The federal government does not collect any data on evictions. State governments, county governments, they don't collect these data. So a lot of our quantitative knowledge about how frequent evictions are in the United States comes from the eviction lab. And we collected filings from county courts from all across the country. Some cases we can scrape them directly from websites. In other cases courts email us, you know, giant PDFs that we scrape. We aggregate all of that and we get this estimate that you mentioned, 2.7 million eviction filings each year. But, you know, what is on these filings? They are extremely thin on information. Of course, like, we know that people have, they have spouses, they have roommates. There's all sorts of people living in these units. So what we figured out is that we could upload about 30 million records to a secure server maintained by the United States Census Bureau. And with our partners in the Census, they were able to probabilistically link the names and addresses that are on the filing and associate that with a person who responded to some sort of survey that was done by the Census Bureau, like the Decennial Census or the American Community Survey. You know, the American Community Survey is done each year and it covers about 1% of the population. So we were able to use those linkages to figure out not just how many households receive eviction filing but how many individual people receive that eviction filing. And then going beyond that, we can use the ACS to find out the characteristics of each of these people in the household.


Wait, hold on, hold on, hold on, hold on. Tell me this guy is not George McFly from Back to the Future. And actually, the girl next to him looks a little bit like Marty McFly's mom. Time traveler's confirmed. Hey guys, welcome back to my channel. I am so glad to be back. Today we're gonna be going through a 1950s yearbook, and not just any 1950s yearbook, it is the 1950s yearbook. This is the first year of the 50s. And it is a yearbook from Gainesville High School. And it is from Gainesville, Georgia. So this yearbook is made out of a very sturdy cardboard, maybe, with a light layer of leather. And it's so funny, this is what it looks like with clothes. The mascot was a radiator, which isn't very common.  But it's really interesting and unique of its kind. Now the school does still exist, but their mascot now is called the Red Elephant. If you go to the school, make sure you comment down below. So on the first page, it says, with pleasure and pride. And you can see the picture of the school, which is so cool. And you can see a bunch of kids walking to school in their outfits. So here's what a few of the pages look like. You can see the page where the administration and faculty is, and a few people have signed it there. This is really cool here. They have an official motto, official flower, and official colors. So the motto is, yesterday's triumph is insignificant in the excitement of tomorrow's possibilities. And their flower is the American Beauty Rose. And their colors are green and silver. So when you open the page, the first thing you notice is the photos coming in, all of the senior photos, and little photos that they took while they were at school. And what I really want to show you guys is this speech right here, which is a little taste of what it was like for them to go to school. And you'd be surprised how similar their experience was to ours. It's a few lines, so I'm gonna go ahead and read it. Way back in 1939, we walked up the walk to our first day at school. Many of us were scared to death. The rest of us so excited we couldn't keep still. Now as seniors in 1950, we look back on those last 11 years as history already made, tell me about it. For seven years, we struggled through grammar school. Then that glorious day in September 46, we were freshmen in high school. To some of us, the building was not new. We had spent two of our grammar school years here, but to all of the teachers, classes, people, and routine were all new. For the first few days, we were lost and scared and had a senior spoken to us we would have dropped in our tracks. Well, we got through that year. Then we were sophomores and did we think we just about owned the place. Next came our junior year. By now, we were very much at home and settled in Gainesville High, but we had to work. Thanks to the teachers who were so patiently stuck it out with us and the junior store, and there's a continuation. We gave the senior a grand banquet. We stepped into the roles of seniors. However, we didn't remain calm for long. Before we knew it, along came the job of electing class officers. Then we started planning our class trip. We sold everything from newspapers to Christmas cards. Then came May 1950, the largest graduating class in the history of Gainesville High. Wait, hold on, hold on, hold on, hold on. Tell me this guy is not George McFly from Back to the Future.  Tell me I'm wrong. And actually the girl next to him looks a little bit like Marty McFly's mom. Freaking me out right now, time travelers confirmed. Now the one thing that's kind of strange that I've noticed in a few pages over is that they have a class prophecy and they pretty much tell you how you're going to, oh there it goes with thunder, perfect timing. It's telling you how you're going to die and it's not supposed to be serious, it's supposed to be a joke, but it's kind of strange to put that into the yearbook. So I'm gonna read you a couple of them. So one of them here says, Betsy Tucker blew her trumpet a little loud one morning and the teacher who was giving a test that period took care of her. And Bobby Ledbetter, who was making too much noise beating his drums. Another one here says, Dr. Fay and Nickerbocker, the famous surgeon made one grave mistake. She was operating on somebody but she cut herself open instead of her patient. It's a little bit morbid for a yearbook. So the next thing we're gonna look through is the superlatives. Now if you guys don't know what a superlative is, a superlative is a title that you're given in high school and usually the most popular people get the title because they're the most recognized and they get a title based on what they're the best at doing. Now I had a superlative in high school and my superlative was most likely to become a celebrity or most likely to do celebrity fashion, something like that. So that's the one I got. And here are some that they got. So the first person is most likely to succeed and the people who've got chosen for that is Nicky, Nickerbocker and Dub Jones. The next one is Most Intellectual and Mandy Joiner and Leroy Skinner got that title, this is them. The next superlative is Friendliest. Joanne Franklin and Bobby Grant got Friendliest, most popular, Sammy Willis and Marvin Free. Most talented, Nicky, Nickerbocker again and Bobby Ledbetter. The cutest, Frances West and Fred Culberson. Best looking, Joyce Paris and John Holsey. And usually, I knew it, I knew it. Some of them weren't in the radiator staff which means they made the yearbook which means they've chosen themselves for some of them. And so when you turn the page, then you start seeing the junior class which we're not really gonna go through because it's a senior yearbook. Now when you turn the page, then you're gonna start seeing the athletics teams and we're gonna start off with the cheerleaders. It's so cool how their outfits look. That's definitely not how we dress anymore. So it's always fun to see the change of uniforms and here are the football players. Now here's the basketball team. The women's sports team, there's women's basketball, there's the dance team, there's... Oh, over here is the baseball team.  So these are a lot of little clubs that they've formed. Here's the Edison Science Club. And then at the very back are all of the sponsors who sponsored the school throughout the year which is so cool. I think that's my favorite part about looking at anything old like this when they have companies that don't exist anymore. That's really cool to see the company names and look up to see if they still exist too. And that is the end of the yearbook. So at the very end, I'm gonna read to you guys really quickly all of the signatures that Mary has gotten. And I love reading these kind of things because they're so personal and you get an insight of what Mary was like because usually these messages are a compliment. They're usually like written in a compliment format. So let's get started. First one says, dear Mary, you are one of my best friends and I hope you will be a good little girl while you are around M.H. I love you lots, Rufus.  They must have had a thing. Okay. The next one is, dear Mary, you are one of the sweetest and nicest girls I know and one of my best friends, lovejoy. Oh. This one says, dearest Reese, I wish you luck and best of wishes all through your life. Keep as sweet as you are now and you will do okay. Love June. Why am I getting emotional? This is so sweet. Dear Mary, this is to a very nice girl. I wish you the best of luck in future, Jane. The one in bluing says, dear Mary, best of all luck all your life. You have been a delightful home room pal all of 49 to 50, lovingly Margie J. There's one down here as well that says, and the final one up here in the corner says, Mary, remember the first, oh, hold on. Mary, remember at the first of last year, you know when we walked, sat in sixth period? Well, I ain't changed a bit. I don't think you have either. Love always napkin. Wait, that, that's so sweet. Oh, why am I, I don't know. I don't know where that came from, but I think it's because like, so we are all done with this yearbook. I was shocked to discover how similar our yearbooks still are. I expected it to be vastly different because of how old it is, but it's actually, if not almost identical to the yearbook format that we have today, which is really cool. There were two things that I've noticed that were very, very different. One was what I already mentioned, and it was the death jokes. I don't know if it was against the teachers or students, but the death jokes were a little strange for a yearbook. They must have had a difference as a humor back then. Another thing that I've noticed, and I don't know if you've noticed, but everyone in this yearbook was white, which was a little unsettling for me to realize after I finished it.  In the year 1954, that is when integration in the school system began happening. And so you're not, like all the videos, pictures and yearbooks that you find with people of color. That was definitely after the year 1954. Before that it was only white people out at the school, which is a very heavy part of history. And I'm gonna branch off of that topic really quickly because I get this question a lot. And the question that I get is, can I indulge in history? Or can I get into or dress like a certain era if there was a really bad part of history involved in that era? And I get that question a lot, especially from my POC followers. And I'm gonna answer that in this video because I get it so often and I've never found the right time to kind of get into it. So I'm gonna quickly answer that question. And this is just my opinion. This is a very opinionated thing. No one can say for a fact if something's okay to do. But this is the way I see it and I believe it's a very healthy way to see it and a very fair way to see it. When you get into an era is to respect and to acknowledge what happened, the bad things that happened in that era and make sure to not romanticize the era like it was this picture perfect time. I get that a lot in the comment section as well that they'll romanticize the 50s. And I'm like, I know pop culture in the 50s was great. I know architecture was great, films were great. The entertainment world of the 1950s was great. But socially, politically, awful. And to pretend like that part doesn't exist is very dangerous and toxic and unfair to the people who suffered during those times. So if you truly respect an era, it is to respect all parts of it and to not romanticize or fantasize about the era. So that's something that I personally don't do. I don't fantasize to go back. If anything, the farthest I'll go back. If I were to get a little time machine right now and they said you can go to any era right now. I would go to the 80s or 90s. So it's definitely not the 50s. And I think it is totally acceptable to dress 50s, 60s, 70s. You can dress vintage very well. And it shouldn't be a problem because there are people in your culture who have made an amazing, amazing impact in the world of its time. There's people of color who've won Pulitzer Prizes and have became famous singers. And I think when I dress, in my head when I dress 50s, sometimes especially for this channel, I think about the women who were Hispanic, Puerto Rican and who have made great accomplishments being singers and dancers and entertainers and being involved in science and stuff like that. So I believe it's a way to represent them and to honor them and to honor the people who have made impacts in the world. And so I would say feel comfortable wearing vintage clothing because you're a reflection of the men and women who have accomplished wonderful, kind and respectful things. So that is my opinion on that. Remember the motto, vintage fashion, not vintage values. That is the motto I live by. A lot of the vintage community lives by that. So keep that in your mind. Vintage fashion, not vintage values. I hope I explained that well. I have a hard time explaining how I feel a lot of times, especially when it comes to opinions. So I hope that makes sense. But yeah, that's just something I wanted to touch base in this video because I never find the appropriate time to do it until now. So that is the yearbook video. Yay, okay. So thank you guys so much for watching. I really hope you guys enjoyed this video. If you guys wanna see more of my vintage collections, make sure you leave a comment down below. Make sure you like this video if you enjoyed it. And if you guys wanna see more vintage and princess content like this, make sure you subscribe and turn on the notification bell so I can see you in my next video.


If you want to get on the ball more often, this video is for you. And I have to start by saying it is extremely important that you get on the ball as often as possible.  Now, if you're watching this video and you're saying yes, this is something that I want to do, this is the video for me, I want you to take responsibility because a lot of us out there are saying, oh, if only my teammates pass me the ball more, then I would get on it more often. If only they saw my great runs and gave me better service, then I would get the ball. If my coach wasn't playing me out of position, if I didn't have to play winger and I was more in the central midfield, then I would get on the ball more often. There may be some truth to these statements, but the reality is these are just excuses that are holding you back from getting on the ball more often. So let's move forward, but before we do, I have to say that it doesn't matter how many of my videos you watch. If you don't take the ideas and implement them, you will not improve. Some players are out there, they're saying I've watched all your videos and I'm not getting better. It doesn't matter how many videos you watch, what matters is the ideas that you take from these videos and implement them into your practices and games. So in your next game or your next practice, I want you to honestly ask yourself, did I do the things that you talked about in this video to get myself on the ball more often? I promise, if you make these efforts, you will see the results. So let's get into it. The first thing you need to do if you want to get on the ball more often is understand that what you do when you do not have the ball will dictate how often you get on the ball. So I'll say that again, what you do when you don't have the ball, that's what's going to determine how often you get on the ball. A lot of us, we complain that we don't get on the ball enough, but if you analyzed our play, we're sitting in the same position, maybe we're playing full back here, maybe you're playing in the central midfielder here. Okay, and you're hiding behind players. When you're off the ball, I want you to always think about, where should I be right now to create a passing angle for my teammate? That can mean making a forward run, a forward run. That can mean supporting a play, giving little passing angles. Okay, always think about the guy on the ball. If he turns, or if he gets his head up, am I available for the pass? Or am I cut off by whatever? Okay, if I'm playing in the back here, I still have to be thinking about, how can I be an option for him if he does get trapped? Don't react, so you want to be ahead of the play. If you know he's on the ball, you want to be ahead of the play. Okay, so what I mean by that is if you're reacting, he gets trapped, he gets turned, and because we were reacting, now he's turned and now we kind of make these angles for him and try to help him out. Okay, you want to anticipate that he may get in trouble, so before that even happens, we're already thinking about, where are these potential passing angles for the player on the ball? Okay, so think about your off the ball movement. Be more active, cover more ground.  Okay, what you want to do is you want to be productive, you want to be efficient, you don't want to waste your runs, but if you know that there's open space and you should be into that space, then make the run. Okay, be honest with yourself, ask yourself, am I being lazy with my off the ball movement? So the next time you play, be a little more productive, work a little harder off the ball when you don't have it, make those runs, always create those passing angles, whether that's behind the ball or forward ahead of the ball, but always think about where should I be when I don't have the ball off the ball movement. Okay, another thing that you can do, if you want to get more involved in the play, you want to get on the ball more often, is do more defending. Okay, a lot of us complain, yeah, I wish I was on the ball more often, but the truth is the opportunity to win the ball is there and you just stand there and watch your midfielder or just stand there and watch your defender do the defending.  If you want to get on the ball more often, can you start pressing from the front? Can we win it up here? Now suddenly you're an opportunity to get on the ball more often.  Defending is a great opportunity for you to win the ball back for your team and get on the ball more often. I promise you, if you put more effort into your defending, the next time you play, think about how many passes can I intercept, how many tackles can I make, how many times can I nick the ball, how many times can I force my opponent to give up possession and make a mistake, then you'll get more involved in the play. Everyone thinks about, oh, I have five shots or I scored two goals, I may want assist. Okay, but how many tackles did you make?  Okay, so think about adding some defending to your game, it's gonna get you on the ball more often. Another thing I want to say is, if you get on the ball and then you lose the ball, I've talked about this before, it's so important because it happens all the time, I still do this and players do this every time you play. You may have to admit to this yourself. Let's say you're this red player here and you took too long in the midfield and you lost possession of the ball and you made a mistake or the ball came to you and you had a bad first touch and it bounced off and you made a mistake. Most players in this situation, after they make that mistake, what happens, they don't want the ball anymore. They won't admit that, but they don't want the ball anymore. So when it is time to receive a pass, maybe in a tight area, they really don't want it. So maybe they don't make the run into that space or when they do, they're hesitant and they're already thinking about getting tackled or in the attacking third, okay, a pass was played and they missed a chance. So the next time that opportunity comes, they don't make the run because they're scared they're gonna get it again and miss the chance again. So if you make a mistake, you give the ball away, you miss a chance, you have a bad touch, you take too long and you know you made a mistake. The very next opportunity, you go and search for that ball. Give me that ball again. Have that mentality that it doesn't matter how many times I screw up, I want the ball again and again and again and again. Okay, so wanting the ball, desire to get on the ball is what's really going to get you on the ball more often. Okay, a lot of us say we want to get on the ball, but if you look at our movement, it's like hesitant, we just stay in the same spot all the time after we do make that mistake. Now suddenly we don't want it. If we do get it, we're just making simple passes rather than being direct, being productive, being confident with our play. Okay, so you have to have the ability to shake off mistakes quickly, especially if you wanna be a top level player.  Give me that ball.  Thanks for watching this video. If you found it helpful, please remember to give me a like, a thumbs up, share this video on social media, subscribe if you wanna watch more videos, hit that bell notification, and please remember, it doesn't matter how many videos you watch, what matters is how many ideas you take and implement into your own game.


Hi you guys and welcome back to my channel. So today I have a little bit of a different video but before we get into that I just wanted to kind of do a little explanation. First of all I haven't posted a video in a few days. It's been a crazy last couple days between this project and if you're new to my channel I'm a mom of three little girls that are the under the age of two so I'm potty training my two-year-old my one-year-old is still cutting teeth and then my five-month-old is starting to cut teeth so it's been a little crazy needless to say but I'm back in the swing of doing things and I get just the craziest ideas at the worst times to do projects I'll be honest with you guys but it's like therapy for me I love to paint I love to redo things and I'm constantly changing things and just making things the way that I like them I have a certain look I like to go for and so it's just fun for me to do that but I wanted to tell you all that we actually rent this home so I can only go so far with some of the things I do like paint is my best friend paint makes things look a lot different and so I did a law with paint on this project and I will be linking everything below that I possibly can of the different things that I used in case you guys want to try doing this I know that Amazon probably will carry some of the things I use to do this project and over here rumbling sound it's my husband leaving anyways I'm really really thrilled with how this whole thing turned out I still have a couple little knickknacks to do but I wanted to show you guys and also I do a lot of vlogging and cleaning videos and things like that on my channel so obviously you guys would see that the kitchen looks a lot different and would be like what did you do and all that so I just wanted to get this video out there and I hope that it inspires you to work on projects if you have been kind of thinking about doing some things and the first clip that you're going to see right after this is an evening clip I usually get my ideas of what I'm going to do if I have the stuff to do it at night it's just I don't know what it is my mom is the same way we're just project people and usually we get the most inspired in the evening or at night and we start projects and then it goes on for a couple days and whatever and with my kids going to bed of course that also probably brings inspiration on but anyways without further ado I'm going to show you guys what I did the process that I did and I hope that you all enjoy it if you're new to my channel don't forget to hit the subscribe button for a lot more videos like this and just inspiration in general like if you need cleaning motivation and those sorts of things and I'm just gonna stop talking now and you guys can see how I did everything all right so this is obviously the before and I started off by just taking all of the knobs off of the cabinet and the screwdriver didn't cut it so I got my husband's drill also completely ignore the horrible painting clothes and the nasty looking hair this paint is just from walmart and it's their white grab and go paint and I just always use this so that I know that anything I paint white is that white because there's a lot of whites out there all right so it's the next morning and this is what one coat of white looks like oh sorry about that um you can see kind of it's a little bit streaky and then um here you can see like what the other color looked like so I'm really liking it I can definitely tell like that the lighting in here is a lot different just from it being white and that's what the open shelving is looking like I'm going to eventually get um some probably from my dad this weekend get some nail filler and fill this and just sand over it and then just paint this side so that you don't see the nail holes and whenever I paint on the subway tiles I'm actually going to paint them in here too so it's going to look like it goes all the way up and you'll be able to see it behind like all of the glasses and stuff and I drip some paint on here and just so you guys know if you ever get paint on anything glass um just use a razor blade and it will scrape it right off and also I wanted to say that like if I get it onto the hinges um the way you can get it off is just some nail polish remover and a q-tip so I'm not too worried about the hinges although I did go around them with that little paint brush um just to make sure I don't get too much on them and make it a little easier to clean up so I will check back in with you guys once I get the second coat on I really really scrubbed the backsplash very well with the Mrs. Meyers soap because I needed something to make sure that it got all of the grease off of the backsplash and any other grime that would prevent the paint from sticking to it then I just got this clean release tape from duct tape brand and it's at walmart and that's what I taped off all of the edges with then I just borrowed a sander from my dad and I sanded over the walls um I didn't like go into real depths with this I just kind of went over it and more or less it probably just got rid of debris extra debris than really making it scuffed up then this little roller is also from walmart and it's the one that is for smooth surfaces all right so I have this part all painted with one coat and you can see there you can definitely see the difference in it and I think it's going to take at least two coats if not three coats to get a really like solid white going on and I am doing it with this roller brush because I feel like it's going to give it a more smooth looking texture like tiles versus doing a paintbrush so because that would make it have like brush stroke streaks a lot like the cabinets do like you can see there in the light that it has brush stroke marks and I didn't want that for the backsplash so now I just have to do this side since the backsplash was like an off white so were the switch covers and outlet covers so I am just going to take this um white spray paint and just spray paint paint them white and save a little bit of money on not buying white covers I'm working on the second coat now of paint on the backsplash the white paint and if you can kind of see there I think you can see the line by the light switch this is what I've been using for the edges because again I don't want the brush strokes so I've just been using this and dabbing it along the edges and looked up how big most subway tiles are and I found a couple different sizes but I'm going to go with a three by six so I have a yard stick here and I actually just marked where I'm going to be measuring since I'll be looking at it a lot and it'll just make it faster I'm going to draw it all on with pencil first before I actually do the taping and the painting all right I don't know if you'll be able to see them but there's really small marks I made every three inches all the way up and now I'm going to do it in here I'm actually going to fill this whole thing in first just for some practice and I think I'm actually going to do a third coat of paint on the the actual backsplash so I'm going to practice doing the tiles up in here anything that I'm messing up with the pencil I'm just using a mr clean eraser just because it cleans things up a lot better than a regular pencil eraser I made myself this little tool to be able to know how far apart I put my tape for the grout and I used a quarter inch this is a quarter inch I have the first few done and you can see the skinnier lines is where I'm going to do the grout I just wanted to explain to you guys a little bit why I'm using this method um if I was wanting to make it and look like brick I would actually freehand it so that it was like a little bit more imperfect but subway tiles are like perfect like they're very pointy they're very like square corners so that's what I'm going for so that's why I'm using the tape instead of just freehanding it over top of the pencil lines all right so the whole thing is taped up and my camera is having major problems focusing to me but I think you can see there you go now you can see it I had actually ended up getting two different colors because if I was going to do the countertop gray I would have used like a gray or tint but since I'm not going to do the countertops now because my dad kind of gave me a little bit of constructive criticism this corner of our countertop lifts up and he said whatever I put on here will probably crack because this is loose so I'm just going to leave the countertops the way they are which I think will work out if I use the right color grout and eventually our landlords will probably replace this anyways so I'm not worried about it this will be painted and so I can paint over it again if they replace it a different color it's kind of flexible so just so you guys know I got this at Walmart in the craft's aisle and it is in the color beachcomber beige is the color so this is what I'm going to be sticking on up there and I'm probably going to have to do more than one coat I'm assuming and we're back so now I put on all of that color on the grout lines and I used another one of these thingies just dabbing along so that I wouldn't have brush strokes and it would look a little bit more gritty looking so I'm going to let this dry and while this dries I think I'm going to put the last coat on the backsplash area I'm just afraid in daylight that you're going to be able to see the print through it so I want to do one more coat just to be safe all right so I put the last coat on the backsplash so that is completely done and then I had enough paint left to put one coat underneath of the cabinets and you guys might be wondering why I did that well for two reasons um one reason is because I'm ocd about stuff like that and wouldn't leave it go just like I'm going to be painting the inside of all of the cabinets kind of taking my time over the next couple of weeks like each cabinet so I don't have to empty the whole kitchen at once then the second reason is because of the color it would actually reflect on to the backsplash so if I want the backsplash to look really white I have to have this white too otherwise it's gonna like reflect that yellowy looking tint um onto the backsplash if the underneath part is not painted white too the other thing I wanted to mention super quick is I have done all of the stuff you guys have seen with half a gallon of paint I had this sitting in our basement and that's what I've been using um and I don't think I'll need to buy any more for the stuff I've done now to paint the inside of all of the cabinets I'll probably need to get like another half a gallon but um and I also use the same color on the cabinets as I did on the backsplash just so you guys know um it's the same stuff from Walmart I put the second coat of the grout color on this and I also got the second coat of white on the bottom of the cabinets so I think tonight yet I'm going to peel those off and then um get it going get the grout lines going the other way and then I think I'm going to do the pencil work on the backsplash but I really would like to let that paint sit overnight before I put tape on top of it I have the tape going the other way and it's almost dry enough to peel off up there um for the grout going the other way and then I am starting to draw in all of the tiles on the backsplash at this point I'm definitely starting to question my sanity and what in the world I was thinking of doing but at least this part's all done so now I just have to put in the paint and so this is the grout going one way and then I will be doing it going the other way and then I am doing the herringbone pattern on the backsplash of the sink part here because when I went to measure it out for the tiles it actually is like one inch difference on either side so you would have been able to see that so um I had to do something that would kind of play with the eyes so that you wouldn't be able to see that it was different and it wouldn't make the window look crooked or something like that we are making some progress but we hit a hiccup so I got all of the tape taken off for the grout going this way this wall was pretty simple this happened right here and um I don't worry don't freak out I think I can fix it and because I figured out what's going on so this is the sink area and it's the window so I'm pretty sure that there was moisture on the wall whenever I painted it so I'm just going to start over I'm going to sand it again really good and then I'm going to um actually probably use a hair dryer on the wall um really make sure it's dry before I paint and like you can see there so like anywhere it was kind of funny at the closer I got to the window the more um it seemed to have issues although this area didn't really have any issues so I I don't really know other than it has to be linked linked to moisture so I'm just going to redo this part and more than likely this would be my last little clip that I'm going to record because I'm going to get the rest of it put together and then you guys will see the rest of it there is some other little spots that peeled up and I will be just touching them up I kind of figured that would happen and then I'll be sealing it all so once it's sealed it won't get moisture and stuff in it and the other thing is too is if you guys have a newer house that's not just drafty um you won't have to worry about this also if you're doing it directly on a wall like directly on the drywall you wouldn't have to worry about this either because it's a combination of the moisture and the texture of this back splash so I will see you guys when it's done here is the end result and I couldn't be more happy with it I do need to do a couple things yet just like fill those nail holes but I did go over all of it you can see the shine there with a polycrylic I did two coats of the polycrylic and let it harden and so it's cleanable and I can wipe it all up but I just really love the look of it and I just like that the cabinets are brighter and lighter and I don't know what more to say about it other than I'm just very very happy with it all thank you guys so much for watching today I hope that you enjoyed this and it inspired you if you're new to my channel don't forget to hit the subscribe button I will see you guys in my next video


So the latest so let please introduce yourself. Oh, I'm Ching-Tang and Is it true that you invented the OLEDs? That's true How many years ago now? 1978 How's your feeling? Knowing that it's changed the world so much like so many people use the OLED, right? Well, I'm happy to see you all that being used, you know, the widely It's for researchers that some You know, it's a good reward. It makes you feel just because not everybody can research something that Become such a big success, right? Many people research for stuff and it's hard to see where their impact goes. Well, I mean in most research Particularly, you know, the one that I know about OLED I, you know, you came up with the idea or maybe you accidentally ran into it And you discovered, you know, 50 years ago not quite 50 years ago The point is that it takes tremendous amount of effort not just yourself, your team in my days at Kodak and you also have to have somebody willing to invest in a factory and That's how you have it today. So it's not a single man effort. It's a tremendous industry But maybe I can take a little credit being the first one to come up with it So, is it by chance? Did you come up by chance with it or you focus on this direction? I focus on that one direction and then OLED came about and then I refocus so you can say it's by accident and Is it How did you manage to or did you have to convince more and more people to join and and to work on this direction? Or is it thanks to display week like 45 years ago? There was a display week and everybody's like wow and everybody says okay I want to invest one billion or no, I mean the basically the invention was to switch the material You have LED at a time, but you don't have organic material based LED So once that was to even that was not discovered by myself It's something called organic electro luminescence. That was discovered maybe a hundred years ago All right, so but you you get it down to practical level Not practical, but you know in research wise it's practically enough for you to invest into to invest time into And so it's a switch from Semiconductor first ring semiconductor to organic amorphous material that is a major change And after that everybody recognizes that's a good material to use and you have something to that How good is it today? Is it much better than you could imagine or is it not as good as you hope it should be? No, no, it's much better than I expected so much better much much better these are if we check this one for example, so this one is a it's an organic based Display right, but the biggest the challenge is to put the RGB together and They trying to use a very brutal effort Like this what do you say put what together to put it together Closer Yeah, sorry, I'm just trying to put the photography Photography is the base to make the RGB pixels Nice I'll be doing a video with you just after about about this So you can introduce so I Was just on a uber and there was this guy with a foldable Samsung phone and he said it was the third one he already bought and like so many people have foldable Flexible is this enabling some flexibility? One step further All right, I'm not trying to do a commercial phone. No, of course, but Normally you do it by shadow masking Yeah, even the foldable, but this one they cut pretty elimination of asking which is a big deal well All right, so but it would take some time for them to You know commercialize it and really bring the cost down and so All right, what's up all this stuff you talk about the shadow masking and everything was that already happening 30 years ago? No, no, no, no the shadow masking happened maybe 15 years ago or something 15 times when that enabled all the technology Because LCD and all those they they used for the top of you mainly But all that requires shadow masking technology to put down the RGB Except for the TV TV completely just different I'm very happy with my OLED TV, and I was trying a little bit with a with a LCD but I My my wife she said no no we need to get the OLED When she look at the store, you know how the quality and now They also Not only doing the phone displays now to do the TVs Is it's completely different world the OLEDs on TVs and Mobile was it very similar the order TV has credit to set to not to Samsung to LG LG is the one who pioneered a TV Yeah, so you should go to their booth to see the order TV But now they're also doing the OLED TVs, right? But they come late They came much later yeah, so You know it's still over TV, but the Technology get started By you know first at Kodak, and then the LG TV Is it amazing to think in the the scale of these companies how much you invest in the factories? And you can sit there and you imagine You can ask them how much money they spent on there. Yeah Investments, I mean how much money you spend on the investment How much the investment that you have to make to build an older TV It's a secret right They're talking about in the unit of hundred million dollars. It could be ten of such unit But you know a hundred million dollars to build a manufacturing But you know there's now we eight billion people Everybody needs an OLED, right That's a good investment. I I don't think everybody would need an OLED No Not everybody. No, I mean you need to put food on your mouth first All right, but maybe you can become more and more affordable. Is that possible? It definitely will be more and more affordable. Do people want to print them as difficult Well, I mean they can do the evaporations the printing would come whenever they can make it But it's not there yet All right. It's it's true. You got the Nobel Prize. No, no No, you should No, okay. All right. How about meeting all your colleagues here? That's what you're gonna do now Yeah, we just want to walk around and you know to see what's new here. Okay. Thank you so much Okay, can you give you my card? I have it. Yeah, it's right there You guys can send me some money you can send money on wise it's really smart Oh, you don't have to send me money you can send money to your friends to your family Are they in a different country? Do you need to use currency transfer like to different country transfer? Do you need to pay for stuff? Do you want to travel around the world and pay for stuff?  This is a visa debit card Check out my video where I explain some more it works in a hundred countries all over the world Maybe a hundred fifty it's crazy and it's really amazing and it's free you can sign up use your Android pay your Apple pay or Order this optional seven euro debit card and just pay for stuff around the world It's great to pay for stuff, right or send some money tiny little fees. It's smart. Check it out


Oh, yeah, it's going on everyone Sam here with late in sports cards We are ripping two boxes of 22 tops dynasty formula one racing hobby for Kyle T It's good luck here Kyle. Let's do it with these all open them and then I'll just give you the box and then just once we show it just put it back in the box and just put them back there And I think we send them in the box. Okay, I don't know but that's how we did it last year So I'm just gonna sign all this slide to the box over All right Card number one Seven of ten that is good. They're Steiner for ha's on the principal card. Nice one there congrats Kyle There you go, buddy. Goon. They're Steiner Where was he he was somewhere else? I believe he was on a different. He was a principal for a different team Nice one there though seven of ten congrats on that The patch card My crack my crack in this too. Yeah, my crack is in this All right, here we go That's huge. I mean it came undone, but how about Lewis Hamilton? five of five boom Let's go congrats Kyle on the Lou Ham. Let's go dude Big time a hit man. Again, you can see that the little foam piece got stuck. That is Insane congrats Kyle Five of five. There you go, buddy That is gonna do it for your break Kyle massive Lewis Hamilton coming your way. Thanks again for the support my bed We'll get those right out to you buddy


Welcome to NPTEL NOC, an introductory course on point set upology part 2, module 62 connected some and classification of surface. Last time we have introduced the notion of rubber sheet models and stated a big theorem which is supposed to give you all compact connected surfaces. The same result we will try to explain in a more geometric way this time. So I have defined one single notion here, start with any two connected surfaces. So this time let us not bother about the boundary, boundary may be there but keep it far away, even if it is there. Start with any two connected surfaces, start with two embeddings of the disc D2, the closer disc D2, eta1, eta2, each of them in S1 and S2, okay, B2 embeddings. Put Ci equal to etai of the boundary, the boundary circle, take phi equal to C1 to C2, C1 is you know this is an image of this one, so it is contained in ZS1 and that is contained in ZS2, right. So take phi to be eta2 composite eta1 inverse, where I mean by eta1 inverse I am restricted to the boundary here, okay. Then the quotient space obtained as follows, namely you take S1, throw away the interior of this disc, the image of that disc, interior you throw it away, keep the boundary, similarly from S2 throw away the interior. So you start with two surfaces, now you have made two holes there, okay, when you make a hole, hole means what, now removing a disc, interior of disc, the closed disc is there, the boundary of the disc is there, so those things are C1 and C2, right, here. So identify X with phi X, where phi is this map, by this map, namely for every point X inside C1, by this map phi, eta2 composite eta1 inverse, that is a homomorphism. So that quotient space is called the connected sum of S1 and S2 and is denoted by this notation, S1 connected from S2, that is the way I read this one, okay. So here is a picture here, picture may be confusing, I do not know, this is one surface, there is another surface, there is a disc here, there is a disc here, so these are embedded discs, so you remove the interior of this, remove the interior of that, there is a circle here left out, namely image of a circle, so this looks like an ellipse here, this is an image, so identify them like this, so bring them together like this, identify the two circles by a homomorphism, that homomorphism is not an arbitrary homomorphism, it is from this circle, see this one is eta1, so you get eta1 inverse composite eta2, so that is a homomorphism from here to here, you identify that, okay. For example, if you take a disc, remove an interior disc from that, you will get an annulus, do the same thing on this side, take a disc, remove the disc from the interior, you will get another annulus, now you have got two interior circles in both the annuli, you identify them what you get, you will get back again a cylinder, actually annulus and annulus they are cylinders, so but when you identify two of the circles, one circle from here and another circle from another one, you will get one cylinder, so the world connected some precisely refers to this one, you start with connected surface here, the end result is also connected, there are two of them here, the end result is connected, so two of them you start, but each of them must be connected, so then you make them connected by this performance, okay, if you just join them at one point, it will fail to a manifold, that is the simplest way of doing connected zone, if at all, but in topology, general topology we will do like that, one point union, but in manifolds, it will fail to a manifold, so what you have to do is, do the trick namely, remove a small disc, remove a small disc, okay, what happened, the boundary of those two circles, the resulting circles you identify them, the following observations which are intuitively clear, of course need proofs, okay, which we shall skip, so what are these observations, S1 connected some S2 is a connected two manifold, it is compact if and only if both S1 and S2 are compact, okay, see there was no statement about this being compact, so I could have taken any two connected circles, that is all, alright, so so far whatever I have stated, they are not at all difficult, okay, very easily, only because we have time limits here, I cannot go on explaining everything, the homeomorphism type of S1 connected some S2 does not depend upon where and how you have chosen these embeddings eta i from D2 to S i, S i surface is you have chosen these things, right, how you choose these, how you choose these things, no problem, all of them will define the same, same means what, up to homeomorphism the same surface, so this is a deeper thing, this requires some proof, not this one, these are easy, so this requires some proof, if you take S connected some S2, okay, S is some surface, S2 is the standards here, what do you get, you will get back S itself, why because you have to remove a disc from here and disc from here, right, when you remove a disc from S2 what do you get, you have another disc, now you are filling that disc back in the gap that we have produced here, so all that amongst doing nothing, so that nothing is back to homeomorphism, so connected some, taking connected some with the sphere produces no effect, that means it is identity operation, so that is why you know S2 I told you it is like a zero element, this connected some more or less represent you know some additive operation, you can see that it is associative, it is commutative, only thing is there is no inverse here, it is like natural number, you see, there is a beautiful you know algebra here, out of this, what are called as cobaltism theory, so that I cannot go into this detail, the cobaltism theory is connected some operation is the sacrosanctus, so this can be defined in all dimensions also, but now we are learning it in dimension 2, let us denote the torus S1 cross S1 by this simple symbol you know this Euler T, I will just read it as T and the projective plane by P2, this we have already done, this was a new notation, this is an old notation, let us denote the connected sum of G copies of T by TG, what is this S1 cross S1, again take S1 cross S1, again take S1 cross S1, G copies, take the connected sum, let us denote it by TG, similarly the connected sum of N copies of the projective space, let us denote it by just PN, so again this G and N are coming just like in the last lecture, so what is it I am writing here, TG is T connected sum, T connected sum T, I do not have to put any brackets here because SOCA tail, similarly PN is P connected sum P connected sum N copies, what is T1, it is nothing but T itself, P1 is just P upper 2, because only one copy is there, you have performed any operation, so this is notation, short notation for this long thing, now the big theorem here is like we did after long long in the last time, but this time we have easily the following, every connected compact surface without boundary, I want to emphasize that here, compact connectedness but no boundary, is homeomorphic to exactly one of the three things, actually there are three lists here, this is a single element, but this is an infinite sequence, this was an infinite sequence indexed by natural numbers, exactly similar to the previous theorem that we had, I will just show you that theorem which we did last time, this is the theorem, the AA we have told it is also H2 here and these are going to be the second list TGs, these are going to be PN, every compact connected surface without boundary is homeomorphic to precisely one of the surfaces defined by these reduced polygons, so this is some kind of a technique to obtain such a result, the finally we would like to have this description, so why these two are the same, I will try to explain that one, not a proof but just some explanation, the theorem has two parts, you see every compact connected surface is exactly one of them, first of all take any compact connected surface, you must be able to find the means what, up to homeomorphism, but there will be two different ones, they will be homeomorphic in the list, no, there will be every element here is a different homeomorphism type, so that is the second part here, there are two parts like this one, it asserts that up to homeomorphism there are no more compact connected surface is other than the ones mentioned in the list, the list is exhaustive, thus the list is that means, the second part is which you may call is non-overlapping list, namely the uniqueness part, asserts that members of the above list represent distinct homeomorphism types, the proof of the exhaustion part, there are essentially two different approaches, the first approach one proves that every compact surface can be given a smooth structure and then uses what is called as Morse theory, you can read something many books are there but you can read for example my book, the other approach is the one that we have been discussing in the last module, namely this rubber sheet geometry, the canonical polygons or whatever you want to call, so let me explain because we have done some work there, let me explain the relation between the previous theorem and this present theorem, namely in the second approach, one first proves that every surface can be triangulated, what is the meaning of triangulation, just you may be able to cut it into finitely many pieces, each of them homeomorphic to a triangle, homeomorphic to a triangle is anything homeomorphic to a disk but you would like to think of them as a triangular pieces with three edges, so this is the idea, the proof of this is not at all easy, the proof of that giving a smooth surface is even much harder actually in that sense, may not be but this is much more harder anyway, so you have to assume that they are triangulated, from the triangulation what you can do is you can get a regular 2 n gone with edge identification as indicated in the last module, you cut the surface into all the strangles while cutting down what you do, you keep a label wherever you have cut down you are introducing two different edges right, so make them all labelled in the same way a comma a and put an arrow also which way they are getting identified, so this is this will keep you for the surgeon to patch up where wherever he has cut that is the whole idea, so look at all these triangles, now lay down them on the table one by one side by side wherever the edges come you know in any arbitrary fashion it is like a jigsaw puzzle when you are doing jigsaw puzzle nobody tells you which piece you have to take first and forth, you take one first then keep putting this jigsaw puzzle try to arrange them, how do you do that there is only one rule, namely wherever an edge indicated by a letter you look for that letter in one of the triangles it will be there, so put it there put it on the side keep putting like that re-adjust the whole thing you are allowed to stretch the triangles whichever way you like, so that every every time you have a convex polygon re-adjust that the shape of the triangle that is all, so you have union of finitely many triangles and that is a convex polygon, so one of the extra edges there you will get exhaust all the triangles you will get a convex polygon, now what will happen there will be all these boundary edges of this convex polygon they are identified as some edges where are they they are also there in the same polygon but on the boundary now because everything interior they have got their pair they have been paired already, so these are the last ones which are left out, so you will have exactly a even sided polygon two end sided polygon because there must be a pairing and you perform that you will get back the surface that is how the exhaustiveness has been, so every surface can be got by a rubber sheet scheme, now there is another part now you have to say that the list contains all the representatives, representatives means what up to homeomorphism, so that is the harder part that we have done in algebraic topology course part two also you can read it from my book in algebraic part, so these combinatorial arguments to cut it down to just canonical polygons as listed last time they are justified by one main topological observation what is that if you have made two cuts in a surface you can get back the original surface by performing the two corresponding patches and patching up whichever order you want you may all you may first you know stitch this one and then stitch the other one or the reverse way there is no problem the resulting the surface that you get will be the same provided you have performed all the stitching back wherever you have cut that is all, so this is the beauty you can cut as many times as you want, every time you have cut sometimes that cutting must be stitched back it has to be identified that is all, we shall not go into details here but we shall indicate how to get 12.50 from 12.47 now, so that is the main thing there are two different description I want to relate them somehow first of all note that list A in both the cases corresponds to S2 there is A here that A here they are same they will they will give you S2 now come to the list B start with the rubber sheets came A B A inverse B inverse and some C do not matter note that the resulting surface as has one boundary component because this is not identified and that will be the circle because both the end points are in one of these so they will get identified which is a circle correspond into the free edge C if you identify this entire circle to a single point you have some surface and it has a one boundary component namely keep that make this circle smaller and smaller and bring it to a single point that quotient space S0 is the same as the quotient space corresponding to the rubber sheets came A B A inverse B inverse as if that edge as we have been shortened shortened shortened to a single point so no edge left out that is all right so which is now we know is a torus therefore this scheme represents a torus with a hole do you understand this this this I will repeat it what I start I do not start the torus with a hole I take A B A inverse B inverse I know that is a torus but now I have different scheme here namely there is a pentagon right A B A inverse B fifth side is just C when you identify that this C will become a circle whatever the other surface I do not know what it is do not matter but there is a hole here now you move that hole to a smaller make it smaller smaller and make it a single point so that surface is the same thing as as if you have got it from A B A inverse B inverse therefore this surface must be the original surface must be what the torus with a hole all right that is the whole idea so reversing this argument we see that if you start with the torus and make a hole in it then the resulting surface with boundary is nothing but the surface obtained by this A B A inverse B inverse B so this is the scheme for that all right so this is the picture here so A B A inverse B inverse so that C is there which we do not want so if you when you perform you have got something here this A becomes one so one loop that B becomes another loop A and there are two A A here they will give you one single loop okay over one over the other so this B is another single loop this C is another single loop dot dot dot dot so these are interior to the surface but this is the boundary so make it smaller and smaller is the same thing as putting a disk here removing a disk here you get back this one so this picture is as if you have got it from A B A inverse B inverse so this is the picture so you can push it back so putting this making the circle to a single point is same thing as putting a disk here removing the disk from the torus gives you the scheme namely the scheme now what do I do therefore it follows that the connected sum T2 what is T2 T1 T connected sum T right two copies of two copies of torus is obtained by taking two copies of A namely A1 and A2 so A1 is what A1 B1 A1 inverse B1 A1 C1 A2 is what A2 C2 I have I have changed something C1 I have put here cyclically I can put it right in the beginning so that is what I have done that is because I want to bring them together C2 A2 P2 A2 inverse B2 inverse I could have put it C2 here but cyclically I can put it here of no problem so you take these two first identify the two free adjacent C1 and C2 you can identify whichever order you want is the main you know guiding principle here to get the rubber shades came what will be one you identify C1 and C2 this is one this is one disk this is another disk but they have a common edge now on which we have identified so entire thing becomes a one single disk C1 and C2 go into the interior and you get A1 B1 A1 B1 inverse B1 inverse followed by A2 B2 A2 inverse B1 inverse ok this is the picture C1 and C2 they have brought we have been brought together here in this picture then re-aligned the whole thing ok this dotted dotted thing here is C1 C2 one identified with the other the rest of them is A1 B1 A B A inverse B inverse ok A2 B2 A2 B2 inverse this is the scheme for remember in the old theorem this is the connected sum of two connected you know whatever A1 whatever C that polygon in the list two with G equal to 2 here right on the other hand if you perform this one first perform this identification first what we have seen is both of them are looking like this without this disk that means they are torus minus a disk torus minus a disk two of them join C1 and C2 this time at the last what you get you get a connected sum therefore connected sum of torus with itself is represented by this K now a common induction tells you that if you do G of them ok like A1 B1 A1 inverse B1 inverse dotted dotted AG BG that is nothing but what connected sum of G copies of the torus ok so this is the sum of two torus here so that will be you so repeating this process it follows that the two lists list B here and this B there in the two theorem give you the same class of surfaces exactly similar argument is valid for the list C as well ok therefore 12.50 follows from 12.47 alright finally let us see two different geometric ways of constructing all the TNs as embedded smooth objects in R3 ok there are I want to tell you two different methods because they are both interesting and useful in the first method we begin with the union of N circles in R2 such that C1 touches C2 C2 touches C3 and so on like a chain ok so they are not disjoint what are the disjoint C1 and C3 are disjoint C2 and C4 are disjoint and so on whenever I minus j is bigger than 1 they are disjoint when they are consecutive they have a single point in common they are attaching each other ok in the picture below I have taken three of them because picture has to be limited you cannot take N anyway alright so three of them the same radius R that is extra extra thing so that you get a nicer picture and so on now put C equal to union of CI finite union C1 C2 Cn and let Xn be the set of all points X inside R3 such that the distance between X and these circles union of circles is less than delta ok wherever where 0 is less than delta less than equal to R so this is an open subset take less than equal to delta you get a closed subset compact closed subset of bounded subset of R3 alright equal to delta delta should be chosen correctly that will give you a surface that is the whole idea so this is a picture here the dotted circles here these are the beginning circles they are touching at one point one after another they are inside R2 the entire solid here set of all points which are at a distance less than equal to some delta delta must be so these are circles of radius R so this delta must be less than R strictly less than R for the sake of this picture I have taken perhaps R by 2 ok take all the points which are at a distance less than R like that and then look at the boundary that boundary is the connected sum of 3 tori here if you have taken n of them it is the connected sum of n tori if you take only one of them circle first thing you have to see is that it is actually the torus ok so that part is just some elementary 3 dimensional calculus ok you should know some differential calculus to see that this is actually a surface nice surface alright so of course it takes some 3 variable calculus to show that the boundary of Xn is diffiomorphic to Tn whereas it is intuitively quite clear you take a circle you thicken it like a wire thicken it lightly bigger ok the boundary of that is a torus so that is what it is ok so in the second approach one approach is over so you have got a model of the surface right the boundary is a surface which is Tn so it is inside R3 over no for Tn you have got so actually I should write Tg here n ok in my notation I should write Xg and Tg here fine in second approach I merely start with an equation so this should be liked by say algebraic geometry for example so you can take equation here of course this is all real values inside R3 all the coefficients are real you can look at what is this funny equation see the left hand side is just some polynomial and X and Y the right hand side is just so there is separated variable equal to minus that square that is how ok so look at this one there is one special factor here and then there are similar factors here carrying from 1 to n ok what are they the first factor here is X square plus Y minus n plus 1 Y minus n minus 1 square minus n plus 1 square which is nothing but if you put equal to 0 this is a circle with radius n plus 1 and the center equal to 0 comma n plus 1 similarly here is center with 0 comma k and the radius is 1 by 3 I have taken the product of these polynomials put them equal to minus that square this time I take Yn to be the set of all points XYZ inside R3 which satisfies this equation 39 and claim is that this represents Tn ok so here the picture is here so how many circles are there 1 2 3 and 1 big circle what is this big circle this is the circle represented by this one so where are the circles these circles they are inside R2 X comma Y the z I exist on this way ok so I will tell you a little more about this I do not want to prove anything here namely take this equation on the left hand side just put equal to 0 what is that meaning of that third coordinate put equal to 0 means intersection with R2 what are that if some product is 0 means each factor or at least one of the factor must be 0 when you this factor is 0 you get a circle this factor 0 you will get various circles what are those circles they are the circles here one is the biggest circle all of them have centers on the Y axis with some radius ok the radius of the first circle is n plus 1 the radius of the second all the second third on the all of them they are just 1 by 1 by 9 1 by 9 but what is the center 1 2 3 4 and so on on the Y axis X is always 0 up to n but this as n plus 1 is the is the center and the radius is also n plus 1 so that big circle actually touches the X axis ok so it encircles all the circles here and these circles themselves do not encircle any of them that picture is very important so they are you know mutually exclude exclude each other they are not contained you know interior does not contain the other circle whereas the big circle contains all of them in the interior so that kind of distribution is necessary alright now what happened look at this area here bounded by the big circle and outside the all the small circles so how do you get that area how do you get any point in this I am not interested in the area aspect but point in this domain so how do you get that one they are inside this one means the first equation must be less than you know the first factor must value of first factor must be less than 1 less than 0 and this negative ok equal to 0 is the circle less than 0 will be inside bigger than 0 will be outside the same thing here ok I want it to be outside here now so they are all positive so all positive 1 negative so the entire product here is negative whenever entire product is negative it represents a point inside take that negative number take the negative of that that will be a positive number take the square root of that that is your result so that is the meaning of this equal to minus that square ok then there are two square roots accordingly you will get two points one above here one below here so to take that once you take the positive thing you will get the graph of that ok that function precisely this part and then there will be another copy below this minus of that the union of those two circles those two graphs is precisely this one namely square root of this one minus the square root of this plus square root of that so that is z you see minus z square is there what is z take minus of this and then take square root then you have two square roots ok so z equal to something is the graph of this ok there are two functions plus minus so that is the union of these two graphs this is the surface so once you know that ok you will see that precisely above a point here there is nothing here right because a point here the function will be what is the function this function this value of this function will be will be what positive so you cannot have minus of that the square ok there is a real number so this is a real number that is a value ok so these are holes there you see outside also if you come here the function the left hand side will be will be positive because all of them are positive if you come here outside here ok positive then there is no square root minus of that will not have square root that is all that is a trick here ok so it is easily checked that this is smooth surface if you intersect y n with the plane z equal to 0 what you get a disjoint union of n plus one circle all that I have written down here finally this is nothing but union of two graphs z equal to plus minus square root of minus f x y f x y I have denoted by all this factor the function the polynomial x and y this part so in two different ways I have shown that there are embedded sphere embedded surfaces inside R3 up to homomorphism they represent each of them represent the class in what in the list B ok list A is obviously there already we know that list C cannot be represented by embedded surface is in R3 look at P2 you cannot look at the Mobius band Mobius band is also non orientable but this is a boundary that can be represented what is the meaning of that Mobius band we have seen is the same thing as make a hole inside P2 as soon as you make a hole you have boundary right take any surface in the list C namely P connected some P connected some P n times make a hole in that that surface can be represented by an embedded object inside R3 not very difficult to prove but I will not prove that here alternatively you do not want to make a hole then what best you can do you can get an embedding except there will be one single crossing around a circle ok that is called a self-intersection of the of the immersive surface such things are called immersion not embedding ok so there will be two circles in the original surface and a map which will be an embedding except along these two circles these two circles will be identified to a single circle in the image that is the meaning of that so that is the best thing you can do for all the non orientable surface namely those which occur in the list C ok so this is what I have P n cannot be represented by objects in R3 the saving grace is that if you allow just one self-intersection along the circle then it is possible or equivalently suppose you grant for this one then you can put this one namely wherever there is a intersection you cut that circle inside there will be a disc so you remove that disc which was extra then you do not have to cross it out so that is how you can get this embedded circle embedding after removing a disc ok now comes the uniqueness part I will tell you a few things uniqueness part cannot be proved cannot be proved by pure point set topology ok it is not like you know classifying the one-dimension manifold which could be done which we have done just point set topology you have to bring some tools from algebraic topology you have to bring some you know some invariant you may use something like very heavy machinery like a complex analysis you know not elementary complex analysis again ok so like Riemann did them in the beginning ok so you have to have some high high machinery here so I will tell you the simplest thing is that you can use the fundamental group ok yes use fundamental group you compute the fundamental group of all these objects they will be all distinct groups distinct means what non isomorphic that is not difficult to prove once you know what is fundamental group and how to compute these things for that now if you know that homeomorphism not only homeomorphism if they are two spaces are homotopy equivalent I am assuming surfaces connected surfaces nice surfaces and so on nice topological spaces if they are homeomorphic to each other they will have isomorphic fundamental groups since the list will give you different fundamental groups they must be non-homomorphic so that is the way the proof is completed instead of fundamental group we can use what is called as homology groups these homology groups may take little more time but they are much easier to understand easier to compute than fundamental groups actually ok they will also give you that these lists have different homology groups just you have to look at h1 and h2 both of them you have to look h2 will be good enough to distinguish between the the list b and list a list c list a is easy to differentiate list b and list c but within the list c or within the list a list b you will have to use h1 ok there are h1 h2 h3 and so on they are homology groups ok so finally the big thing here is which is very special for surfaces or just one dimension manifold it turns out that the classification of connected compact surface is without boundary the same whether you consider homotopy types homeomorphism types or diffeomorphism types this is a very deep result ok so same thing we have done we have not done same thing we have easier approach namely for manifolds of dimension one house ok the classification that we have done could have been just by homotopy type right lightly you have to be careful with boundaries do not use boundaries we connected manifolds without boundary boundary you can later on deduce it from once you have what the classification without boundary similarly here up to homotopy you can determine the whole thing do not you have to assume that they are without boundary otherwise they will have some other problems which can be sorted out ok so we have come to an end of the chapter as well as an end of the course here now ok so I would like to thank all of you first of all if you have really come all the way to the end of this course many people drop out in between that matter so thank you all I thank my team of TAs who have been especially you know useful for even getting the material in order and all that and they will be also helping you all the time in understanding this one they have been helping you for in the tutorials or what you call assignment and so on right also in the discussion forum so big thanks for my team not only that the team from NPTEL they have been very very encouraging and very helpful so I thank them all ok see you some other time thank you.


Hello and welcome to the session. In this session we will discuss one area theorem. According to this theorem we have with equal areas and altitudes. We are given two triangles and so we have that the area of triangle is equal to the area of the triangle PQS perpendicular to PQ. Now since we have these two triangles that is triangle PQR and triangle PQS are on the same base PQ and they have equal areas. So according to this theorem we have to show that they have equal altitudes. That is we need to prove is equal to Sn of the triangle PQR is equal to the area of the triangle PQS. Now this theorem is equal to half into base into height is given as half into base which is PQ is equal to same base have equal altitudes. So this completes the session. Hope you have understood the proof of the given area theorem.


Now here's a video that I've been wanting to make for a while now. I actually forgot that I had this video saved up for my computer but I think it's a really interesting one. I want you right now to forget about how good LeBron and Carmelo are right now. Forget who's better, forget who's won the championships and bring yourself back to the 2003 NBA season where you didn't know who was going to be a better player. I will say that I agreed that the NBA gave it to the right player for the rookie of the year but I also think that Carmelo Anthony has an extremely strong case and I wouldn't be surprised that if after you watched this video some people may think that Carmelo Anthony actually should have won rookie of the year and beat LeBron James but it's up for debate. Let's get into it. I will admit that LeBron James is one of the top five players of all time. I could argue that he's top three or even top two but that doesn't cover up what he did in his rookie season which don't get me wrong it was amazing. He is amazing. One of the only three rookies in NBA history to average at least 20 points, five assists and five rebounds at that time. The only other two players at that time of 2003 was Oscar Roberson and Michael Jordan. He was an incredible player especially since all the hype was on him that year and he lived up to the name of the chosen one. He was a beast on the court however when he was awarded rookie of the year another player could have easily taken it from him. Carmelo Anthony. Okay now let's compare the two players in their rookie seasons obviously LeBron averaged 20.9 points, 5.5 rebounds and 5.9 assists per game that year becoming only the third rookie in NBA history to average a 25 and 5 line per basketball reference. Anthony meanwhile averaged 21 points, 6 rebounds, 2.8 assists per game but had a higher field goal percentage and more win shares than LeBron James. He also helped guide Denver into the playoffs while Cleveland didn't make the 2004 postseason. To make it clearer to compare here is a side-by-side comparison between LeBron James and Carmelo Anthony that season. As you can see LeBron he is a beast 25 and 5 more of an all-around player but Mellow win shares is higher, field goal is higher, P.E.R is not as high obviously, assists we know Carmelo Anthony doesn't pass the ball. I guess the last couple of seasons he's improved with a terrible New York team apart from pretty much poor Zingers. Derek Rose is, I don't even know how Derek Rose is anymore like I can't even understand him I don't know what he is.  He's kind of still got athleticism but he doesn't even like dunk anymore. He's a weird player it'll be interesting to see what happens with Derek Rose but we're going off topic right now. I want to ask you who would you have chosen as the rookie of the year? Just by looking at the stats, Carmelo has LeBron in points, rebounds, field goal percentage and a higher win share which when you break it down is four out of the six categories. Now this is good and all but it still doesn't mean Carmelo Anthony should have won the year since it's not mentioning defense and well let's just say we all know who is better on that side of the floor. LeBron James will come along Anthony with defense yeah we don't really need a brain searching to figure that one out just if you watch a basketball game you know who's better but it still gives you a rough idea of how similar LeBron and Melo were and honestly Melo's offensive game was better at that time just by looking at these stats not by much but it was better. Now let's look at the actual wins between the two players because I always hear the argument that LeBron James had much worse players than Melo did and that his team was far worse than the NBA before LeBron got to Cleveland but when you actually break it down the year before they both got drafted in 2003 the Cavaliers and Nuggets both finished with exactly the same record a record of 17 and 65 keep in mind that the Nuggets did play in a stacked Western Conference that year and to give you an idea of how stacked that conference was the Pistons who were the first seed in the east would have tied fifth in the west but possibly even the seventh seed had they versed more Western Conference teams which that is crazy going from either the first seed in the east to either the fifth or seventh seed or sixth seed that is crazy but anyway back to my point the Nuggets and the Cavs both had a record of 17 and 65 before they drafted LeBron and Melo respectively those records changed the next season however the Nuggets rose from 17 wins to 43 wins and made the playoffs in a stacked Western Conference keep in mind whilst the Cavaliers went from 17 to 35 which is still a major improvement but they didn't make the playoffs so as LeBron James took the Cavaliers plus 18 wins that year for a 35 and 47 record but failed to make the playoffs in the week Eastern Conference Carmelo however became the second youngest player to score 30 points in a game since the ABA NBA merger the other player being Kobe Bryant Anthony was also third youngest to reach 1000 points but the impressive staff that most stood out was how Kamala Anthony led the Denver Nuggets who were tied for the worst record in the NBA the previous season to a 43 and 39 record this meant the Nuggets made the playoffs for the eighth seed in a very tough Western Conference with Minnesota Sacramento San Antonio the Lakers Dallas these these guys were really really good teams and the fact that Kamala Anthony led them to the playoffs comparing to what they had before previously that's a pretty good effort but in fact if you want to talk about players winning that year I still think the Duane Wave deserves recognition for taking Miami into the second round of the playoffs and finishing as the fourth seed in his rookie year but hey that's none of my business I guess I'm just salty that he's not in Miami anymore anyway this is pretty much where I want to ask you who do you think really should have won rookie of the year in 2004 in hindsight picking LeBron James for rookie of the year will look good when he makes it to the Hall of Fame but Kamala Anthony has his case as well and I just hoped this video I guess changes some people's opinion on Kamala Anthony because I know he cops a lot of criticism now and personally I love mellow I've always been a fan of mellow I loved him when he was in Denver that the cornrows man that was Kamala Anthony that was cool obviously when he went to New York they had a little bit of success not the amount of success that they wished they could have had but now he just cops criticism every single day and I wanted to make this video hopefully just sharing some insight on who you think should have won rookie of the year because Kamala Anthony seriously has a case the reason I said that at the start I'd still have LeBron James winning it is because LeBron had an all-around game even coming into the NBA as an 18-year-old he made his teammates better offensively but most importantly defensively as well which is where mellow kind of lacks another thing is LeBron was in a team with only boozer as solid help Kamala had an a Miller can be in a bunch of other veteran roleplayers so take that as you will I guess the team was a little bit better on Denver but in saying that mellow going from the worst record to the NBA to the playoffs is still a great effort also once again LeBron James was and still is a much more versatile player as he can play through one to four positions in the NBA which is crazy from point guard to power forward even if he played center he would do some work and he can give any player trouble which is why mellow didn't win rookie the year LeBron James did he's just a way more all-around player than Kamala Anthony who only really plays small fold and a little bit of power forward here and there which in the end is why LeBron James won plus if any voters had lingering doubts about the 2004 rookie of the year race LeBron James second season in the NBA would have silence critics everywhere from that point on Kamala Anthony would never come close to the throning LeBron James as the league's best small forward I mean even now we can clearly tell who the better player is but if you look at the 2003-04 season it is really close and that is what we're just looking at we are just looking at the rookie of the year in 2004 and I hope you guys enjoyed this video let me know who you think should have won rookie of the year and if you're new around here and you want to see more videos just like this one be sure to hit that subscribe button and if we can smash 3000 likes as well that would be amazing thanks for all your support and I'll catch you guys in my next video peace