Hello, friends, myself, Sanjay Mutt, assistant professor from Mechanical Engineering Department of Vulture Institute of Technology, Solapur. Today I am explaining regarding the how to draw the orthopic projection, that is introduction part of the orthopic projection. The learning outcome for this topic is student will able to discuss the basics of orthopic projections. In orthopic projections, here you have to whatever the three dimensional view or object placed in front of you, you have to convert it into two dimensions. When you have to convert it into two dimensions, you have to draw the front view, top view and side view. I am explaining later one. Secondly, it is a form of a parallel projection in which all the projections lines are orthogonal to the projection plane. The pioneer of this orthopic projection is Gaspard-Boneject. Now, I am showing this three dimensional colored view, colored, so here you are observer and here is object and here is the screen, a parallel vertical plane, which is front of you, which is parallel to your eye side, this vertical plane. And in between vertical plane and the observer, the object is placed in between them. When the ray starts from your eye side, when it gets collides with that object, whatever the shadow, you get it on that plane that is called as a view. So here you get a shadow on that vertical plane, on that projection of plane, that is the plane of projections and this colored one that is a shadow, this is called as a view. Imagine that, suppose this plane is obscene, object is here and you are observer and the ray starts from your eye side, it get collides with that object, you will not get that image. So to get that image, you have to take a imaginary plane, a vertical plane. Same thing, one more plane you have to take it, this plane is parallel to your eye side. And one more plane you have to take it, which is perpendicular to your eye side, that is called as a horizontal plane. So that I will show you. So this is a vertical plane, just I am explaining, which is parallel to your eye side. Another plane is there that is called as a horizontal plane, this is a parallel to the HRP, parallel to the ground, parallel to, sorry, perpendicular to your eye side. So this is a vertical plane and this horizontal plane. One more plane is there that is called as a side or a profile plane. When these planes are, there is a vertical plane, this one and this is a horizontal plane. When they get collides with each other, you get as a four quadrant, that is the first quadrant, second quadrant, third quadrant and fourth quadrant. So when you have to draw the orthopic projections, there are two angle projections are there. What is the two angle projections method? The first one is a first angle projection method and another one is a third angle projections method. What is the first angle projection method? Imagine that whatever the four quadrants you had to get it, when the intersection of the vertical plane and horizontal plane, you get as a four quadrant, in that four quadrant, this is the first quadrant, in that first quadrant, imagine that the object is to be placed in that first quadrant, whatever the shadow you get it, that is on the vertical plane and horizontal plane, that is called as the first angle projection method. What is the third angle projections method? Here I am showing the four cotton unit, first angle, first cotton, second cotton, third cotton and fourth cotton. This object is replaced in the third cotton whatever the images you get it that is called as a third angle projections method. Now I am explaining the first angle projections method. In the first angle projections method whatever the images you get it I am showing this colored one ok. Here is the front view. So, here is the observer. When you have to see that object whatever the images you get it that is the red color one and the bluish dark blue color is to be there that is the front one that is called as the front view and now you have to here is the observer you have to imagine that you have to rotate it through a 90 degree. You have to see that object from the top view from here from the top view. You have to rotate it yourself through 90 degree and you have to see that object from the top view whatever the images you get it that I am showing below the reference line that is it is greenish one and this yellow blue color one is to be there that is called as a top view. And one more view I am showing here is the observer then one more view I am showing here when you to go to the right hand side view. Here is the observer I am seeing that object from the side view. When you to see that object whatever the planes are parallel to that is a yellow color one again the green color one so it is a side view. Here I am showing that in the first angle projections method here is a reference plane the front view is above the reference line and the top view is below the reference line and the side view whatever the side view I am showing here right side view I am drawing in the left hand side. Now you go from shift to the third angle projections method. In the third angle projections method you have to assume that the object is placed in the third quadrant and this colored views I am showing here. Here is the observer when you to see that observer from in this direction whatever the images you get it that I am showing in the front view. But the basic difference between the first angle projections method and the third angle projection method is the first angle position method object is placed in the third quadrant. So that's why this front view I am showing above the reference line and top view below the reference line. But here the third angle projections method the object is placed in the third quadrant. So that's why front view is below the reference line and the top view is above the reference line. So that is the basic difference between the first angle projections method and the third angle projection method. Now I am showing some lines here you have to draw it the visible lines which is a dark one hidden lines are there that is a rotated one center line one lot is to be there in these are arrows to ends that is the dimensions lines and construction there is a fair one. These I am showing here you take example for this one in the direction of arrow I this is the object and you are observer here when it to see that object you get as a plane rectangle as it is this rectangle as it is. But these edges are there they are invisible from the front view. So that's why you have to show the dotted line. So this construction line you have to hidden lines are there on the same thing when it to same object here the observer and you see that object there are you get a three rectangle the first rectangle second rectangle and the third rectangle because these edges are visible for you. So that is the basic difference between these two objects. Now I am taking a simple example for this one here I am drawing the reference lines and in the direction of arrow I am seeing that of that is the front view when I to see the front view this what you call blue color dark blue color plane as it is and the red color is as it is. So it is a two planes. So what about the this brownish color you know is there think all that what about this plane the answer for this one is to be whenever we see that object in the front view this plane this brownish color plane is perpendicular to your eyesight. When the plane or a line is perpendicular to eyesight you get as a line age view for this plane it is a age view. Now I am going for a rotating through a 90 degree and see that same object from the top. When you see from the object from the top view which planes are parallel this yellow color one is there and this brownish color one is to be there. Okay this yellow color and brownish color I am drawing then what about this red color think all that what about that plane where how you have to represent it just I am explaining previous one in the front so what I am saying in the last previous one when you have to draw the front view when any plane just like now this red color plane is to be there and when you have to see that object here you have to see that object when the red color is to be there this plane is perpendicular to eyesight. So the plane is act as a line or age view that age we are showing here. Okay now I am going for the side view here is the observer I am going for the side view how to draw the side view draw the 45 degree line draw the respective generators vertical generators and horizontal generators and through 45 degree rotated it and when you have to see that object whatever the planes are parallel to you you have to draw it then what about the brownish color here. Again you have to think all that how you to draw it. Yes exactly in the previous one I am showing this brownish color as a age view in the top view this red color plane as a age view now again when I have to go for the side view this brownish color plane is a age view. Okay so this is a simple orthopedic position it is called as a front view it is called as a top view and it is a left hand side view for this I am taking the reference of NPTEL okay thank you.


in today's video we are opening an ultimate rare old school collection what's up guys we're back with another epic video opening some amazing cards in this collection but first we have a giveaway i'll be giving away these 14 darkwing blast first edition packs there's a 17 dollar super in here there's a 50 dollar ultra rare so could be some pretty good packs just like the video be subscribed turn on notifications and i want to remind you guys to go check out the community tab if you haven't yet because there you can see if you want a giveaway also speaking of giveaways if you get a telegram comment in the comments that is a scammer i've said this many times but not enough apparently because a lot of people are still asking me is this a scammer but it feels like most of you guys are knowing at this point but i just want to remind you guys one more time let's hop into the binder this is a binder opening you guys know how that goes so we're gonna cut from the face cam go right to just the binder footage so you guys can see it really well and we'll hop back and forth between that all right so we have an ojama king this is a bunch of ultimate rares and secret rares from gx for the most part we got a manama naga very nice there's a new one there's the arm dragon level 10 that's actually a really cheap ultimate rare which is kind of weird we've got the burst oh there i am look face cam we've got the burst dream of destruction we've got ourselves a bunch of decent stuff okay a little bit old school here which is nice all right so we're going from the underworld that's first edition and first edition ring of destruction then over here we have oh the sacred beasts from shadow of infinity the ones we have never pulled by the way cybert our dragon armatyle very nice first edition mystical elf and we're looking at some good stuff stardust dragon unlimited you got destiny and dragoon i mean there's a lot of really really nice stuff in your call of the haunted we've got our old vindictive is that from champion pack that's really nice we've got ourselves the ojama king first edition which is cool the ooh a little uh diamond due turbo over here very nice d time little d time you know i'm saying all right next we have a elemental hero tempest that's an ultra rare unfortunately that'd be really cool if it wasn't if you know the ultimate rare we've got the flame wing man should have brought that to get signed by jade and that would have been pretty cool i didn't get anything signed because lines were pretty long and i i missed them unfortunately we've got dart neos so these are all appear to be ultra rares for the most part see if we see any ultimate rares these all look like to be their ultra rares which is still a really cool collection all right inferno wing we've got thunder giant flame wing man we've got some secret rare stuff these are from the the e h c these are actually pretty valuable secret rare versions of the elemental heroes which is pretty cool spark man all the vanilla's the emergency call the hero blast okay i don't say elemental hero blast which is basically is it just doesn't say that all right very nice skyscraper is pretty cool for the heroes if you play that in a skyscraper hero deck back in edison miracle fusion is really really nice gonna end up hanging on to that one probably for my uh edison deck the secret rare neos he finally did get a nice printing in the pharaoh rare but that took him a really long time there's a wing caribo wing caribo level 10 transcendent wings i love that set that's cool to actually have grand moles in here oh okay we got the dark panther it's sliding down a little bit let's fix that that flare scarer we've got hummingbird another wing caribo wow that's really cool all right now we've got air neos the forbidden yugioh card another element to it man this is a really nice hero collection this is really cool magma neos we got gaya we've got two bubble man we've got the lightning golem man this is super nice rainbow neos ghost rare if that's in near meant i would probably actually need that for my collection of you know the binder collection we've been doing a couple of wild wing man those need to get back in there we got a call here the ulti's okay plasma vice from glass though we've got two flame wing man we've got a couple of thunder giant we've got a dark bright beautiful really really cool rampard blasters wow we've got a wow okay this is a really really nice collection this is going to be really expensive oh my goodness we've got the glow neos and yeah make sure to let me know in the comments how much we should pay for this but this is going to be a pretty big one that's a an unlimited tempest if it was first edition we would probably be broke right now i've got a oh pot of greed what does it do i'm not sure what that says chaos neos beautiful i think i need that one that's really really nice and then we've got glow neos and is this the uh i think that's the gold letter yeah so that's actually the real one which is cool then we have grand neos oh my gosh look at these thunder giant insane like this is insane oh my gosh UFO road fighter a favorite of mine i like that cyber twin three ancient gear golems oh my gosh we've got a couple of flame wing man one unlimited one first edition oh my goodness wait we will be checking out some of these afterward like we're going to get up close and personal with some of these don't skip that that's a new to warm tp3 by the way oh my gosh yeah so i am going to be purchasing this i know sometimes i don't purchase them uh we are most likely going to be purchasing this because we've kind of discussed the terms ahead of time a little bit so yeah hit me up if you want any of these it should be working out i think one of the recent collection videos i didn't end up purchasing but oh what in the world okay we're okay this is this is going to be a big collection that is the sacred beast ultimate rare wow oh my gosh there's another one right there that's unlimited oh my goodness dds dark magician this is maybe the biggest collection we've ever bought wow the uh the phoenix enforcer the cyber and dragon oh there's an ultimate rare forbidden yukio card wow this is insane this is insane super poly he kind of told me what he had but i kind of forgot how much was it i don't think i read all the cards because this is insane i think i need that card that's like a twenty dollar card i'm like oh i need that card overload fusion also really nice oh the uh is that rush tool very nice okay we've got a rampard blaster then we've got a another chaos neos which is cool hopefully one of those is really nice okay i'm gonna have to get that out later but we've got another wingman a cyber dart dragon and a cyber in dragon wow all right let's see if that is the end because okay whoa rush tool we got potting greed we got ash blossom and then another dark magician girl i think that's the end so ending with a little rush tool all right let's get up close and personal with some of these and just see what they're looking like all right let's check out a few of these cards see what they're looking like first the utopia ray which first of all is hitting right now check this thing out it does have some scratching on it which you guys can see i always think it is weird how these like these lines here they're actually supposed to be there it's kind of weird they kind of look like scratches uh there's a few scratches on here it's actually pretty nice overall pretty excited about that i'd say it's near mint uh it's hard to have a ghost with no scratches so just a few scratches they usually consider near mint i might actually need this because it's unlimited so those unlimiteds are kind of weird to find so i'm definitely happy to have that i just checked that one out for my binder but for the rest let's check out some nice ones we have an air neos here all right we had a triple sleeved card so that's nice we have air neos the forbidden yugio card ultimate rare it's all there's something going on down there let's see this card looks really nice on the front nice on the back it does have of course the imprint which is not really a conditioned thing so like you know if it's like at least near mint and that's good you know that's all we're really looking for it doesn't have to be like psa 10 condition that looks really good though uh that is definitely near mint forbidden yugio card beautiful all right that's i mean that's a nice card so uh this is gonna be quite the collection for sure this is a very nice collection let's see so these are all triple sleeved i'm gonna try and pull them out very very carefully these small sleeves are kind of sketch sometimes but it looks like they're coming out pretty decently so we have the cyber end a dragon this is an ultimate rare this is not the euro print this is the n a print you can tell because it's a little flatter not as much texture back looks really really nice for sure oh wow that looks really really good okay so we're talking like very good condition on some of these cards so this is gonna be this is gonna be an expensive collection all right here's a card that i don't know if i've ever owned maybe like owned once or something but i don't own one now dark magician from dds the game promo this is before they switched to cr ru and the you know the pink guy and all that stuff all right let's uh let's get this thing out of the triple sleeving be careful with it because all these cards appear to be in great shape dark magician dds okay back got some weird stuff going on with it what is that i don't know what that is we're gonna have to check that one out so i don't know i don't know about that one the front looks good it's got some weird stuff on the back but i mean it's not like bent or anything which is good you know that's always a good thing so dark magician we'll check that one out later just one more quick look at that that looks great the dds just has a really nice pattern to it all right sacred beast time let's go wow uriah first edition lord of searing flames okay these look really really good this one's not as perfect as some of the other ones but it's still pretty good condition overall very nice uriah lord of searing flames very beautiful all right raw vial let's see how he's looking all right so that was definitely i would say okay but maybe the dark magician was the worst that was like one of the worst conditions and it was still looking pretty good you know compared to some of the collections we've picked up recently which have you know had some you know more played or old school cards that people played with raw vial lord of phantasms that looks really nice wow check these cards out we are talking about some serious cardboard today we are talking about some nice cardboard that definitely has some scratching on it so we're not looking at near mint probably on that one but still very nice card either way beautiful all right come on time so far these these two have been like maybe like lightly played something like that off to really check them again but they looked for the most part pretty good besides the back scratching oh this one was not treat three sleeved it was only two sleeved okay i'm on lord of striking thunder ultimate rare and looks pretty good a little bit of edge wear at the top maybe back actually not bad like a slight stuff in the middle but overall this one's pretty decent honestly they're all in decent condition they're just not like you know mint or whatever just give those a look ultimate rares that is insane you don't see those very often i mean those are expensive cards for sure all right now we have the rainbow neos from phantom dark it's just unlimited but wow the ghost rares guys they look so good the originals especially wow all right looking good looking good slight scuffing but overall very nice card here i mean that's probably near mint i would say beautiful beautiful rainbow neos now we have a tp3 worm i haven't had one of these in a while like i used to have one and then i sold it i got one from sasiatto a really long time ago then i sold it i was buying something i don't remember what it was and then you know haven't had one since then surface looks good it looks good back surface looks pretty good i mean there's a couple like they're like not really dense but they're like they're like small in dense there's a little bit of stuff going on there overall this is a pretty good condition card pretty fair at least fair is probably an understatement but you know i think that's like a real condition that using like Europe or something here's one i don't know have i ever owned this card i think maybe a long time ago i had one because like back once cards were like 300 max i owned a lot of cards you know and then that you know if they changed hands and stuff i sold them or whatever but they got a little bit too expensive to like pick them up anymore here we go flame wing man we saw one of these at collector con yugimo picked it up there's a little scuffing at the top we're not scuffing but uh edgeware that's like it though this card looks great if it wasn't for that scuffing but or not scuffing if it wasn't for the edgeware this card be like literally amazing like really really nice but still awesome we're not going to go through every card because obviously there's way too many nice cards here but i did want to show some of the big ones to see like you know you guys can let me know how much you think this is worth because we're talking big cards in good condition so we don't have that every day so let's see what we can see out of here ancient gear golem ancient gear golem beautiful card beautiful card i've tried to grade like these multiple times and i always get nines this one looks like a really nice card like this one looks minty this one looks great i've had a couple that look like this they both got nines so we'll have to see all right tempest time time for a little a little storm action elemental hero tempest is unlimited but it also looks like a euro print which is really nice very very beautiful back looks very good i mean this card just looks great i mean very nice looking cards here chaos neos here we go beautiful beautiful wow that is super clean on the front backs cleaning stuff that has this line through it which having something it's almost like a roller mark like in magic that's what kind of what it looks like it's like not like a print line it's just like a weird kind of not dent either i don't even know how to print line out of the roller marks how i would describe it all right let's check out this rampart blaster for the last one because we have spent a little bit of time checking these out i think this is one we can check out i do have a ps a nine of this card that we graded from collecticon which is pretty cool but uh this is a euro print one check this out really nice i mean you can tell looks a little bit different than the uh the american print back looks pretty good i mean we are talking great condition for the most part on average near mint on this collection like most of the cards that i've checked out so far near mint some are slightly below some are slightly above this is going to be a fun one i mean this is going to be quite expensive so i hope you guys enjoyed seeing all these awesome cards because this is one of the coolest collections we've ever picked up i'm really excited to actually pick it up a few moments later all right i just wanted to add this little part to the end of the video because we recently didn't buy a collection that i showed a lot of people message me like hey can i buy these this one we did end up buying and we officially just closed the deal i paid for it it was seventeen thousand five hundred dollars you can let me know if your guests at the beginning were close you know you guys can see whatever you're thinking because a lot of people comment before the end of the video which is good so that way you can uh you know see how you did right there but uh this is the most expensive collection we've ever bought and i think it was worth being that expensive because these cards actually turned out to be for the most part really nice condition what you saw on the ones we looked at were pretty even across the board like most cards were like that very few under light play there was a few like mod places like binder dings or whatever but barely anything almost everything looked really good so i wanted to add this at the end let you guys know that uh i did buy this collection so some of this will be for sale of course because can't just eat seventeen thousand five hundred dollars but actually some of this i think maybe we'll send in a PSA which is going to be pretty fun so look out for those PSA graded videos i'm actually really excited i don't think most of it can be graded but some of it can and some of the nicer stuff we're going to send in probably at the faster rate and get it back in a couple weeks so there's the update if you guys enjoyed the video make sure to subscribe to the channel for more epic content shout out to toe info show daxter tomato juice jt chode tcg trusted cards puffins of doom or nesto diana dizzy flexi boy hopis choice three three three miss cycle melancholy and then his high show christopher warden moosa john nolyn junior barding mike nance mimic gecko stanley and thomas bookland thank you guys for supporting the channel and i'll see you guys in the next one peace


So, I am here to talk about the physical web, but this is going to be a little bit more of a change, a little bit more of a personal conversation because I want to talk a little bit about the journey about what I've discovered along this process. First, I have to ask just how many people here know about what the physical web is? Can I just see a show of hands? Because I don't think not many people of you know about what it is and so I'm happy to talk more about that. The one thing I will tell you is that the physical web is shipping right now and it's available to you right now. Beacon has been here the whole conference, has been broadcasting the agenda for this conference. If you have an Android phone and you have Bluetooth turned on and you've got data, you can see the various beacons that are in the room. And by the way, is Tim Perry here? Tim? He's not here today. He was basically broadcasting the URL as well so it wasn't just him. And you can actually see the URLs that are being in the air around you and pull it down. If you happen to have an iPhone, that's okay. You can also just have Chrome and it's not quite as easy. Android, it's built into the operating system. But for Chrome on iOS, you basically just turn on in the TodayView widget the Chrome widget. It's a few steps. It's not the easiest thing to do. It's not as easy as Android. But you can also see these URLs in Chrome as well on iOS. So I've been speaking about this for about four years now, both initially at Google. I left Google for a couple years and then I came back. And this is just a list of a few of the conferences that I've spoken at over the last four years. And it feels like a long time. Someone once said that the physical web is Scott Jensen's personal quest. And I feel like that sometimes. But I feel like I've learned so much in the process and it's been so interesting. But too often, people don't really appreciate what it takes to bring an idea to a product. They often think that you have an idea.  And actually, the process looks a little bit more like this. And this idea of how long it takes and how it works and what you have to do to kind of get it. And honestly, for the physical web, we're kind of somewhere in the middle. I think we've got it shipping in Chrome. We've got it on Android. We've got an iOS. Opera has got it. So it's an interesting state that it's kind of getting started, but it has a little ways to go. But more than anything else, this whole process has just taught me just how amazing the web is and what it has kind of given back to the physical web project. So the subtitle of this talk is really how I stopped worrying and loved the web. Because the web has added so much to the physical web, it makes us look better than actually I think we originally started to be. So let's take this talk in three parts. Part one, what is the physical web? I think I'll take a few minutes explaining it to you guys what it is. Part two, what did we learn? How did it kind of influence what we learned of the web in general? And part three, where can we go? What can we do with this technology? First, what is the physical web? We've all seen these smart devices that are coming out now. There's smart TVs, there's smart vending machines, there's even smart bus stops. And the problem is every single one of these devices has its own application. Even this conference has its own application at a web conference. Sorry, I can't help but just teasing the guys a little bit about that. But if we were to believe in Moore's law at all and there's going to be even more of these devices in our lives, what's going to happen in six months when we basically have a few more devices? In a stadium or an airport or a train or even a little bit longer and we have even more devices? Are we really going to be installing an app for every single device we want to talk to? They just can't possibly scale. Well, we actually have a technology at our disposal. The superpower of the web is interaction on demand with a single tap. You can be anywhere, within seconds. That kind of seems useful in this situation. So how would we do that? Because over the last 25 years the web has made amazing strides and so many neat technologies like WebVR is there, but all the magic goes in this little white DOM box. We've hardly ever really touched this area on top. You know, the URL bar. Now, really, there's only two ways you can leave a web page either by clicking on a link or by typing something at the top. We've taken the most amazing rendering engine on the planet and we've strapped a goddamn DOS prompt on top of it. Really? This is how we aspire to do. It's about time that the web became mobile like the phone that it is in. In effect, we are living in this lovely island where we can go from room to room with a click but we don't ever really escape out of that into the rest of the world and that's the whole point of the physical web. How do we have a discovery service for the web so that I can walk up to something and get it to URL without having to fiddle around with it too much? So the intention here is let's say I walk into a space where these devices have a URL. I'm in there and I want to be able to discover what is around them but I don't want to just see the URL. I want to basically fetch and get some information about them and rank them so I can get a list that says oh, here's a vending machine and here's a bus stop and then if I pick one then it just takes me to the website. I kind of get in and out very quickly. So let me show you how this works. Here's a parking meter demo that we built where I'm pulling down the notification manager. I can see the URL being broadcast. I pick it and now the physical web is done. The physical web is done. We're on a website now and all you're seeing is web sockets. It's just setting a web socket event. So I hit up, up, it makes that go up. I hit pay and then it starts counting down.  But that's all it really is. I'll admit I cheated a little bit. I assumed I had already gone through it once before but it was kind of a payment system. But even then you'd be like, well, what do you want to use? And people always ask, well, what's the payment system? I don't know. It's the web. Pick whichever one you want. That's the whole point about the web. You just would pick something and then from then on it would just work really easily. So the idea of the physical web is to bridge the web in physical devices. And so I would walk up to the payment meter. It broadcasts. I see it. But there's a couple of critical things to say about it. First of all, it's open like the web. You're trying to sell you a Google product. This is like web sockets or React or any other type of open web service. It's meant to be used by any company. It's also just a web page.  It flips the whole thing on its head because every individual device could have its own unique web page. And it's really meant to be a walk-up and use type of thing. If I'm up in a park and there's a really famous statue that's there and I want to learn more about it, I'm not going to download the app. I just want to pull it up and get more information about that particular thing. But here's the most important thing. This cannot be an interrupt thing. This cannot vibrate in my pocket. This can't generate because it will be the most amazing spam vector on the planet. If I could walk into a mall and my phone would dance out of my pocket anybody who remembers Bluetooth messaging in the 90s it would be like that. So this has got to be a user-driven thing. We have to respect the user's attention span and only do it when they ask to see it. So how does this work? The intention is that that parking meter has a little beacon and it's just broadcasting. A URL. If you know Bluetooth Low Energy, it's called the advertising packet. It's a small packet and it sends out a URL inside of it. That's really important. We don't use some ID that requires a Google server. It's just a URL. That means any scanner can see that and take you to that web page. By definition, this is not going through any company's specific server. The phone comes by, sees it and goes, hey, you want to see it? And it shows it to you. So the simplicity of this is meant to be quite... a device that's broadcasting a URL that takes you to the web. But I always get two questions, and so I might as well answer them right now. The first one is, isn't this just QR codes? Well, yes. Technically. But QR codes kind of suck. And I kind of describe this as saying, we're like QR codes, but we're awesome. There's a big difference to it because we've seen QR codes. QR codes have been tried for many, many years. We've seen them in malls with things like this. Have you guys seen the Tumblr? There's a Tumblr page that's called Pictures of People Scanning QR Codes. Have you seen this one? Now, to be fair, the QR codes have been successful in some countries, but they tend to be on things like receipts and posters, and they're very, very limited in very, very simplistic use cases. So it's not like QR codes are by any means a failure, but they're very, very narrow. And it's so much easier to imagine a room with multiple things in it. And how can I see what's available to display to me? Or what about something that's far away? Do I really want to go really, really far away and go over and try to scan it when I just want to pull it down? So, and by the way, no one's putting QR codes in their products. That'll just never, ever happen. I can promise you that. So it's also just simply a matter of just making things look a little bit nicer as well. So the second question I get a lot is, isn't this going to be spam? A little spammy? And I think there's two aspects of that. One is the fact that it could be spammy, like phishing and so forth. And the other one is just simply lots and lots of things. The first one is, yes, I think there is a little bit of a risk, but it's inherent within the web itself. The browser will already protect you to a certain extent. But just to be safe, the scanner that we wrote actually has a proxy, takes all the URLs, puts them through a spam filter to try to filter out some of the worst offenders. This operas browser does the same thing, but it uses their own scanner, right? It's a feature of that particular one that can be implemented by different people. As far as being able to handle lots and lots of devices, that's going to be a really great problem to have. And I expect that over time, we're going to kind of have this UX evolution. Initially, it will show you what we find. Then we'll start to rank them based on distance. Then we can rank them based on your preferences. We could even then start to group them into folders. So there's a lot we can do as this grows to handle more and more items. So that was just my quick 10-minute overview of the physical web, just to give you a rough idea of what it was like. But now I want to talk about what we learned, because honestly, we started off with kind of a simplistic idea. We're just going to find URLs and show them to people. And in the process, I got a much deeper appreciation of how awesome the web is. So the first is this fact that we use a URL. I want to talk about what we learned about URLs. And the second is to talk about the web itself. So URLs. The actual advertising packet for Bluetooth Low Energy is currently 31 bytes. That's fairly small. Bluetooth 5, which has been ratified this month, in fact, will be shipping next year. We'll actually let that be significantly longer. But right now, it's only 31 bytes. And if you actually take a look at what you can put into the actual frame, it's 20 bytes. And after you include a couple of, you know, header bytes in there, really the URL that you can fit is 18 bytes. It's a little small. Now we have a compression scheme in there. So things like HTTPS colon slash slash dub dub dub dot can be compressed into a single byte. A lot of the demos I'm going to show you today are on pwdemo.org. And that can compress down to six bytes. So you can fit an awful lot in there. But most people have to use a URL shortener. And this is kind of what happened. Whenever I tell people I have to use a URL shortener, I kind of get this reaction. Which is like, you're kidding. Really? I have to use, like, no. Just get the hell out. No. But it's actually not that bad. In fact, I was initially really frustrated with the fact that I had to use a URL shortener because I didn't want to do it either. I wanted to put it in my website. But it turns out that URL shorteners are kind of awesome in a way that I didn't really expect. Because what can happen is if you have a URL redirector that takes that. The shortener is one thing, but then it redirects as a three or three, right? You can actually change that dynamically. So there were companies that immediately jumped on this and created a timing system. So in the morning, it would go one place. At noon, it would go to another. And in the evening, it would change. So you could actually have a timing and it could kind of dynamically go. I had never expected that. It's kind of cool. So in fact, when people use a URL shortener, I recommend that they use one like tiny.cc. Because tiny.cc lets you change it after the fact. Good.gl is fixed. And we're actually working on that. But the other thing that we also had when the URL goes nowhere, it's 404 is into nothing. We won't show it.  So you can actually have this beacon broadcasting all you want to and nobody can see it because it's 404s. And then when they want to turn it on, they flip the switch. They've effectively taken beacon management and put it entirely in the cloud. That kind of blew me away. The other thing that's annoying physical web beacons compared to iBeacon is about ten times cheaper because you don't have to fiddle with specific beacons in specific locations.  And then after they're up, you can then redirect them to wherever you want to go. The other one is this company called Ruvio. They just was on Kickstarter. They have a new open source beacon that's really quite good. And what they do is they have a URL that actually encapsulates and they just compress it so that when you hit that web page, it takes that off and then tells you the temperature and the pressure and the speed and so forth. So the URL becomes a carrier of dynamic information. Even though every beacon takes you to the same domain, what you see every time you use it is unique. That's quite clever. And the final one is the fact that, again, beacon and another company, another actually open source project by IO, effectively takes a time code on the end of the URL. And actually when you redirect it, they wrote their own redirector as well and they can actually validate that it was actually the correct URL at the correct time. So they can do things like coupons and so forth which have a time limited aspect of it. So I've always been really surprised how much value, and this is just how the web works. URLs is this universal thing that can be changed. Cool. Changes things a little bit more. The second point was about the web itself and we started three years ago at Google and it's been shipping now in Android in the last couple of months. But the web itself has gotten so much better and it just keeps making us look really good and it kind of makes that saying no one fails who bets on the web. I'm beginning to feel that way. Take a look at this restaurant buzzer example. In this case, pull the physical web down. You can see Bob's deli right here. You click on it, physical web is done. We're just going to the web. But now we're going to a website that actually is registering for push notifications. There's eight people in front and you say get in line. You've now subscribed to a push notification. In this case, you've opted in. Now when it's your turn in line, your phone will vibrate in your pocket because you asked for it and then it's your turn, you go in and you can kind of get your point in line. So you know those restaurants have a $25 coupon and it changes it all to the whole thing. So it's kind of an interesting way of thinking about it. We didn't do a damn thing. The web just got awesome. Here is a little remote control Bluetooth toy called Ali. And in this case, we're going to broadcast a URL to a web page and then when we connect to it, we're going to use Web JavaScript Bluetooth, Web Bluetooth, and we're going to connect directly to the device and control it with the web using JavaScript. So it says, yes, this is a debugging command we're going to get rid of, so we won't have to do that in the future. And then now you have a joystick and as you move the web page up and down, it drives it across the floor. No app, no nothing, and that device, by the way, has no internet connectivity at all. It's basically stealing all the connectivity from the phone itself. So this is a really quick and lightweight way to kind of have anything to be controllable just using standard web technologies. I think that's kind of awesome. Oh my God, the web is still awesome? We've had this kind of been beaten up.  And it gets kind of old after a while. But recently, I think we're finally beginning to realize the web actually is getting quite good and so many interesting things are happening. And to me, it all kind of came together how we can do this one little technology and these new layers are happening on top and it all kind of, you know, works together quite nicely. Because URLs plus the web, and again, maybe I'm just preaching to the choir on this, but I was really kind of deeply appreciative of the fact that they're just so damn flexible. We are doing a tiny thing with URLs and web pages, but people are doing really crazy inventive things on top of it that are kind of independent of us. And because we are doing this very thin discovery layer of just a URL, it allows people to do crazy stuff on top. But I don't want to pick a fight. About four years ago, I wrote a blog post called Mobile Apps Must Die. That was probably a mistake on my part because it kind of created, it set up this fight like web versus native and it got a lot of press and traction. And in hindsight, I realized I was picking a fight that we shouldn't do. There's no reason web and native can both do very, very different things and it's okay for them to both be around. What I have discovered with the physical web is the fact that the physical web enables interaction when apps just aren't practical. You want to play World of Warcraft? Great. Get an app. But if you just want to give somebody a little bit of information, well, then just use something a little more lightweight. So it's like each to each their own. So now that we've talked about URLs and we've talked about the web, there's a third point I'd like to bring up, which is thinking small. Because the issue with the physical web is that we came out with a Bluetooth beacon after Apple did iBeacon. And so almost 90% of all the questions that I ever get is trying to reinvent iBeacon with physical web. And so in this particular case I want to show something really, really lightweight, which is to say here is a fake pill bottle and it's a fake pill bottle with a fake prescription but my name on it. And the intention is to show what it would be like to have a very low power, very cheap beacon. They're actually expecting in less than a year to be able to buy these things, make these things for less than a dollar. In which case it just simply broadcasts a URL to the prescription, clicks on it, and then because the web browser knows my default language it can show me exactly the language I want. And it's nothing fancy. It's just showing a YouTube video and some information. Just lightweight, simple stuff that can be done very, very simply and easily. More about just information. And I feel like these lightweight scenarios are a totally different way of thinking about it. And I mentioned before about the smart toaster. You guys have all seen this before. You buy some new, brand new device. It comes in a box with URLs and QR codes and you unpack the device and it's the first thing you do, you throw the box away. And some poor marketing person loses their wings. Because the idea is they desperately want you to go to their website but we don't make that possible. Again, a toaster could just simply be a lightweight way to tell you a little bit of stuff. It could be how to clean the crumb tray, how to recycle it. It could even give you, once a month, give you a new toaster recipe if it wants to. But the intention is that we don't necessarily have to think complicated thoughts for this to be useful. The web is famous for this idea, this long tail of content that was talked about in Wired Magazine. The idea that the millions of tiny websites are significantly bigger than the three or four biggest ones. They really add up to this big, big, big amount of usage. And I think whether you believe in the vending machine example or the bus stop or the pill bottle or the toaster oven, each one of those is kind of ok, but taken together they create this big, much more long tail of interaction. How can we like interact and talk to almost any device effortlessly? And that's what we're trying to do and that's why this has to be a web standard. This can't be anything by a particular company. And by the way, people love to equate the physical web to the Internet of Things. The Internet of Things is cool. It's slightly overhyped right now, but this is just simply access to information and yes, it can bridge into smart devices but that's kind of an extra use case of it. So the final thing that I learned, number four, is that it's not just beacons. We have these beacons right now and whenever they think of Bluetooth they just think of these beacons and it's not cheap to be around. But it's actually also quite interesting to use your phone. So the guy before that was broadcasting here actually installed an app called Beacon Toy. And if you install Beacon Toy your phone can become a Bluetooth beacon. You can type in any URL you want to and now everybody here can see your beacon. Now, we originally made a physical web app and that physical web app was meant to scan, but it also does in effect broadcasting. So it's now demo time.  There we go. Not that one. Delete. Here we go. Can you smile please? Thank you. Now let's just see how good the Wi-Fi is here for me to tweet this. Tweet. Okay. Now what I'm going to do is I should have realized under a slow Wi-Fi might be a problem. Okay. Now what I'm going to do now is simply hit the share button in Android and then when I share instead of picking Gmail or anything else I'm going to pick the physical web app itself because our physical web app gives you effectively the ability to share anything from any Android app. And now I hit it it's now broadcasting. So anybody right now that has a physical web running on their phone can see that tweet I just took. It'll probably reach, I'm not sure it'll reach to the back of the building because I haven't set a low power but probably almost everybody here in the first 15 rows can actually see this tweet right now. I can't confirm it but has anybody seen the URL? Can anybody tell me they see it? No one's looking. Anyway the point though is that I'll just leave it here if you want to see that. But the intention is that this opens up a whole different kind of way of looking at it. Imagine if you were to have just simply a vendor that could actually make their own little web page and hit go and then they could then simply just broadcast it or you could share something with your friends. So what did we learn? Quick summary you are all shortners for the win. They're actually quite good. The web just keeps getting better. It's the small use cases that I think are really interesting. Not these big corporate ones. There's nothing wrong with big corporate ones but I think the small personal use case of sharing I think it's quite interesting. And it's not just beacons. We can actually build this into the phone itself as a new way of sharing. So that's part two. Part three, where can we go? And I find this is the part that I'm going to get a little bit more maybe not philosophical but more like where does this technology take us? The first thing I really want to stress is that everything that we do is open source. This is my first open source project. It's been very eye-opening how it works. We have an amazing community on GitHub of people that help us out. So the application that we did is open source. The scanner that we built in the proxy service we built is open source. We're working on this beacon image right now. This is all written in ARM embed. We're going to make that open source. People have written Node servers or Arduino code. All sorts of different things have all been done in this open source community and it's been so much more interesting because everyone's kind of working together with us. So initially we released a single app on Android. We also released it on iOS. And that was just to get started. Then it got built into Chrome. That lasted for about six months. We had enough traction that the Android team got interested and they integrated the code into ... I'm sorry, Opera also did it. Then we integrated it into Android. So right now it used to be in Chrome and now it's in Android itself.  We hope in about four months it's going to do it as well. So there's a little bit of momentum going on behind this. So it's really kind of fun to see that if you give it away people are actually going to use it. And this is what you do. You just simply just open it up and let people play around with it and kind of go back and forth. So who is the actual we part though? Because yes, I work for Google, but more importantly I represent, I like to think I work for the Chrome team in Google. I think there's a certain kind of esprit de corps that we have in the Chrome team that's very kind of more of the web. And what we do is to make the web better. But I don't want to be this shill for Google product. In fact, a lot of companies that are using the physical web right now are actually getting angry with us because we're not pushing this. We're not taking out ads. We're not really making this like a corporate thing. Because the point is this has to be of the web. This can only succeed if the web wants it to succeed. If we were to push this too hard, it actually would backfire and it wouldn't be considered to be part of the web. So this will only work if we kind of as a community wanted to work. And I do think that means it's going to be a little bit slower to get adopted. But I also feel like that's the natural, better way for this to go. This can't work if Google wants it to work. So we are continuing to experiment though. We keep pushing out crazy ideas in our Android app. So just recently we've put in Wi-Fi direct support so that you can broadcast not using Bluetooth but using Wi-Fi direct. We've also added MD&S support, just a variation on that. That's actually quite useful for industrial use cases.   And then when you click on it, it makes a connection back to the beacon, yanks the web page out of it and displays it for the user. So that way you can use it without having data. That makes no, there's a lot of questions that come up about this. And that's why we do this as an experiment. We kind of put it out and have people kind of throw rocks at us and ask questions, because there's obviously a lot of security concerns about putting up any random beacon that goes through absolutely no, you know, vetting of any kind. But it's worth talking about, and people are getting quite excited about the possibility of being able to have something work without any data at all. This is especially useful in developing countries. But I really want to stress, this is the tricky part. I work for Google, but I'm on an open source project. This is an experiment.  It's like, no, no, it's an experiment. Okay? It's really I'm sort of really underlying the fact that we're just playing with these things, and that's, but we want to be more of the open source side of things and play around with it. So now it's time to talk about my starry-eyed vision of where we can go with this stuff, because I think there's lots of different directions we can build on top of it. Because right now the simple scanner that we have to find a list of URLs that you click on feels kind of like Mosaic. Right? It's just kind of the first baby steps of what we could do. So let's talk kind of a range of things from near to far and where we can go. The first thing that I don't think people appreciate is just how rapidly hardware is evolving. This has got a coin cell in it, and it lasts for about three years under the existing battery. It's the new Nordic chip that came out is called the NRA 52. ARM also has one called the Cordio. These things are significantly more efficient, and it will probably last upwards of a decade on a single coin cell battery. In addition, they've now got it down to only one volt part versus a three volt part, which means it can run on a single photovoltaic cell. Which means these things are quickly going to become powered by light, and therefore we won't be having the ecological disaster of throwing millions of batteries and landfills every year. So these are quickly going to become kind of permanent long-term type beacons that will just run forever. I think this is quite interesting. It's the hardware side of things. So that's the first step. Step two is URL services. Much like we initially had websites, and then we went to Blogger, and then we kind of went to Twitter, and then we went to Facebook. We just had easier and easier techniques for people to work. I think that eventually we're going to have more and more interesting services built specifically for the physical web. We had a summer intern that basically created a URL dynamic page creator. It was basically kind of like mycard.com with an ampersand name and an ampersand phone number and photo, and I didn't know this, but a URL could be 2,000 characters long. So if you were to create a gigantic URL with all of the parameters that you want put into a URL shortener, you now have a web page that's yours. So to me, that's a very lightweight way of people being able to do that. I think there's a lot of interesting things that can be built with that. The other one would be fixed function beacons. You can imagine, say, a for sale sign that you would have for your car or whatever and then it comes with a beacon built into it. You just basically go to it first, register it, type in the information you want to and it works. You don't even care about the service or anything like that. So a lot of things can be built on top of that. What I get more interested in is effectively this idea of getting rid of the beacon entirely. And if we were to have a type of mobile dream weaver, imagine an app that you would write that you could then specify a template and information and pictures and photos and do whatever you want to and hit go and then your phone becomes the actual server itself. And people could connect to it or it could upload it to a server and you could point a link to that. I mean, that's the whole point. There's many different directions that you can go. But it means that effectively people are now going to be dynamically creating content with their phone and then just broadcasting to anybody around. This is especially interesting in the fat beacon case with markets in say rural areas where people could then create information that they want people to see and everybody else could see it and connect to it and there would be no data anywhere. But you could interact and get information on each of these places. I did mention briefly about JavaScript Bluetooth, the web Bluetooth standard. This is part of the W3C and it lets you interact to the specific beacon. But in January-ish or first quarter of next year there's going to be a scanning API and that to me opens up an amazing amount of work because we did do I don't know if you've heard about the Computer History Museum in Mountain View, it's right next to Google. We put in 31 beacons there to try to see what it would be like to walk around and we found out that not surprisingly if you walk up to some exhibit and you pull on the physical web and you see exhibit 6 and you pick it that's fine and then you go over to exhibit 8 and then to pull on the physical web again it gets kind of tedious to keep pulling on the physical web. It's like once you get in stay in the web environment well once you get scanning it means that all of the beacons for the museum would broadcast one URL, it would just say oh you're in the Computer History Museum but once you open that web page it would scan and say oh you're next to exhibit 6 I'll show you exhibit 6 and as you're reading it and you get close to exhibit 7 a little thing could pop up and say oh so and this now completely unlocks the whole UI paradigm because now each hospital or museum or venue can do their own UI the physical web is basically we'll just get you started and then you can have your own experience I'm getting super excited about that we actually built a rough prototype of how this would work for museum and the results were very encouraging but again this is going to happen not too far in the future about 6 or 7 months but then the last point I want to mention is that I think that the scanner that we're building is really primitive and the whole reason that we've built it this way is that other people can build scanners the running joke I have been saying about open source is that everybody loves open source as long as you do all the work and the idea right now is I think people are waiting for Google to say hey if you think this is a good idea you make the market but if it takes off you damn well better give it to us and I'm like fine that's exactly what we're doing we just want to make this part of the web and so yes maybe Google does have to push it a little bit harder but the whole point though is that we're going to do this really basic primitive scanner and we really hope other people do really exciting even better things to kind of move things forward so for example someone has talked about they wanted to do for a summer project beacons that have JSON LD embedded in the page that actually have markers in it so you could browse it as a regular page but it also tells you a little bit more about the fact that it actually has an audio clip to it they would build their own custom scanner that would pull these things up and then for blind visually impaired people they could walk through an environment and then get an audio tour as they walked around I also talked to a researcher that wanted to use this for augmented reality you could actually look across a room find the physical web beacons just through the air but each physical web beacon would have a link to actually what its mesh is what it actually physically looks like you could then pick that out of the various pages and then do visual recognition with what you're seeing and then be able to look at something and know exactly what it is and pull it up again research farther in the future type stuff but this is what happens when you can build on top of kind of the data substrate that the physical web gives you so I was just a couple of the ideas that I came up with but this is why I'm so excited about the physical web so here's the summary so far I talked about what the physical web was I talked about kind of the journey we went on I gave you just a few ideas of the things that were going on but the bottom line is it's only going to work if it's part of the web community sometimes people think that I'm pushing this as a Google product but nothing can be further from the truth this is only going to work if we as a community want it to happen so I hope you're excited by it because I am lots of other companies are and I'm going to stick around afterwards and answer your questions so thanks very much for listening I hope to talk to you guys later lots of questions of course I think you touched on this in the talk maybe you and I know more about this so I'll ask it again isn't the physical web a security nightmare with people being tracked as they walk around etc the big thing about the physical web and our sweet spot use case is this public ephemeral interaction it's the bus stop that's giving the URL we strongly recommend that the user does not have a beacon on their body because for just that reason you could be tracked so we don't recommend that if though you're worried that because you're using the Google scanner and it could scan for all the devices that you could be tracked there's two things to say one is I hate to break it to you but any app on the planet can do that with GPS already and second you don't have to trust Google if you don't want to use Google's physical web use Opera's physical web so pick the company that you trust most and use them cool which was the first browser to implement the physical web gee I'm trying to think some tango thing something like that is there a physical limit on the size of a beacon can it be the size of a grain of sand or as big as a mountain there are beacons that are literally actually smaller than this there's a beacon that was actually Verily Verily's Google's health group they had made a custom beacon that was the size of an American nickel that was 21 millimeters wide and it lasted for about 3-4 weeks because it was a really tiny battery so these things are going to get significantly smaller and how practical is the physical web if you walk by a trash can full of pill bottles each giving you a notification on your phone I get the pill bottle question a lot you can do clever things with changing the antenna design and also turning the power down so to me the pill bottle example is going to be really viable if it only has a very very tiny radius of say maybe half a meter however there are people that probably have 50 pill bottles in their room and honestly I don't have a good answer for that my expectation is that this would only be used for very very high value things and not necessarily for everything but that got to my point about how we will get better and better scanners as we have more and more of these devices cool and what about power consumption of the device that's doing the scanning constantly battery we actually so many people actually do not turn on bluetooth at all because they think that bluetooth is actually a power hog and the new modern browsers or the new modern chips is actually not an issue at all so just turning on bluetooth will not hurt your battery we only scan when you turn the screen on and we only scan for 10 seconds so our battery impact is almost insignificant excellent thank you very much Scott great


Alright, what's up everyone? So this video I think is gonna be a little short, but it's gonna be a good one it's gonna be a good one because This is a tool that I've been I've only recently really used, but it I've gotten so much out of it So you might notice if you're familiar with my other videos My color scheme is a lot different than what it usually is And that's because I found a pretty effective tool at let me turn this music off. It's blurring in my headphones I'm just gonna be talking loud if it's going on. Anyway, I found a pretty effective tool for auto-generating color schemes And you'll see that there's a loose comparison between my background and the actual color scheme I have Now I actually a couple months ago I was talking to a subscriber about like the pains of like getting a cohesive color scheme across all your different programs So, you know your terminal or Vim or all this other stuff And one of this subscriber, I think his name was Louie, right? This is from months ago He might not even remember but he directed me to this little thing called pie wall, which I didn't check out at the time I just sort of looked at it, but I pulled it back up a couple days ago, and it's actually pretty sweet So this is written by Dylan Dylan Erups Erups I don't know how he pronounces that I think that's the guy who made Neofetch But this program is actually pretty simple It's a little script and what you do is you feed it any kind of like picture and it uses image magic to Take all the core colors out of it So like you can get it produces basically I think a 16 color palette from that image Then it puts it as your background and it It enforces that color scheme in all of your programs or whatever So I actually have a couple examples here. So here's the background we have here Now to actually run this actually look I should probably do it manually first So to actually run this thing you just type wall and then I and then the name of a file So I'll put in this one here So yeah, I can't really type today and once you run that it generates a color scheme from that sets it as the background and And you'll see that all of our terminals now have changed to match this background and it actually looks really nice It does a good job at it So I when I when I first started using this a day or so ago, man I just could not stop playing with it like I was just going through every single like You know picture in my wallpaper folder like seeing how this thing would actually work Now here's the thing So far as I know you don't really have to do any configuration depending on your setup So I have urx vt and this thing works automatically with it You do there is I think a special Vim color scheme. Let me check it out You can check out the documentation over here. It shows you if you go to where is it? Customization or something it tells you all the different packages it works with So for Vim you have to set a special color scheme the wall color scheme or whatever So knowing me I don't want to have to type this in the terminal every time So I've set it to a shortcut and ranger so I can just go over one of these and press BW That's how I have it configured and it'll just do it automatically look at that Oh my god every single time. It's just beautiful. Just beautiful So you can it works pretty much on any image so long as it has enough colors I mean if you're working with something that's pretty monochromatic, you're gonna have some trouble But otherwise man just every single time. It's just a great color scheme So again, it works on your XVT out of the box. I can't vouch for any other terminals but this is like the perfect kind of program because Man it does so much that I used to do manually and now I don't even have to think about it So yeah, this thing's pretty great So yeah, the link in the description check this thing out There are other things you can do with it You can override colors and stuff like that if you want to have some other changes But all in all this thing is just fantastic. So pie wall


Hi, I'm Zor. Welcome to Unisor Education. Today we will talk about equations of higher order than 2. With quadratic equations, equations of the order 2, we did have basically purely theoretical material, how to derive general speaking, how to derive the formula for solutions of the quadratic equation. Now, with the equation of the third degree, the cubic equation, where the variable is in x cubed, the situation is more difficult. Actually, there are some formulas which, in theory, might be used, but they are quite complex, and these formulas express the solutions to a cubical equation in terms of coefficients. Now, when you go to even higher degrees, like the fourth degree, that's even more complex, and as far as the fifth and higher, there is actually a very interesting theorem in algebra that there is no general solution for equations of the fifth and higher degrees of its coefficients, which can be expressed in a regular algebraic expression. So, basically, if you have an equation of higher order, higher than 2, people don't usually solve these equations in general. However, since we are not really pursuing the idea of solving the equation, but rather equipping you with certain approaches and guessing and tricks, if you wish, just to develop the mathematical thinking and just to be able to face the problem which you might not really know the solution beforehand, I will use these higher order equations just to illustrate certain approaches which you can take, and hopefully they will be educational enough and just help you to develop certain logical thinking, etc. So, again, I will use the higher order equations just to develop the brain power, if you wish. All right. Now, first of all, what is the representation of the higher order equation? Well, in a concrete example, you can say something like 3x fourth minus 2x equals to zero. This is just an example of an equation of a fourth order which, well, it can be solved, and by the way, purely algebraically, but that's not the problem right now. Right now, this is just an illustration of the polynomial on the left and the equation of the fourth degree altogether. Now, if I wanted to express generally how any equation of the higher order looks like, I would use the following symbolics. Following on the case degree which is a function of x. What is this? Well, this is a sum of coefficient with x to the case degree plus another coefficient with x to k minus 1 degree plus, etc., etc. x to the power of k, x to the power of k minus 1, etc., down to a k minus 1 x plus a k. That's the polynomial of the case degree where x is in the power of k. And these are different coefficients. Generally speaking, coefficients are usually real numbers. But generally, they are complex. So the equation of k's order or k's degree is something like this. Some polynomial of x of degree k is equal to 0. So this is the general expression of the equation of the higher order, of any order actually, k, where r as a function of x with this index, if you wish, k is a representation of this sum of different elements. Each one of them is x to certain power and the maximum power is k, which corresponds to this particular index in my general expression of the polynomial. And r equals to 0, obviously. Sometimes this number, a kth, which has no x with it, usually it's called the free coefficients. And this one is usually the first coefficient with x to the power of k. So this is general polynomial expression of the equation of the higher order. And as I said, there is no such thing as a general solution of this for any k. At least for k greater or equal to 5, there are no general solutions. For k equals 3 and 4, as I said, there are, but they're too complex. So usually if people have a general solution with some coefficients, they go to computers basically to solve it. There are certain numerical algorithms which allow to write the programs for the computers and they will come up with certain quite precise solutions if these solutions exist, of course. Now, in our case, since we are pursuing a purely educational goal, I will emphasize two methods which might, in theory, be used to solve certain equations in certain cases. And again, the art of this is to find these methods, these specific methods to solve specific equations, not the general type of them. Okay, so what are specific methods which I would like to talk about today? Well, there are two. Method number one is the problem. Let's assume that our polynomial expression like this, that it can be expressed as a product of one polynomial expression times another polynomial expression. Now, this is a polynomial of the case order. This is of nth order and this is nth order. And what's important is that both m and m should be less than k. Well, obviously, they should be less than k because if you will think about the polynomial of the nth degree, so k, x is in the nth degree and there is some expression. And q is a polynomial of the nth degree, x had the maximum n. So if you will put this polynomial, complete expression in this and multiply them, the highest order of this one, which is m, and the highest order of this one, which is n, and when you multiply them together, you will have m plus n as a degree. Why? Very simple. Let's just do it in one simple example. Let's substitute. This is a0 times x to the case plus something. This, let's say, is b0 x to the nth maximum plus something times, and this will be c0 x to the nth plus something. Now, if you will open parentheses and multiply, what's the maximum power the x will be in when you have the maximum of this, which is m, and the maximum of this, which is n? So it will be b0 times c0 times xm times xn, which is b0 c0 x to the nth plus n. And if they are equal, the maximum power of this should be equal to the maximum power of this, which means a0 x to the case equals to b0 c0, let's be accurate, x to the nth plus n. That's what we will have. This is the maximum power of x, and this is the maximum power of x. So if these expressions are the same, these members should be the same, which means a0 should be equal to b0 times c0, and k should be equal to n plus n. Since it's identity, it's supposed to be equal for any x, if this is a true identity, true representation of r as a product of p times q. So obviously, if m plus n is equal to k, and we are not considering trivial cases when m is equal to 0 or n is equal to 0, because that actually makes the whole expression just a constant. So obviously, m plus n is equal to k, from which follows that both m and n are less than k. By the way, they are all positive and integer numbers. I didn't mention it, but it kind of seemed that this is understood. So m plus n is equal to k, so m is smaller and n is smaller. So if you can represent a polynomial of, let's say, third degree with a product of the polynomial of the second degree and the first degree, then you have a chance, basically. Then you can have the multiplication of the second and the first degree. So m is 2 and n is 1. You will have k is equal to 3, and that will be the polynomial of the third degree. Now, why do we have to represent r as a product of two polynomials of smaller, of lower degree? For a very, very simple reason. Let's say you know how to solve this particular equation and this particular equation separately. Well, look at it this way. If you found an x when this is equal to zero, then obviously this is equal to zero because it's a multiplication. So any solution to this equation, which is easier than original because the m is slower than k, any solution to this equation will be a solution to the original equation r k x equals to zero. This is what you have to solve. If this is what you have to solve and r is represented as a product, then any solution of the p is equal to zero and any solution of the q is equal to zero would be a solution to r is equal to zero. So one problem of solving an equation of let's say third degree, you might reduce to solving two problems. One is the first degree and another is the second degree. Just as an example. Which is easier? Obviously the lower degree, the lower order of the equation is, the easier it is to solve and if you can reduce it down to first and second degree polynomial, well, you know the formulas and you definitely can solve a quadratic or linear equation without any problems. So what's important is to reduce solving the equation of the higher order to solving the two or more equations of the lower order. That's the approach which you can take. That's one thing and let me illustrate it as an example. So if you are given an equation, let's just think about it this way. Whether it's a math exam or anything like that you have given an equation x to the third plus 5x squared plus x minus 15 is equal to zero. Obviously you cannot solve this equation using any kind of a formula because there is no formula, at least you don't know the formula for the cubicle equation. Which means you have to find something which will simplify your job and again my first recommendation is to find some representation of this polynomial of the third degree as a product of two polynomials of the lower degree, like first and second. Well, absolutely the most difficult problem is how? Yes, you know that maybe it is possible but you don't know how. Well, here it is. Here is my recommendations. Let me just say that somehow, magically, I have guessed the following thing. Let's represent 5x squared as 3x squared plus 2x squared. So x cubed stays. How I guessed it is not really the question right now but let's consider that I have guessed it and I will represent 6x as 6x minus 5x. So this is the same as this and this is the same as this minus 15 equals to 0. So this is the identical transformation. Now, why do they do it? Here is why. Now let's consider pairs. One pair, second pair and third pair. You can factor out x squared here and you will have x squared times x plus 3. You can factor out 2x from the second pair to x squared plus 6x factor out 2x, what will be left from 2x squared you will have x and from 6x if you factor out 2x you will have 3. Minus 5x minus 15 the third pair I will factor out minus 5 and I will have x plus 3. You see, so far I just did a couple of identical transformation and I have seen that you see x plus 3, x plus 3, x plus 3. Now I can factor out x plus 3 and what will be left x squared plus 2x minus 5 equals to 0. So what did I did actually? I have represented my original polynomial in the third degree with the multiplication of two polynomials of the first and second degree. Obviously you can solve each of these equations x plus 3 is equal to 0 separately that's x equals to minus 3 and this x squared plus 2x minus 5 just a plain quadratic equation you can solve that too. Now solving these equations basically again as I told you in the general case gives you solution to original equation x cubed plus 5x squared, etc. equals to 0. So what was the important part of it? The most important is not really solving these equations because this is trivial but how to guess basically is these coefficients like 5 x 3 plus 2 1 x 6 minus 5, etc. That's the most important guessing game which you have to accomplish because after that everything is just trivial. It's like going along the paved road. So first you have to climb the mountain and then you see everything, how to do it. Now is there a general recommendation which I can give in this particular case? Well, yes there is. But again it's just a general recommendation it doesn't mean it will always work or something like this. Think about it this way. If you are given an equation of this type and somebody really asked you solve it. Obviously you understand that most likely solutions are relatively simple because otherwise you would not be asked to do it.  So usually it's integer numbers and if they are integer to look for a solution would probably be very easy among factors of the three coefficient. The one which has no x, y. But here is why. Look at this. If you have some linear equation and quadratic equation. Linear expression and quadratic expression. Three member will only be obtained if you have no x here which is 3 and no x here which is minus 5. And that would actually multiply them. That's the only two numbers which will give you the free member of the original equation, 15. Everything else will contain x in some degree. So if you open all these parentheses all different products, x times x square or 3 times 2x, etc. All of them will contain x except one. Three member from here and three member from there. So only one gives you the multiplication of these three members will give you the free member of the free coefficient in the original equation. So you might just suspect that if there is some kind of a linear expression which can be factored out it should be x plus some factor of the free member. Now how many factors does this guy have? Well, 5 and 3 and minus 5 and minus 3. So these four different variations should actually be tried. In this particular case the factor minus 3 is the one which is used here. So x plus 3 would be something which you can look for. So you can try another one. You can try for instance minus 5 which means let's try to do x plus 5 and try to parenthesize this out to factor it out. Let's just try and see if it works. So let's consider I would like to factor out x plus 5. Well, then from these two I have to factor out x square I will get x plus 5, right? Now this is not x plus 5. This is x plus 5 but I have to have minus 15 so I have to have minus 20. This is definitely something extra. So x plus 5 doesn't really work in this particular case. Well, let's try x minus 5 for instance. Well, if I want to have x minus 5 and I have x cube plus 5x square what should I have? I should have x square but now I have minus 5x square I need 5 plus x square so I need to add 10x square. Now I have converted plus x minus 15 equals to 0. Now, I need x minus 5 again. Now, if I will factor out x and get x minus 5 what do I have? I have 10x square so this is fine but now I have plus x but here I have minus 50x so I have to add 51x to satisfy this and minus 15. Again, x minus 5 x minus 5 but this is something which is completely extra. So x minus 5 also doesn't work. So by trying a few divisors of this free coefficient I can just eliminate a few and finally if I will get x plus 3 let's just think about again how do they do it? Okay, I know that this thing has 15 has 3 and minus 3 among divisors. So let's try x plus 3. Okay, if this is x plus 3 now this is supposed to be factored out 2x square. Now I have x cubed plus 3x square but I need 5x square so I have to add 2x square. Okay, so far so good. Now I have plus x minus 15 equals to 0. So now this is already x plus 3x square now I have 2x square so I have to factor out 2x and I need the same x plus 3, right? So what do I have here? I have 6x, sorry yes, 2x square plus 6x. Now, if I have 6x but I need only 1x so I have to subtract 5x and lo and behold if I will factor out minus 5 I will have x plus 3 my guess is correct. So by just trying to guess which one of the divisors of the free coefficient fits this type of a schema you will be fine. So if there is a solution you will find it. But again we are talking about simple cases when solutions are looked for among integer numbers obviously and hopefully you will not be given more complex equations because it's much more difficult to solve and hopefully people don't really try to solve these equations in some kind of a formulas even if there are the possibilities obviously. So again if you are looking for a solution of equation which contains integer coefficients and you are looking for a solution which is also integer it's helpful to look at the factors of free coefficients. In this case it's 5 and 3 minus 5 and minus 3 so you have to plus x plus 3, x minus 3, x plus 5, x minus 5 only 4 cases you have to just go one by one and you might find some if it exists. It might not exist in which case, well, sorry there is no such a good solution. Alright so that's the first example which I wanted to present. The first way of solving equations of the higher order so you have to somehow guess in certain particular cases you can how to represent it as a product of two expressions of a lower order. Now the second approach which I might suggest you is the following. What if you can represent this particular equation of the case degree with a substitution. Let's say you can substitute something like some kind of a solution of some kind of expression sorry x squared plus 2x plus 3 for instance. You can represent it as some new variable y and if you can express this particular equation in terms of y but it will be of a different degree degree t which is smaller than this one then what you can do is you can try to solve this equation in terms of y and then having the value of y you can solve this equation in terms of x. Now I am not clear enough in this particular general case let me just express it in one particular example and it will be quite well understood what I mean. Let's say you have an equation x4 minus 2x square minus 3 equals to 0. Well this is an equation of the fourth order x is in the power of 4 but you notice that if you will substitute x2 equals to y in terms of y the equation looks like y2 minus 2y minus 3 is equal to 0. Well in this case it's very easily visible that x2 can be substituted and you will get a quadratic equation for y. Now how to solve this quadratic equation for y? Firstly I don't remember the formula so I will represent it in terms of a full square which is y2 minus 2y plus 1 minus 4 equals to 0 so I represent it minus 3 as 1 minus 4 and this is a full square this is y minus 1 square equals to 4 minus 1 square so y minus 1 absolute value is equal to 4 so it's y minus 1 is equal to 4 or y minus 1 is equal to minus 4 2 solutions to this right oh sorry it's square root square root of 4 so it's 2 2 and minus 2 2 and minus 2 ok which means y is equal to 3 and y is equal to 1 goes here minus 1 so we have 2 solutions for y and we know that x2 is equal to y so now we can find what the x is in terms of real numbers square root of 3 and minus square root of 3 will be solutions to x and in terms of real numbers this one doesn't produce any real solutions because x2 cannot be negative in terms of complex numbers if you are solving the problem in the demand of complex numbers you can additionally x2 is equal to minus 1 so it's plus i and minus i as solutions to original equation of the force order I have represented as this equation of the second order substituting x2 with y well obviously there are more different substitutions maybe it's not just straight forward x2 equals to y maybe it's something like x2 minus 1 is equal to y but again you have to guess this type of thing and that's not easy I understand that express certain x to certain degree some kind of a polynomial like x to the second degree plus something in terms of the substitution of the variables then you can reduce it you can reduce the solution of this guy this higher order equation 2 solving this particular equation which is of the lower order and then once you have obtained the y you can solve the next one in a little bit simpler way because it's in this case it's just a quadratic equation well basically these two methods one is representation as a product and another is a substitution of certain expression for x in such a way that it gives you a better handle over the equation this particular thing gives you a really good two methods to solve equations of the higher order and they are very specific these methods there is nothing general about them and they are working only in certain specific cases alright well that's basically all I wanted to talk about today I would like to take a look at the Unisor.com website there are many other interesting things there and as far as the higher order equations I'll try to provide certain examples and problems which some of them I will solve on the web and you are definitely invited to take a look at them thank you very much and good luck


What's your name? Emma. How old are you, Emma? Ten. Presenting the Medal of Honor, Emma, is Director Giro Maducci. 9-1-1 for kids is really an opportunity to not only train people on how to use the 9-1-1 system, but it also recognizes the work of dispatchers and recognizes the people who actually call 9-1-1, particularly youth, because we're trying to train the youth from a young age how to use 9-1-1.


Super last minute video but I had a really sick idea there's an abandoned property with an abandoned barn and the house has been demolished but like there's like all rubble and stuff so I loaded up the bike we're gonna take the bike over brought my GoPro again and I'm gonna do a piece today I went and bought paint yesterday to do like a camouflage piece so yeah that's what we're doing right now I got a road from my girlfriend's house today but she tried to shatter and pulled me over and he wasn't sure which way I was going anyway last time I was riding out here I met a bunch of people I ran into some kids and they were like have you been to the abandoned barn and I was like nah gotta watch out for that sand well so this is basically a stock 110 so stock springs and stuff stock it's not like big water anything so it's quite quite interesting for me to ride so obviously I'm 6'4'1 and uh yeah oh my god I don't remember being like this last time I think I'm in the hard of way there we go supposed to rain later today so hopefully the rain holds off I think it'll pass but who knows California weather's been a bit bipolar lately all right this is the way in the kids told me to go this way it's a bit tricky on a pitway this is where the ruts get kind of bad and sketchy try my best not to fall in whoa it's like too soon so this is a property here I'll go for a quick buzz around so you guys can see a bunch of weird stuff I'm not sure how you get to this spot I think we went in the back door but this must have been the driveway back in the 70s or 80s or something I don't know there's a whole bunch of rubble so this is basically it yeah oh shit there's an old hot tub if anyone wants to go in might have asbestos in it though considering the property is so loud but yeah pretty picturesque back here as you can see it's been well abandoned for a minute I was planning to paint down there so I'm gonna ride around and then we'll try to pick a spot so I thought about painting that back wall there that's probably a pretty good spot it's tucked away and I don't think anyone can see what I'm doing so yeah park my bike and I'll start painting I need some sleep but counting sheep don't help me grow I don't want no bitch to love me all I want is fits and hongies I'm a ghost these flops can't touch me falls you bro I wouldn't trust me all my friends are cussed these times get tough get brushed like dusties whole whip don't smell like musty ever I go these hoes won't fuck me in the world that's blind with fear I can see crystal clear yeah only god knows why I'm here after what I did they didn't have no whip to steer I'll try shift this gear some shed they skin I keep my grin and shed no tears midnight days I was burning trees start off the whip got attorneys keys shy boy got the perks and lean I did what I did I was cursed with greed serving up fiends to serve my needs as a teen on circle streets flathead doc we can see your green please you keep the beef me I just want to get low I need some sleep but counting sheep don't help me grow a bitch and hongies up in stacks big bag that's a fact we rake out the max no new friends it's like that only cussies at the trap we spin in their back if we miss them at the flat tell my shooter just relax he gon be right back just say no they can't go shh with a real man in black damn my bae must hate me I've been on road a bit much lately that shit don't faze me all right baby a real trap baby they stick my lady uh these scouts my baby I think I'm crazy but I'm married to the games burning trees start off the whip got attorneys keys shy boy got the perks and lean I did what I was cursed with greed serving up fiends to serve my needs as a teen on circle streets flathead doc we can see your green please keep the beef me I just want to get low I need some sleep again she don't help me how do we get there how do we get to the barn I'm pretty sure it's this way someone made the fence right up by the skin here getting through here I can just ride right in now anyway it's abandoned by a property baby let's go around trailblazing right now guys yeah I wonder who built this stuff there's a quarter pipe here a quarter pipe there I think it was a half pipe at one point and then there's like a center block ledge here and some type of metal ledge down there and there's a roof bit I still haven't been up yet hanging Santa Claus too it's kind of creepy watch tower thing water tower watch tower I don't know who's property this is and why they've neglected neglected for so long I can just get one good wheelie to show you guys that I'm worthy of motor vlogging if you will happen today give me some time to practice in the next video there's no clutch see so you have to kind of hold it out of gear along my GoPro has left it might die pretty pretty shortly but let's see if we can go from the barn or nearly slid out just now a bunch of bees I should probably get out of here before those bees come and attach me there's like a pit bike track back here that's crazy now I know for next time oh she's tired someone built a track here oh which way does this go big old drunk um I'm probably gonna head home now you guys are listening so yeah catch you on the flip side hope you guys enjoyed that video comment below if you want to see more painting I had a lot of fun with that piece comment down below what you think I could have done better with that piece it always seems to be a good point of conversation on my graph videos is should have done this should have done that blah blah blah whatever comment below follow me on instagram at enuckism check out evening mob.com if you want to swoop in and grab these hats super sick I drew this she's watching the video if you guys want to see more content like this let me know see you guys in the next video