do additions and subtractions, but no floating point. So, you can do divisions, but you only get the rounded result. And we don't really see the size, but it's probably something like a half meter in the two dimensions. And you see the seven-three up there, there are the results. So, they already had kind of displays, but it's not really useful yet. I mean, it was for them, but it's not really what we have now. And then, as they were working at the university and they were bored by calculating averages by hand, they started doing things more useful than something to calculate averages, which is just two kilograms or three kilograms needed power. You had like one, two, three, four, five, six, seven displays that could display one number at a time. And it was probably very slow, but it worked. And it was the beginning of starting to solve problems for people. And back then, as we will come to that at a later point, Jean-Daniel Nico already had an interest in education. What you can see is a logidule. It doesn't have really an English translation, but there are basically building blocks. So, you could have one transistor. You could have flip flops. You could have displays, another one there. And basically, you could teach people how electronic works without having to do soldering for three days, without having to understand how the currents work. But you could get an understanding of the logics. You could say, I have a one that comes out of that cable, and if I put that one there at the input of that transistor, then at the output, I maybe get the zero if the power is correct, without having to care about resistance and all of that. And you could build a lot of things with that. I also used some of these in my studies, and we could build calculators, shifters, lots of things. And then you had just a pile of cables and dozens of these logidule. But you could reach a result and have nice little LED blinking. But back then, interaction with computers wasn't exactly funny. What you see here is the beginning of perforated paper length. That was the way to input code into a computer, into its memory, basically. And then you had to do toggles to access memories and read beats and maybe change bits to see what was happening. So, I hope that works. If I click there. This perforated tape is the program that gives the computer the order to create an image on the screen. I'm sorry, it's French. What can we do with this program at the end? So, here, it's simply a drawing, quite passive on the screen, but I can load another program that, for example, will modify this drawing. It's another study that he's done. And that's it. So now, he will have it jumping. So now, he will have it jumping. It's a little longer. That's four images. So, that was really, really early computing, but people could already start doing calculations. And they started doing things like storing medical records in hospitals with stuff like that. And so, many people around here learn how to perforate paper and understand bits and shifts and registers and all that. Then, when you have sort of computers, as we see perforating paper isn't exactly rapid and useful, though, people starting thinking about how could people really interact with computers? As you know, the mouse was developed by Douglas Engelbart in 1968. He's now dead. That was his first wooden version with two wheels. It had two potentiometers and basically transformed the movement into electricity. And then, out of that, you could have a moving something on something that looked like a screen. But Jean Daniel Nico went to the United States and visited Douglas Engelbart, and he came back with the idea in Switzerland, and then he developed the first Swiss mouse. That had three buttons already, and he moved from potentiometers to optical encoders. But you still had these two wheels, so it's not exactly practical to move the mouse around. But the idea back then, and maybe you've seen that in recent mouses, if you were born after these, was to use something like ping-pong balls. And instead of having the wheels directly on the floor, you have something that touches the ping-pong ball and the ping-pong ball touches the floor. So the movement is much sweeter. So that was Suri 2. Suri 1, I think, this one was in one exemplar and this one in probably ten. And then this was the fourth version that was used for a very long time, also in the machines that I will present afterwards. It had quite ergonomic shape. You could really have your hand on it and the clicks.  And that was the first Logitech mouse. So Logitech was created by someone that worked in that laboratory and that had worked on the mouse, and that was the first model that they commercialized. And this one got copied in 1992 by a Taiwanese X-Apsilon company, so the design must not have been that bad. And one other thing that they were doing was something glass. Maybe you recognize that design. Which year do you think that that was? Nadia for a year. 1972. And they already had a four-lines display to be wear on glasses. So Google hasn't really invented nothing. Maybe it was a little slower and couldn't speak to you, but you could see something. Then out of these experiments and computing, a spin-off of EPFL was created, which name was Epsitech and still exists today. So I will tell you a little about the Smaki Adventure, series business and games, because they have produced quite a lot of games, and I hope including a demo if that works. So the Swiss computer, the goal was it has to fit under a keyboard case. There were already some producers that could produce computers and keyboards, mostly keyboards. And the size goal was to fit in a suitcase. It hasn't worked from the start, but they finally managed after some years to produce that. That was Smaki 1. The screen was quite small, and this was also in one or two versions only. And it fit kind of in a suitcase, but it wasn't really powerful. So after three iterations, they came with Smaki 4, which had one Intel AT-AT, a Cobus network. No one ever knows what that is, but it was a network back then. It had a seven-inches screen and 256 by 10 pixels screen. And it looked like that, and you probably recognized the perforated paper reader, and it had just enough memory to read something, put that in memory, but it had no storage whatsoever. So every time you shut down the computer, you had to read lots of paper threads to actually do something useful. But it already had a display, and they also used something that we see here, that is a tape reader. Camcorder tapes to actually do what this does, but just faster, because you could drive that with a motor and then just read it, and in five minutes it's done. So yeah, that was it. And then some iterations after that, 1978, the Smaki 6 with a portable version. I mean, a transportable version. 256 by 120 pixels, Z-Logs at 80, 32K of memory, and they sold 450 units. And that was the first computer that was sold by Epsitec. And it looked like that, so it's just what we now have as Osioscope, but it used to be a somewhat useful computer. And I think what you see here is probably a floppy reader. If people remember big floppies, it could already read floppies. And then maybe you recognize that 68000 processor, M68K that we used to have in Debian, Smaki 8, 128 kilobytes of DRAM, and two processors already, but this wasn't really a success because that was just an expensive machine with incomplete software, so it didn't really succeed. It looked like that, which already looks like a computer that you probably have used with keyboards and these colored things that were quite the specific thing about Smaki, it had these very nice colored F02, F12, that were then taken by others. And you also see the toggles around the screen because you could change the contrast and intensity of the electron beam directly. And then some years after that, together with the first Macintosh, the 68000 processor 8 megahertz, 3 megabytes of DRAM and monochrome displays, and these were already deployed in Swiss schools. So many of the children back then have used Smaki 100 and the other versions after that to do word processing. That was already graphical, maybe not in colors, but it was graphical. You could have games, spreadsheets, preview for printing, lots of that. I will do a demo after that. But that was why the first Macintosh had a blinking cursor. So it looked like that, it was already a little smaller, and you recognized the mouse that we saw before. Then as the available processors went on and on, the people behind the Smaki kind of looked around to see which processors they could use, and they tried most of the time to use the same mechanical casing so that they could sell partial upgrades to the schools instead of rebuying the whole screen, keyboard and stuff that was very expensive back then. Just reuse the same mechanical casing so that you could just resell a partial card and you just bought that and you could do the upgrade yourself. So this one had also two processors, and it was seven times more efficient and just faster. And the interesting thing of that is that it had up to two screens, but you could put them vertically, which when you think of it is quite useful when you try to prepare an A4 paper. That was unique back then, and I don't think many people are using their desktops with rotated screens, but if you try, sometimes it can be very useful if you prepare something that then goes to paper. So that version was sold in 300 units, which might make you think that it's impossible to survive by selling so few units, but when you see the price, 12,000 francs per unit, then it expires the thing a little. So it looked like that. That's without the casing, and you recognize the logic tools and a bus, because these computers were used in schools, so you could use the computer to drive external electronics using buses. So you could drive bits directly from the computer at a certain speed, instead of toggling bits at your limited speed and then drive external electronics to do other things. I think that's the 324 board, and I have no clue what this circuit is doing, but that's the building blocks that I showed earlier on that students could build things on. You could have register shifts, displays, basically one transistor or one logical element, the D gates and stuff like that. And then I will go a little faster with the next ones, because the technical details for all of the versions are not overly interesting, but the Smaki 300 in the 1990 had a colored screen already, and there's a very cool, super modern design. And then they did another upgrade in 1992, the upgrade of the Smaki 100 with a 25 MHz processor, and that kind of went with the upgrades that you could get on the Motorola 68000. But this was also one of the first pluggable computers, so you could just buy other options, like graphic boards, floating point units, Ethernet interface, video capture, etc. And of these 2000s were sold, and Epsitec tracked the people that had still working Smaki 130 units, and there were still 500 that had perfectly working computers for their use. They certainly look old, but they were still functioning. And that was also a different business model from them, because Epsitec had a list of their clients, because you couldn't just go and shop and buy something. You had to order that to them, so they kept your address and sent you upgrades by mail, by post mail, of course. And yeah, that was that version with color. As you can see already quite some graphical performances. This software was named PAGE. They had very Frenchy names like PAGE, and was it FISH for database, and other things like that, but you could already graphical processing, change the sizes of the things, and have images, colored images to painting in 1992. I don't know if you remember the state of Windows or Linux back then, but it was not that. But in 1995, there was kind of a breakdown, because the team behind Epsitec and the Smaki was something like 10 to 15 people at most. All that was coded in basic. It was working, but the problem is that the PC's price went down, and down, and down, and down. So it was quite hard to keep competing with something Swiss specific, only sold to Swiss schools and Swiss individuals, or small corporations. And there was also the rise of Internet that created new needs, which were hard to cope with a small development team, like just coded TCP IP over Internet is just not trivial. And the other problem is that there are long-term users with clear uses. So I think there is someone that is still using a very old Smaki to keep track of his pictures. He just enters them in that database thing that works on this thing that he has at home, and it's still valid for him, it just works. And it will continue working, because the electronics are robust. So they kind of didn't want to leave these users out in the cold. So they had a discussion to know if the idea would be to put a PC in a Smaki, or a Smaki in a PC. And what was decided was Smaki in a PC, after some tries, which was a PCI card with two processors, some memory, and you could launch an executable from Windows that accessed that PCI card, that had its own memory, so it was kind of a gateway to access this. But this card also had the connectors for the Smaki network, the Smaki peripherals. So at EPFL, while they had Smaki before us, they could just use their Windows NT machines, put that card in too, and continue with the experiences that they had with the Smaki software. So they sold 200 units of these, mostly at universities or schools that already had these hardware. And I think I could use one. So, yeah, showing a picture of a card is not overly interesting, but that was it. And then in 1998, software had evolved enough so that the hardware was not needed anymore. So they used a modified version of Motorola emulator, itself based off an Namiga emulator, to just have something software that would boot the system that was on the card before. So now you can have Smaki 400, which is now Smaki Anthony, on your Windows machine. So if you see that, we have an emulator working on Windows that launches another system. The luck is it works under one. I think it even has sound. So that's basically what you had on a Smaki. So you have a mouse, you have a green and black thing that after using for two hours you're just stunned. And then you can... you can navigate to various things, like launch this database software in which you can input things and add entries in your database, and you have a multitasking, you have different screens, and that's basically the state of the software back then. I don't know if you see enough. Maybe I can do something bigger. And launch, for example, PAGE. So that was the state of the software back then, so you could write... I don't remember how it works. You could add text, you could link text boxes between them, you could move text, change how you wanted things to be displayed, to be uppercase, you could preview things, you could have various pages, graphical things. It's been a very long time, so I don't remember exactly how it works, but that was basically it. You had some stuff like graphical programming, so you had an input-outputs code and you can add decision blocks. So you could have defining screens, for example, one screen, full screen, that, and then you could, I think, do another thing, yes or no, and then draw things. So that was quite... The focus of that corporation was always we want to bring something to people so that they learn something, and it's useful for them. I think they made a lot of money with that, but it worked for them. One thing that was constant in that user interface is the blocks that you see below, that are always there to remember you, the F1 to F12 things, shortcuts. So in that case, if I type F1, it should do... So you can save. No, I don't want to do that. Okay? So yeah, that was basically it. And I think I can probably launch the normal color thing for you to see a later version, something like Picasso, where you could have a drawing and circles and, yeah, I mean, it's a drawing thing, but it's coded in basic and works on Motorola 68000 and worked almost like that 15 years ago. So we haven't gone very far with GIMP. So that was it for the Smaki. I hope you enjoyed the flashback, kind of. And then the EPSI tech still... I mean, had to survive, and they had clients that were using their software on Smaki, such as database softwares and finance software. And now this company creates finance software mostly for Windows clients. Salaries accounting and voicing, and it's not too bold to say that they're between the two leaders in that market in Switzerland, mostly because Switzerland has ever-changing, ever-local, geographical changes, and that only a local company can do that. So that's why it works. Database softwares, they have done quite some... and it's not exactly SQL, it's mostly graphical, how do I handle my collection of CDs type of things. Also graphical software, I don't think they made much money out of it, but they recreated on Windows the idea habits behind Pash, so that their old users that were using that software in kind of how they liked to work. And they did quite a lot of educational games. That was, I think, a third of the programs on the Smaki's, and they ported some of them and then they started to code on their free time for doing 3D versions and all that. I didn't find a whole list, but I can probably lead you through the list afterwards, but that was, for example, DoFan simulator. DoFan was a small system that had a small CPU with toggles and LEDs that was produced back in the 70s for educational purposes and for the 30 years of that company they produced a version that you could use to test how it works to read from a register and the fun to toggle bits and such things. They had Blippi Mania and with this funny little thing, it's not a boy, it's not a girl, it's a thing, named Toto initially and then Blippi that was there for a very, very long time in the early days of Smaki and that had educational games again for small children and that was like logic games, how do I move this person here with this material that he had caught there and how do I go from there to there without pumping out my energy and stuff like that. I don't have a demo of that one yet. Then they worked on 3D things, buzzing cars, that was a car game very funny where your car would lose pieces if you hit things, you had a ghost mode where you could fight yourself to try to be faster than being and stuff like that. I have the CD here if someone wants to try and we don't see it very good on that but they then they tried to get children to program so you could have a bot that had standard like the turtle you probably know it that had go to and turn and advance and motors and draw, pen down, pen up, instructions change color and stuff like that and you could basically go through exercises to learn how you can program but in a 3D environment. That leads me to Colobot which means colonize with bots and the goal of that was to learn programming in a fun way. Demo. So the first mission I will just go through it so that you see how it goes. You have a 3D environment in which you have bots in which you have you and you can move around. So yeah, that mission is really boring so I will abort that mission and I don't have the cheat codes but you can go through exercises and for example you can try to kill spiders so then you're in that moon on that planet somehow and you have instructions so you can see what is going on and you have an objective so write a small program to kill three spiders you have to select the bot and then you have instructions on how you write the function to drive the bots, you can fire for some time, you can turn the bot etc etc Usually you can also find in other instructions if you go in the book, you can search for how does the if instruction work and read through that. So it's quite a good search first enter in programming because it teaches you that there is documentation that you should really read it so as you see we have spiders there and if I approach the spiders then they kind of hurt me or they should anyway let's not try otherwise the game is over. So in that case it's a robot that I can't drive in the missions you have hundreds of missions that lead you from planet to planet and in all the missions you can succeed all missions by driving the bots yourself so you can go through the game without ever programming but for tasks like changing a battery, going to search for titanium ore for an hour and just bring titanium ore back you kind of understand why it can be useful to program so in that case I will just cheat and use the solution you can aim so you just change the direction in which you're turning fire for some time, turn fire again and turn and fire again and if you do that it just doesn't mission accomplished but you have more complicated things like fighter jets so it becomes a little more complicated because you have to think about hate about aiming the cannon in two directions about the wealth of your battery every time you shoot you're losing a little battery you have to use your radar to find flying ants wasps and then the program becomes a little more complicated so you can use objects in which you can use positions you can determine the angle in in in degrees to things you can turn you can use your motor right or left motors to like do things in a smooth way instead of moving then turning then turning then moving so you can like drive your motors in a little more complex way or just use go to and the nice thing is that you can also have step by step and see what the bot will do and you can just so then it aims, uses to chat wait for some time, yeah that's really boring so yeah let's just go through that and at all times you can stop the execution and see what the status of the variables are you can always have the one-off documentation, click on it and get a more extensive documentation and the most fun part of that is probably see how the program goes so it search for a wasp and if it finds one yeah in that case it's an ant ant fatally wounded and then search for another one you see the radar down there and really you have lots of different activities you have a whole set of exercise starting from what is a variable to what is a function to how do I interact within classes and how do I contact another bot to communicate instructions to him so yeah if you want I can show you a little more but we're soon running out of time so we have as I said variables, motors mover, you can use functions, classes etc of course you can save your programs, edit them in another editor outside you can exchange them between you at the moment in time there was quite a community around that, that was like exchanging the best ever shooting program to hunt wasps while you were doing something else and the design is just wonderful so good news although it was closed source it has been open source at the beginning of 2012 and it's full gpl version 3 for both code and data you can find that on github and I filed an ITP I just couldn't upload it yet because of the appconf organization but that's a game that will most probably soon be in Debian so that was the link between the other thing that I didn't mention because I'm almost done the other thing is that although it wasn't open source back then because people didn't know what open source was about people and as everything was written in basic you could basically change what you had in your computer and there was quite a lot of work in making sure that everyone could change their software and then integrating more things and stuff like that but it was definitely not free software based but for the 30 years of the project of that company they decided to release the full sources of the smaki operating system in basic so if you have an interest go on smaki.ch and eventually run that somewhere somehow and if you want to try it there is an executable version that works on wine on jesse you can also go around the interface and see how it works if you have an interest basically there is absolutely no development on smaki anymore obviously that company has moved to making sure everyone can spend their tax declarations to the states of switzerland but I think no one from that company ever regretted that story and making sure that people in schools could get early access to computing these are the sources that I used for that presentation I have a CD-ROM full of these funny very old videos if you want to take a look at them people explaining in french I'm sorry what this all was about you can find some stuff I think a little of it in english on smaki.ch and on opacch.ch slash smaki which was kind of the parallel homepage thank you that was all


Hey guys, so having seen the theory part of Rational exponents of real numbers now it is time to solve a few problems So I am going to solve some of them and then later on you can solve these problems from any Standard textbook. Okay. Now, let us see what is the first problem. The first question says simplify 64 by 25 to the power minus 3 by 2 so how to solve this problem So let us say solution. We are now trying to do for a and this is 64 to the power and sorry 64 by 25 whole to the power minus 3 by 2 Okay, so by now laws of exponents. We know that this particular thing can be written as What can I write about this? So this is nothing but 64 by 25 whole To the power half and then whole again to the power minus 3. So which law did I apply? I applied this Let's say a to the power m by n is nothing but a to the power 1 by n Then whole to the power m, right? This is laws of rational exponents, right now To anything to the power half is nothing but the square root, isn't it? So I can write now as it has 64 by 25 Square root and whole to the power minus 3 correct now root 64 by root 25 So this can be written as root of 64 divided by root of 25 right and this whole to the power Minus 3 and what is a rule? So a to the power a by b To the power m is equal to a to the power m by b to the power m Is it it? now hence root of 64 is clearly 8 and Square root of 25 is 5 and now it is 8 by 5 to the power minus 3 right Which will be nothing but 1 upon 8 by 5 to the power 3 by which rule a to the power minus n is equal to 1 by a to the power in Correct. So hence now what can we do? We can now write this as 1 upon 8 cubed divided by 5 cubed right which is equal to 5 cubed by 8 cubed and hence it is 125 by 512 This is a simplified form right so this is what is the solution to the first question now Let us see the second question so the second question is 25 to the power minus 1 upon 3 into third root of 16 so what to do so if you see 25 to the power minus 1 by 3 can be written as 1 by 25 to the power 1 by 3 is it it and this is 16 to the power 1 by 3 which rules are we using so first rule is a to the power Minus n is equal to 1 upon a to the power n. This is for the first step and Let's say a to the power 1 by n can be written as nth root of a Isn't it so these two things I am using now. What is this? So if you see this is nothing but 16 by 25 This is 1 by 3. This is 1 by 3, right? So hence this can be written as 16 to the 16 by 25 Whole to the power 1 by 3 by which rule a to the power Sorry a by b to the power n will be equal to a to the power n P to the power n and vice versa. So in this case we had this and we went to this Okay, now what so let us write the factors of 16. So if you if you see 16 can be written as 2 into 2 into 2 into 2 to the power 4 and 25 likewise is 5 into 5 Isn't it so this is And the whole to the power 1 by 3 Correct. So what can we say now so you can either write this as 2 to the power 3 into 2 whole to the power 1 by 3 Divide by 25 to the power 1 by 3 whichever way, right? So this can then be written as 2 to the power 3 Whole to the power 1 by 3 into 2 to the power 1 by 3 divided by 25 to the power 1 by 3 Right. Why why is why am I writing like that? So a Times b whole to the power n is equal to a to the power n into b to the power n So in this case, I have considered 2 to the power 3 as 1 entity a correct. So hence you got this So what is the final value then so 2 to the power 3 into 1 by 3 it will become into 2 to the power 1 by 3 divided by 25 to the power 1 by 3 so which is equal to 2 to the power 1 into 2 upon 25 To the power 1 by 3 so it is right This is the final value so 2 into 2 by 25 to the power 1 by 3 now you can go ahead one more step by you know doing some Manipulation by let's say because this can be further done as 2 by 5 square isn't it this is 25 is 5 square to the power 1 by 3 Now what I can do is I can write this as 2 into 2 into 5 I multiply and divide by 5 so this will become 5 to the power q to the power 1 by 3 isn't it see I Multiplied and divide the numerator and denominator by 5 each so 5 square became 5 cube in the bottom right So hence what will this be now? So this is nothing but 2 into 10 to the power 1 by 3 Divide by 5 to the power 3 To the power 1 by 3 isn't it So this will finally become 2 into 10 to the power 1 by 3 divided by 5 why because 5 to the power 3 whole to the power 1 by 3 will be equal to 5 to the power 3 into 1 by 3 Which is 5 to the power 1 hence 5 Okay, so hence the final result will be 2 by 5 Into 10 to the power 1 by 3 So this could be another way of expressing this So this is question number 2 now the third question is Fifth root of 32 to the power minus 3. So hence again, what what would I do? I will write this as 32 to the power minus 3 upon 5 right, which is equal to 32 to the power 1 by 5 Whole to the power minus 3 Right now why because a to the power first is nth root of a is nothing but a to the power 1 by n So in this case fifth root it was y root 1 by 5 of 32 to the power minus 3 and then what a to the power p by q is simply a to the power 1 by q to the power p Right, so hence, what will it become? It is now Equal to 32 to the power 1 by 5 can be written as 2 to the power 5 whole to the power 1 by 5 And this is minus 3, which will equal to 2 to the power 5 into 1 by 5 whole to the power minus 3 Which will be equal to 2 to the power 1 whole to the power minus 3 Which is equal to 2 to the power minus 1 Sorry minus 3 And hence it is 1 upon 2 to the power 3 is equal to 1 upon 8 Okay, what all rules did I apply? I applied a to the power m to the power n is a to the power m times n for this particular step Right, and then a to the power negative n is equal to 1 upon a to the power n. That's for this to this step Okay, and then simply I simplified and then found the final answer. So this should be Uh, this is how you should be Uh, you know taking up some more problems like these and Solving them. Is it okay? So let's meet with another set of problems in the next video


6 Tips You Need To Know About Jobs Teaching English Abroad If you are considering teaching English abroad, you will no doubt be aware that there are many things to think about when planning your adventure. You might also be a little overwhelmed by the whole prospect of packing your life into a suitcase and heading off overseas. Whatever stage in the process you're at, do not panic as tens of thousands of people have been just where you are now and have gone on to have a successful and enjoyable time teaching English as a foreign language. The following top 6 tips should help you focus on the most important things to consider and set you on the road to a new chapter in your life as an EFL teacher. 1. Get TEFL certified. The number 1 tip for anyone who wants to teach English abroad is to complete a TEFL certification course before you start looking for work. During the course, you will learn all the essential skills that you will need once you enter your own classroom. Having these skills will not only ensure that your students receive a high standard of tuition, but it will also ensure that you have confidence in your own ability and knowledge to plan and deliver your lessons in a new and unknown environment. Although having a TEFL qualification benefits both the teacher and the students, it is also an actual requirement in many parts of the world. In some countries, a TEFL certificate is needed when applying for a work permit or visa and many other individual employers also expect their job applicants to be qualified to teach in their classrooms. Essentially, if you want to give yourself the widest choice of available jobs and access to the best paying positions, a TEFL certificate is a must. While you are probably keen to get on the plane and to get your new life and career underway, it is recommended that you allow plenty of time to make the necessary arrangements. Before you head off there will be a variety of things to take care of, including completing your TEFL course, making travel arrangements, and ensuring you have an up-to-date passport, etc. The process of job hunting, applying for positions, phone or Skype interviews, and arranging work visas can also be very time consuming. In reality, you will need a minimum of three months to get everything in place, and in many cases, this could be six months or even longer. If you already know where you want to teach English abroad then you should find out as much about your destination as possible before you leave home. The information you should look for includes potential accommodation options, what to pack and what to leave at home, where to find expat groups for advice and help with settling in, to name just a few. However, if you are still unsure of your preferred destination, your research will also be aimed at narrowing down the potential locations to the ones that suit your preferences. Everyone has different motivations for teaching English abroad, whether it is to earn the maximum salary possible, to learn a new language, to explore a certain culture, or to provide invaluable help as a teaching volunteer. Whatever your own motivations, research is the key to making the right choices for you. 4. Keep an open mind and be flexible. If you are a highly qualified EFL teacher with several years' experience teaching overseas then you will be able to pick and choose the jobs you want, where you want them. However, for the majority of EFL teachers who are looking for their first job teaching English abroad, the choices might be more limited. The key to finding the right position is to be flexible in your choice of location and open-minded about countries or regions that you might not have considered before. Although the Middle East is where you will find the highest paying positions, as an inexperienced teacher your chances of securing them are very limited. Instead, you should consider heading elsewhere to gain experience to put on your CV, resume so you can confidently apply for your dream job at a later date. Similarly, many people dream of living and working in one of Europe's major capitals such as London, Paris or Rome. While this is certainly possible, even for those without experience, the high cost of living and strong competition for the best jobs means you might struggle to earn enough to live a comfortable lifestyle. By choosing a destination with a lower cost of living and less competition such as Prague, Budapest or Warsaw, you will ensure you have plenty of disposable income to enjoy all the cultural and social opportunities that these great cities have to offer. 5. Be aware of visa regulations Before making any final plans for teaching English abroad it is vital that you are aware of the visa situation in the country you have chosen to teach in. There are no rules and regulations regarding work visas and permits very greatly from one country to the next so you need to research the latest requirements to ensure you are eligible. In some countries, you need to apply for a visa before leaving home, while others require you to enter on a tourist visa and then apply for a work permit once you are in the country. You should also be aware that in many countries, particularly in Asia and Europe, a four year degree is required to qualify for a work visa. Certain countries also restrict teaching jobs to native English speakers only. Once again, by conducting plenty of research you can narrow down your options to those where you can realistically live and work as an EFL teacher abroad. 6. Be aware of the hiring process Once you have researched your preferred destinations and are aware of the visa situation, you also need to establish what the hiring process is in that particular country or region. If you are looking at one of the large East Asian markets, such as China, Japan, South Korea, or Taiwan, the standard procedure is to hire teachers in advance before they leave their home country. While in Southeast Asia, Latin America, and Western Europe, it is more common for employers to only hire via face-to-face interviews. In these situations, you should also be aware of the local hiring seasons so you can make sure you arrive in the country at the best time of year to secure employment. Are you ready to teach English abroad? By following these six tips you should be able to focus on the most important aspects of the planning process and get your new life teaching English overseas up and running with a minimum amount of stress. At IDTT we are fully committed to helping you every step of the way. Speak with an IDTT advisor today to put together your personal plan for teaching English abroad. Send us an email or call us toll-free at 1-800-490-0531 to speak with an IDTT advisor today.


Hello you guys, welcome back to my channel. We are doing another episode of Ikea hacks. Now I have done a ton of Ikea hacks videos in the past on my channel and I personally just love flipping Ikea pieces because I do feel like Ikea pieces are pretty simple to start and I feel like that is the basis of Ikea, it's very Swedish style design and it also comes at a great price point so a lot of the pieces are more minimal. But for someone like me who likes a more maximal approach to design, I love taking these pieces and just hacking them and reworking them into really cute decor and I have three incredible projects for you guys today. Normally I do four in my Ikea hacks but these three projects literally shined so bright on their own. I was like these have to just go in their own video. We're doing a decor piece, a rug and an actual coffee table. My camera is literally on top of the coffee table right now and it's perfect. It is literally perfect you guys and it's actually the first time I've used this technique so I'm excited for you guys to see it but without further ado, we have some projects to jump into. Make sure that you are subscribed to my channel if you are not already and you're following me over on Instagram at lonefoxhome for your daily dose of DIY and Drew and let's go ahead and dive on into these projects. Our first project here features a wooden bowl and I personally love these wooden bowls. I have a ton of them in different sizes. They're great mixing bowls for your kitchen space but I actually want to take this and turn it more into a decorative style bowl so something that you can use on a styled shelf or on a coffee table or an entryway table and this is the perfect base for that and it turned out incredible so here's how I did it. For this first project I'm going to be using a bamboo serving bowl from Ikea and I'm starting off by using a flexible ruler here and I'm going to go ahead and mark one inch distances apart so that we know where to drill our holes at the top of our bowl here. Now I literally put my dots directly on the line in the bamboo and then I just measured them out one inch all the way around.  Now do keep in mind that this is a bowl shape so it's kind of hard to keep stable that's why I had it on my lap then I moved to the table but just whatever you feel comfortable with and I did go ahead and mess up on one of the sections but if you guys mess up do not worry just fill the hole with some wood filler sand it down and you're good to go so I just let that dry and then I sanded down all the excess wood filler and then brought the piece outside for spray paint time and I wanted to go ahead and give this bowl a new look completely different from the original bamboo so I gave two coats of a satin black spray paint but if you do like the original wood you can totally keep that but because I was using this kind of orangey-hued suede cording I did want the contrast to be pretty bold and I love whether the black looked with that so all I did was cut a long piece of our suede cording and I'm just simply lacing it through the top here by going out through the front side and in through the back side and it kind of creates a diagonal lace which I love and I repeated this process around the entire rim of the bowl.  For our second project I wanted to go ahead and do another rug for you guys I've done rugs in the past from Ikea and you guys always love them and just coming up with the design is always the fun part so today I wanted to do a more oblong kind of kill-em style checkerboard pattern which I feel like I've been seeing trending across Pinterest and social media lately in terms of interior design so this one's super simple very affordable and easy to recreate so here's how I did this project. For our second project I'm going to be using the rack-love woven rug from Ikea and as you can see here it has bands of color across the center section of this. Now they do have a rug I believe that's called Low House which is essentially the same rug without the bands of color but it was out of stock at my Ikea so I opted to grab this one and then I just removed all of those bands of color super simple and easy just cut the ropes as you go and pull them out because I'm going to want to be creating a new runner rug based off of this vintage style kill-em rug which I have been loving lately. I love this kind of geometric pattern and we're going to achieve that with some tape so all I'm doing is cutting my tape into three varying widths. I really like when the widths of your blocked sections are a little bit different so my left one was actually the smallest my middle one was a bit wider and then the right one was just a bit smaller than the middle so the next process is pretty repetitive you're just going to be cutting out tape and repeating the checkerboard pattern all the way up your entire rug and then once you have all of your tape added on there you can actually bring it outside and use your favorite spray paint to go over the top of your rug I started off with this ivory color because I really wanted a subtle tone-on-tone look for this rug. I know the one I showed with you guys was pretty bold but I just thought a tone-on-tone would be really pretty for this rug and I had so much hope until I started removing the tape. And that is just what I did I actually went ahead and recovered those sections that I pulled off and then I brought the piece back outside because it was just way too tone-on-tone. I really could not tell a difference at all in that checkerboard so I went back and gave a full coat of black spray paint onto our entire rug and then brought it back inside. Oh that's so much better. And I'm sure you guys know how this project ends it's the most satisfying part of removing all of the tape I absolutely love this process and you get to reveal your brand new rug and this is perfect actually to use indoors or outdoors. And it is time for the third and final project which is our larger scale project in today's video I am making a coffee table. Now as you guys know in my living room I've had the same kind of wicker style coffee table that I spray painted in my living room makeover but I've always wanted to swap this out because it is on the smaller side and I found the lack of coffee table at Ikea which is only $20,000 and it's $20,000 and it's $20,000 and it's $20,000 and it's $20,000 and it's $20,000 and it's $20,000 and it's $20,000 and it's $20,000 and it's $20,000 and it's $20,000 and it's because I love coffee table at Ikea which is only $29 I believe it's one of the most inexpensive coffee tables they sell and it really is a great shape and size for my living room so I was like let's go ahead and flip this add some plaster to it and turn it into what could be a $600 coffee table for literally a little bit under $60 and of course you guys know that I had to save my favorite project for last. This is our lack coffee table hack and I started off by firstly assembling the entire lack coffee table which was very simple.  It took like 10 minutes to construct. Very, very simple. And you guys, this coffee table is only $29. So it's the perfect base for this project. This is what the table looks like once it's constructed. And our next process is actually to cover the entire table in some mesh drywall tapes. You're going to want to cover every single piece that you are adding plaster to, which is essentially the entire table for me. I'm going to be covering that in mesh drywall tape. And this right here is what your table top should look like once you have it fully covered with our mesh tape. I also added, of course, to the sides. Now we're going to want to go ahead and mix up our plaster of Paris. So this comes in a box like this, only $4. Now sadly, Milo's only had small boxes, but you can get bigger bags. What you're going to want to do is actually add it into a bucket with a little bit of water and mix it up until you have a nice, smooth, kind of like chunky oatmeal-esque consistency. You're just going to want something more on the wet side than the dry side because this product does dry very quickly. That is something I want to tell you guys for sure. I went ahead and I used a spackle tool like this, which is essentially just a spreader for, you know, joint compound or spackling. And I spread it at first off on the top of our table. I wanted to go ahead and work in a large area so I can get a feel for the actual plastering. And it really is a simple process, but I do suggest that you make more batches of plaster and work longer than trying to plaster it all at once with what you have because the plaster really does dry in about 10 minutes or so, and it's really not workable as it gets harder. So I suggest making smaller batches and work with it so you can smooth it out with a spackling tool. But if you do want a more smoother plaster finish on top, you can go in after about 10 minutes of the plaster drying on your surface with a damp sponge and just go over the top of the surface. It's actually really going to smooth down that plaster and kind of remove any harsh edges if there are any. And you can really smooth it down as much as you would like to, just go over it multiple times with the sponge. I made some fresh plaster when I went ahead and did the sides, and really all you're going to want to make sure that you do when you do the sides is that you also get that very, very corner of the side so that it transfers to the top so it looks like one cohesive piece. So when I did the legs and the sides, I just ensured that I was getting all of the sides. And as you can see here, I did go in with my hand at one point because it was just taking quite a while, but it is a fun process. I'm not going to lie. It is a extremely messy process though. I will tell you guys that, but once you have all the plaster smeared on your piece, this is what my workstation ended up looking like. The following morning, I whipped up a smaller batch of plaster just to kind of fill in any areas where I felt like I either wanted more texture or I was still able to see that mesh underneath or I just wanted to add more in general. I also went in and used some fine grit sandpaper. This is a 180 grit to just go in and smooth out any areas in the plaster that of course needed a little bit more smoothing as well. I made sure to do all of the legs just to ensure they were nice and clean. When I added it to my living room, it was going to look nice. And this is what the final state of the table looked like, which was perfect. But of course, we do need to go in and just give it a protective finish. So I got a map clear coat. This is the perfect option. I'll link this one below for you guys. It's great for a plaster project like this because it does dry fully clear. So I went around and I gave two full coats of this, just wait about four or five hours between coats. So I did one coat.  A little update on the table, you guys. I actually filmed this about a week and a half ago. So I've been living with the table for I'd probably say 10 days or so and I absolutely am obsessed with it. Not one thing has chipped. I really want to do like a little bit of an update for you guys because I knew I was putting the plaster over the top of like that Ikea finish and I wasn't sure if it was going to stick properly, but it looks incredible. It's really nice to just kind of randomly and sporadically place items. I think it looks really fun and I feel like overall just this table is just a unique piece. I love the texture on the corners. I also love how it has this bottom shelf as well. I added these ceramic beads, which normally had a couple books over there, but I totally forgot that I put them up there. But that's the table. I just wanted to give you guys a quick little vlog style update to let you guys know that it is going strong. Plan on keeping it here. The other table is actually already out and I just love this. I want to get a new rug for the space. So if you guys have any recommendations that will go with this table and this chair, please, please let me know in the comment section below. Those were my Ikea hacks for you today. I hope that you enjoyed this video and if you guys like more Ikea hacks, I have so many more of them on my channel. I will link a couple more in the description box below for you guys and also make sure to subscribe because I'm always posting brand new videos here on Lone Fox. I post almost every single Thursday and Sunday. So make sure to subscribe and click that bell icon if you are not already. And I would love to know which project was your guys' favorite. Was it the bowl? Was it the rug? Or was it the coffee table? There are some options, but they all turned out really cute and I hope that you guys loved this one. The website LoneFox.com is finally fixed. It was down for like a month. So if you want to go ahead and get some new decor or just shop around on the site, it's finally up and running you guys and everything is functioning properly. I'll catch you guys in my next video. Have an amazing rest of your day. Bye guys.


Good day, fellow investors! Today I'll discuss Chinese pick number 4, MOMO or however should I pronounce it. MOMO is a live stream broadcasting platform similar to YY which we analyzed in the previous Chinese stock video. The Chinese live stream market is exploding and this is because 3G and 4G have entered the country and the internet penetration is constantly growing and there is still plenty of potential. As you can see here internet penetration in China is just at 53.2%. This is very low when compared to the 88% in the US or even above 90% in the UK. Just another short introduction about the Chinese live video stream market. It is expected to triple by 2020. The growth rates will be smaller than they have been in 2016 but still you want to be exposed to a market that will triple in the next 3 years. The top 2 leaders are YY which we already discussed in this video and you can check the videos in our Chinese stock idea playlist. And the second investment is MOMO which we'll shortly analyze today. The company is relatively equal to YY. See the front pages so live stream on YY and live stream on MOMO's page. So the two businesses are live stream businesses where broadcasters entertain their audiences, they get subscription, money, virtual gifts and the sites are also monetized through advertisement but that's just a small part of revenues. Going back to what's the business model. Well 80% of the broadcasters are females that entertain 80% of the males population that are the customers. A business model there is no pornography in China so you get the picture. However this works, the business is booming and I think the business is there to stay especially if China doesn't allow pornography for a long time. So what's the difference between YY and MOMO? MOMO is relatively newer. This is YY's streaming revenue and you can see how it has been growing pretty fast since 2012. However MOMO's revenue has been 0 in 2015 and has reached almost the same level as YY in Q4 2016. So MOMO is a faster grower than YY and if we check the last quarter's highlights we can see that net revenue increased 420% year over year. Net income went from 7 million to 81 million so 11 fold increase. These numbers are simply crazy. However if you listen to the company's webcast company expects revenue to grow 7% in the next quarter. 7% per quarter comes to 30% a year. Something similar to what YY's guidance is and this is very important for an investment decision. You'll see later in the evaluation part. Going back to MOMO its revenue stream is diversified and all the revenue streams are growing which is very important because with such online businesses when the customer base is made you never know which one of these revenue streams will explode in the future and will be perfectly monetized. So both YY and MOMO have a large customer base, slowly growing customer base, high growing monetization so they're really focused on monetizing. Both companies are very profitable and both companies expect to grow at the same rate around 7% per quarter, 40% per year alongside how the market grows. So extreme growth offered from both companies. A look at fundamentals will show us which one is the best investment. So MOMO's PE ratio is 48.9, YY's is 14, price to book again better at YY's, price to sales again better at YY's and price to cash flow better at YY's. As both companies expect the same growth in the future, YY has the huya which is also growing very fast which is something new like MOMO offers. I find YY a better investment from a margin of safety perspective. Now I didn't dig in which one is the best, perhaps the best way is to diversify into both and then if one of those investment explodes you are set especially as YY has a margin of safety. However if the companies continue to grow at the same rate their valuations will have to even out. So much more upside for YY and less upside for MOMO. I think MOMO has a higher valuation now because of the past growth but if the management doesn't see future growth then it's probably just a market mispricing. However I think that the PE ratio 40 is fair for a company that will grow 40% year over year. So YY is the underdog here, it's the undervalued company. So to conclude I think both are excellent investments, both MOMO and YY. The business model is certainly there to stay. More and more people will use mobile phones in China, more and more people will be entertained with such a form of entertaining. So the Chinese economy is growing, there will be more money for virtual gifts, there will be more phones, more internet, more everything. And you have to understand that such entertainment platforms are one of the only sources of entertainment and shopping for a Chinese citizen that is living in some lower tier cities. So the investment case I prefer YY however even MOMO I think will do well because at such a low price earnings ratio and the expected growth of 30% with the high potential it also looks like a good company. What are the risks? The risks are regulatory implications however both YY and MOMO have all the necessary licenses and the regulatory risks are more oriented to smaller players that went more into pornography than into entertainment and the government banned them immediately. Other risks, competition we have Alibaba Tencent coming in with their live streams but they are more oriented towards selling products, commercializing. So a bit different than MOMO from what I have seen. So given the growth of the whole market I think both YY and MOMO with their stable customer base will continue to grow and continue to monetize their projects. Very interesting stocks. The stocks jumped recently so it's a bit higher but the potential is very very high. Please leave your comments below your thoughts about which one is better MOMO, YY and if you have any questions please ask them in the comments below. Thank you for watching don't forget to subscribe as we will dig into I think more than 10 Chinese companies and I'm sure out of the 15 that you will get information here that you will find some good investments for your portfolio. I'll see you in the next video.


The next special element that might exist in a set that I want to talk to you about very quickly is just the inverse element the inverse element In this element Let's just have a look at that. So again, we're going to have a set of elements x. We're going to have a binary Operate operation on that. Let's make it that and we have to have a unique an identity element So there must be an identity element here My identity element. We're just going to make that U Just that identity element and now I'm going to have Two elements in that set x sub 1 and x sub 2 they are elements of my set And I'm going to say I'm going to define again as human beings. We define it this way We decided that x 2 is an inverse element of x 1 if the following holds So x 2 is an inverse element of the following if the following holds That if I take this binary operation That is going to equal this basically but that equals The important bit is that this equals the Back to the identity element A nice example a very easy example if we just take the set our set to be The rational the rational numbers Let's say that my element that i'm looking at x 1 is 3 what would be under my binary operation being multiplication Multiplication What would it be? Well, if that is 3 then this is going to be a third because 3 times a third equals 1 And we defined 1 under this for this set Under this binary operation We define this as the identity element which we have there So that is our definition of an inverse element


Conceptually, we understand that the area moment of inertia represents the bending stiffness of a given cross-sectional geometry about a given axis. But how can we go about calculating it? It is just a mathematical expression, and you could argue that you simply need to evaluate it, and you would be right. However, with a bit of understanding of what the quantity represents and a bit of clever thinking, we can greatly simplify the calculation, as we will see in this video. First, let's briefly recap the two area moments of inertia we have encountered so far and what they mean. We encountered the first moment of area, or the integrals of x times dA, and the integral of y times dA, when locating the centroid of a geometric shape. We often denote these moments of inertia as qy and qx, where the subscript refers to the axis which the moment of area is calculated about. We can use these moments of area to calculate the location of the centroid for a shape with respect to a reference xy coordinate frame by dividing the first moments of area, calculated with respect to this reference frame, by the area of the shape. Conversely, the area moments of inertia, which is often referred to as the second moment of area, quantifies the geometric bending stiffness of a given shape about an axis. It is defined as the integral of the perpendicular distance from an axis squared multiplied by dA. So for calculating the area moment of inertia about the x-axis, this would be the integral of y squared dA. If we zoom into our element, we see that the area element has an infinitesimal width of dx and infinitesimal height of dy. The area of the element is thus simply width times height, or dx times dy. This means that our integration is in fact a double integral. We have to consider the summation of all columns and rows of differential elements. In most practical cases, we can reduce this back to a single integral by making some smart choices with our differential element, as we will see in a moment. Enough with the theory already. Let's just get to the business of calculating. Okay, well, I'll hand it off to you then. It's about time. So let's take a look at the following problem. We have a rectangular cross-section of width B and height H with two defined axes systems. We are asked to calculate four area moments of inertia associated with the two different axes systems. Ix and Iy are to be calculated for the x-y axes located at the centroid of the rectangle, while Ix-prime and Iy-prime are to be calculated for a parallel set of axes, the x-prime and y-prime axes system, located at the lower left corner of the rectangle. Let's start with looking at calculating the area moment of inertia about the centroidal x-axis. By definition, Ix is equal to the integral of y-square da. As we saw earlier, this is technically a double integral, as a standard area element will have an infinitesimal width dx and an infinitesimal height dy. However, we can be a bit smart in how we define our area element to simplify this integral. Our integration is effectively the summation of the function y-squared times area over the entire cross-section. So if we take a contour plot of the function y-squared and overlay it onto our geometry for the given axis system, we can visualize what we are effectively summing over the domain of the shape. As our integral is an infinite summation of area elements where the function being integrated does not vary, the area element needs to be infinitely small so that the value of our function, y-squared in this case, is constant over the area element. But we can see from the contour plot that y-squared is actually constant across the entire width of the section. Can we exploit this to simplify our integral? Indeed, we can take advantage of the fact that y-squared does not vary across the width of the rectangle and expand our differential element across the entire width of the section. DA thus becomes B times dy, which reduces our integration to a single integral as we do not need to worry about translating the differential element in the x direction anymore. In order to encompass the entire domain of the rectangle, we need to integrate between the limits of y equals negative h divided by 2 and y equals positive h divided by 2. This leaves us with the following definite integral. Now we are ready to integrate the expression. Integrating B times y-squared, we get B times y cubed over 3, which we need to evaluate between the limits of negative h over 2 and h over 2. Substituting in these limits, we get that ix is equal to B times open bracket h cubed over 24 minus negative h cubed over 24, close bracket. Simplifying this, we obtain the expression B times h cubed over 12. This is our final expression for ix about the horizontal axis passing through the centroid of a rectangle. Before we look at the area moment of inertia about the y-axis, let's first consider the area moment of inertia about the axis parallel to the x-axis, the x-prime axis. Since the x-prime axis is parallel to the x-axis, our formulation of the area moment of inertia is nearly the same as before, just with x-prime and y-prime as the coordinates rather than x and y. This results in the ix-prime being equal to the integral of y-prime squared da. We can use the same differential area element as before, only in the new coordinate frame da is now equal to B times y-prime. To evaluate this integral over the entire domain of the area, we can observe that the limits of our integral change with the new coordinate frame. Rather than varying between y equals negative h over 2 and positive h over 2, y-prime will vary between 0 and h. So despite the result of the integration being the same, the overall result is dramatically different due to the different limits. ix-prime is equal to B times h cubed over 3, which is 4 times larger than ix. I see you notice that ix-prime is 4 times larger than ix, but you determine that by performing the integral again. Don't you recognize that there was an easier way to calculate ix-prime if you already know ix? But I calculated the integral. Isn't ix-prime just the integral of y-prime squared da? How could that be easier? Well, the x-y coordinate frame is a centroidal coordinate frame. So ix is simply the bending stiffness about the axis we have to consider when we reduce a section to a single point. The rectangular cross-section is equivalent to the single point at the centroid with the same area as the rectangle and the bending stiffness ix we calculated for the rectangle. So rather than performing the integral on our rectangular area, we can do so on our simplified point model. Here we simply have to sum the various contributions to the area distribution about the axis in order to get ix-prime. So ix-prime is equal to ix, the area moment of inertia we have to consider in reducing the rectangular section to a single point, plus the distance from the x-prime axis squared times the area of the point. Here we have to recall that although we reduce the section to a single point, we still consider it to have the area of the original section. Although we did not rigorously derive this expression, you can indeed mathematically prove that it does hold, and it is known as the parallel axis theorem. Here we will use the bar symbol above ix to explicitly state that the x-y axis must be the centroidal axis of the area in order for this theorem to work. If you are interested in the mathematical proof, it is available in your textbook, or you can easily find it online. I'm not so interested in you knowing the proof, but understanding what the theorem means and enables you to do. If you think about how we calculated the location of a centroid for composite shapes earlier in the course, you might already recognize that this theorem allows you to effectively do the same for area moments of inertia. For completeness, this theorem also applies to other axes. The area moment of inertia about the y-prime axis can be calculated by adding iy about the centroidal axis plus the area of the cross-section multiplied by the distance between the y-axis and the y-prime axis squared. I guess that would have been easier. I'll make sure to take that into account in the rest of the problem when I calculate iy and iy. I will only need to integrate once to calculate iy. Since iy is equal to the integral of x squared da, I will have to define a new differential area element of constant x. This can be achieved by spanning the element along the entire height of the rectangle, resulting in da being equal to h times dx. After performing that integral, I can then use the parallel axis theorem to calculate iy-prime. I guess you could do that, but is it really necessary? Take a look at your shape and the new differential area element for a minute. What would happen if you rotated the entire system counterclockwise 90 degrees and then flipped them around the x-axis? Okay, so rotate the system 90 degrees and then flip around the x-axis. I get something that looks like this. Since I moved the axis and the shape together, it shouldn't change the solution. Correct. Now compare that to your previous solution for ix and ix-prime. Comparing to my previous solution and... Oh, well, both shapes are rectangular. There's just a swap in the dimensions and axes. So I can infer that iy and iy-prime for the image on the right would be equivalent to ix and ix-prime for the image on the left, with the width and the height dimensions swapped. iy would then be equal to h times b cubed over 12 and iy-prime would be equal to h times b cubed over 3. With that, I have then solved for everything the question asked for. We solved for ix and ix-prime directly using integration, although I could have saved some time using the parallel axis theorem, and we were able to infer what iy and iy-prime are due to the similar distribution of area about the x and y axes, just with the dimensions swapped.


Studying climbing my grandfather by Andrew Waterhouse. Here's how you can analyze this poem. In terms of structure, this poem is one stanza of 27 lines. The poem opens with this alliteration and says zero, setting up the speaker as a climber and the grandfather as a mountain. He uses the words old, dusty and cracked, which belong to the semantic field of age, to emphasize how old his grandfather is. These words belong to the extended metaphor of mountain climbing. He's using this metaphor as a way of getting to know his grandfather. These words, which belong to the semantic field of body parts, show the tough life his grandfather led. Yet even if he had a tough life, this simply shows that his grandfather is still a soft person at heart. The Anjomwant here, as well as the Cesiro here, shows how he sees his grandfather as someone who he can lean on. The Ascendant here shows how curious the speaker is to get to know his grandfather. He reaches a summit and this is a metaphor for reaching the top of his head. He feels like this journey has taught him a lot about his grandfather.