Hi, my name is Natalie Rogers. I'm the Public Information Specialist for New Mexico EPSCORE and I'm here today to talk to you about presentation methods and skills. Should be a pretty brief webinar.  So we'll start off with a quote from Albert Einstein, which is really pointed, not just giving a presentation about your research, but a presentation about anything really. If you can't explain it simply, you don't understand it well enough, and that's a good place to start. When preparing for your presentation, no matter what kind of a presentation it is or what it's about, you first want to ask yourself, what is my communication objective? Some objectives might include you want to inform your audience, you want to propose something, maybe you're asking for something, perhaps more funding, or maybe you want to engage in a discussion. And of course, this all depends on who your audience is. You're not going to give the same presentation to a group of PhDs as you would to a group of seventh graders. No matter what kind of presentation you're giving or what the topic is, you always want to tailor your presentation to your audience. Something else to remember is you can remember through a quote by Maya Angelou, which is that people will forget what you said and people will forget what you did, but people will never forget how you made them feel. And this can be true for presentations. You can really reach your audience and reach their feelings, sort of make them feel excited about what you're excited about or make them feel, you know, concerned about the topic that you're researching and make them feel that it's worthwhile to continue researching. Invoking people's feelings is one of the main keys of a successful presentation. So when we're talking about presentation methods, you first want to pick your poison, pick which one you're interested in. Most events allow for poster presentations as well as oral presentations. You can submit an abstract for both. Poster presentations or poster sessions are pretty straightforward, but there are several types of oral presentations you might encounter in your academic careers or after you're out of school. Some of those include speeches, which are often long and formal, with no visual aids. You can also give a keynote, a conference keynote, or perhaps a TED talk. They're both very similar, depending on the conference and also the TED talk itself. It couldn't be kind of long, but they tend to be anywhere between five and 20 minutes long. Conference keynote can sometimes go a little bit longer depending on the conference. Most keynotes will go, you know, anywhere from 30 minutes to an hour. Those often have very few visual aids. Sometimes at a TED talk, there'll be some slides in the background, but the presenter always has his back to the slides and always talking to the audience and there's never any sort of reference to the slides or very rarely. The presentations that you're used to are the ones that are less than an hour. They're usually a seminar, a lecture, or a talk. And these can include seminars and lectures that professors can give in university classes. They tend to be less than an hour and they rely heavily on visual aids. So you're always going to have some slides in the background and obviously that can present its own set of problems if you don't know how to use PowerPoint well. And finally, you could also hold a workshop or a class.  It's a very, very hands-on and the length can depend. It can go anywhere from, you know, a couple of hours to all day to, you know, a week. To prepare for all presentations, I've talked about this in some of my previous presentations before, but these are the four main steps that you want to do to prepare. You want to think about what you're going to talk about. Obviously, like I said, you need to know your audience. Set a goal for what you want that audience to walk away with and make a plan for how you're going to get there and how you're going to get there in a concise and simple way. You want to also make a draft and sort of write out what you want to say. This doesn't necessarily have to be word for word, although that does help some people. You definitely want to make an outline of the big points that you're trying to make. You would definitely want to try and tell a story. When you have 20 minutes to fill or even an hour to fill, you're definitely going to lose some of your audience if you don't bring sort of that personal touch to it and telling a story, whether it's about your research or about sort of the experience that you had while in the field or while in the lab, something like that will sort of hook your audience and allow their attention to sort of stay with you. You want to have a good design, obviously, when you're using tons of slides, you want to avoid death by PowerPoint, which I've talked about in previous presentations. Your slides aren't a crutch. You need to be able to know what you're talking about and you need to be able to give your presentation without turning around and staring at your slides for guidance. Your slides should have very, very few bullets on them. Mostly, they should be a visual guide and can, you know, your slides can help you along if you get stuck, but you don't want to depend on them. And then finally, you want to optimize your presentation and that means practice.  So poster presentations are a little bit different. They should be considered a snapshot of your research and should communicate, communicate your research clearly while encouraging a reader to want to learn more. It's sort of a concise version, a more visual version of an academic paper. You have room for your conclusions and your results and your methods, which you may not have a whole lot of time to discuss and say an oral presentation. You can actually display it on your poster. You don't want to go overboard though. And posters are an important component of communicating science to the public students and faculty. You want to make sure that your poster draws in the reader. You want to bring those, because you'll be standing next to your poster, you'll want to bring those people to you. There's some similarities between a poster presentation and an oral presentation. A lot of conferences, like I said, have both. They both have oral components.  There are some similar design rules in terms of you only want to use two to three fonts at the most. You want to use lots of lovely imagery, pictures, graphs, charts, things like that. You're still going to have an audience and you're still going to need to tailor your poster to that specific audience and you still want to tell a story and you want to include some data to back up what you're saying. Some of the main differences include the media. Obviously, you're using a printed-out poster rather than a computer or a slide projector or an overhead projector.  There's a little bit more room for interaction. People are going to ask you questions as you're explaining your poster. So it's a little less structured. You still want to be able to concisely describe your research, but you don't have to be real stiff about it. You can be a lot more personal. The length or time that someone will spend at your poster will likely be a lot less than it would at an oral presentation. Some oral presentations will say are 20 minutes. It's likely you talk to someone about your poster for less than 10 minutes. The detail that you'll have in your poster can vary compared to oral presentations. Oral presentations, you're not going to have a whole lot of detail. You're kind of going over the main basic points of each section. This you can add a little bit more detail. To prepare for poster presentations is a little bit similar to oral presentations in that a lot of the work, in fact, most of the work will go into the design of your poster. There's not as much preparation for the oral portion of your poster presentation.  You want to practice in front of people. Poster presentations, you don't necessarily have to do that so much. Most of the work will go into the design. So you want a stated purpose of your poster. You want to make sure that your poster has a reason for being there. And that should make clear, you know, are you trying to engage your readers in a discussion? Are you expressing your interest in a collaboration? Are you trying to convey a really exciting new discovery? So you just want to make sure that your poster states that up front or that you state that up front if your poster doesn't. The title of your poster is extremely important. It's probably going to be the most visible part of your poster. And it should be akin to a newspaper headline, which is concise and attention grabbing. Don't use all caps. Use sentence case so you don't want to capitalize every letter necessarily and try not to make it too long. You know, I've seen a lot of poster titles that are just ridiculously long, you know, three lines. Try to make it a little bit more concise. You can always have a subtitle, but your main title wants you want it to be big and you want it to be pretty short so that it'll fit on just that one line across your poster. Again, your presentation even for a poster should be audience catered. Not everyone reading your poster. In fact, most people reading your poster probably will not be in your field. You want to avoid jargon not only on your poster itself, but also when you're speaking to people. And you want to make sure that everyone who approaches you can understand your research. You can use your abstract to create a simplified content. But again, abstracts can be pretty jargon heavy, so you want to try and avoid that. So you want to create clarity and not confusion with your poster, meaning your poster should be easy to read.  You want to have a font that's really clear and easy to read. Layout and format are almost as important as the content itself. Your poster should guide the eye easily from one logical step to another. This includes margins and grids and white space. White space is the space between your words and between your images. You want to make sure that everything has room to breathe. There's a trick that you can use to make sure that your type is big enough on your poster without printing out the full poster and wasting that money. You can print out the full poster on an eight and a half by eleven sheet and hold it out at arms length. If you can still read the text and make sense of the pictures and graphs, then it should be big enough when you print it out on the full 48 by 36 inch poster. You want to keep your content concise. Everything on your poster should contribute to your main message. Use negative space or white space. Provide graphs and images and don't overuse text and edit, edit, edit. If this is your first time presenting a poster, be especially ruthless with editing the amount of text on your poster. Honestly, less is more when it comes here. Nobody's going to read all of the text on your poster and you don't necessarily want them to force yourself to be concise and clear.  It can be more personal than a paper. Use a unique display that'll allow your poster to stand out among other posters. And you can go online and look for some great examples. And I'll also share some at the end of this presentation. So here are some general presentation skills. And we're going back to it again. One does not simply give good presentations with no prep. And that includes poster presentations and oral presentations. A one hour oral presentation will require 30 hours of prep time. So that means for half an hour presentation, you'll still need 15 hours of prep time.  Pets, family, friends, make them sit down and watch your presentation.  And you want to revisit your content again and again and again. Mark Twain once said, it usually takes me more than three weeks to prepare a good impromptu speech. Luckily, this isn't an impromptu speech. So you have plenty of time to practice. And the more you practice, the more comfortable you'll be during the event. You'll want to, you know, practice your presentation and show your PowerPoint to anyone who will sit and listen to you and provide good feedback. Not just on the presentation itself, like I said, but also on you, your habits, your nervous giveaways. When you say um, when you say like, you can practice in front of a mirror. I can, I would also suggest practicing in front of a video camera, which can be really painful to watch of course, but it will also help you realize there's certain things that you might do with your hands or the way you stand or the things you say that you might want to work on. For poster presenters, practice and hone your elevator speech. Poster visitors are usually busy people. There's a lot of posters to see. So you want to come up with a two sentence overview of your research before explaining anything else. If those two sentences are interesting enough, you'll, your poster reader, they'll want to learn more and they'll, you know, ask you questions and they'll want to hear more about what you were doing. If those two sentences bore them, they'll kind of move on. So you want to use that as sort of your hook to bring them in. So really practice that and test it on other people to see if they may, you know, it makes them want to learn more about your research.  You know your research best because you did it and you wrote the papers and you wrote the presentation and you made the poster. So you know it best. So have confidence in yourself. As I said earlier, use your slides or your posters as a guide when you're talking to people. You don't want to turn around and stare at it and read off of it.  No cards are always okay. Sometimes people get nervous with just sort of winging it. So if you have some cue cards, no cards that you want to use or read from, I think that that's totally okay. And remember to use the imagery that helps tell your story. You don't want to just throw a picture of a gopher up on there just because it's cute. You know, make sure that your images relate back to what you're saying and what your research is about. And you always want to remember to drive home your important point, your main point that you started with, the one objective that you wanted people to take away from your research. You always want to keep in mind the big picture. If your point is too narrow, no one will care about the kind of research you're doing. You want to try to be able to connect it to sort of the bigger picture of why people who aren't in this field might care about what you're doing. Winston Churchill once said, if you have an important point, don't try to be subtle or clever. Use a pile driver, hit the point once, then come back and hit it again, then hit it a third time, a tremendous whack, just to make sure that everyone gets it. And then just some final quick tips, some general do's and don'ts here. You're supposed to love your research, so show it. Always thank your visitors and include some personal interaction. Again, don't talk to your poster or your slides. You do want to dress nicely and show enthusiasm. Speak clearly and speak to your audience. Tell a story and say thank you. Try not to fidget. Definitely don't chew gum or anything else. Don't use jargon. That includes in the words on your slides. You can include a little jargon on your poster, but when you're speaking to people about your poster or about your research, don't use jargon. All it does is confuse people, and so you want to try and pair that down. That's part of, excuse me, that's part of your preparation for your presentation is, how do I explain this without using jargon? And I know that can be difficult sometimes, and I know it can sometimes seem like you're dumbing down your research, but it's better than alienating people in your audience who may not know what you're saying because they're not going to take away anything from you if you can't bring it down to their level. And it may be just that you're talking to a PhD who's in sociology or in mathematics and not biology and not physics. So it's just important to remember to sort of avoid that jargon. Don't turn your back to your audience. Try not to get off topic. It's really easy to do, and don't be vague. Be real specific about the things that you're talking about. And finally, a little quote from Beyonce who said, I don't have anything to prove to anyone. I only have to follow my heart and concentrate on what I want to say to the world. I run my world. So just concentrate on what you want to say to the world. Concentrate on what you want the world to know about what you're doing and the importance of what you're doing and what it means to you. And you'll rock your presentation, whether it's a poster or an oral presentation. So I hope that was useful. I know it was pretty quick. If you have questions, you can always email me at nrogers at ebscore.unm.edu. We have on our website, we have some PowerPoint and poster presentation templates. They're on our resources page. If you have trouble finding them, you can always contact me. And I do want to show real quick a couple of examples. So I'm going to pause the main screen here so I can get out of this presentation and I'll show you a couple of examples of some posters. So let me go to full screen here. Okay, so I've got some poster examples here. This one is a little strange. The table is a problem. It's hard to read. The background is distracting. Same image for both kids and it's kind of hard to read the title. This is a before somebody fixed it and it looks a little bit better now. You have a little bit more of the negative space. The table looks much better. And it's just easier to understand and it gets rid of that distracting gradient. Here's an interesting vertical poster, which is pretty rare. It's a good use of color, good choices of font, tracks attention from far away because it's a little bit different and it uses a good title. So what's the problem? Well, the problem is, you're not really sure where your eye is supposed to go. It doesn't really guide it around. So if we take a look, take a look at the after over here. You can see that you added, the person added a little bit of negative space kind of brought it down. So we look, we're supposed to go across first and then down. And the legend, or I'm sorry, the text at the bottom is a little bit smaller, which is really helpful for more space as well. So just a few tweaks to help the eye flow and this poster will certainly stand out at a large conference. This one's a little bit different. I'm not thrilled with the dark background, but it makes, definitely makes the poster stand out. It's viewable from a distance, catches your eye. It's got a great title. Websites right up there. You know, you got to get up close when you really want to see some detail, but it's still got some great imagery in there. And it's a pretty good use of flow. Your eye sort of knows where to go here. If you want to see something really risky and different, this is it. This is as simple as you can get. It's extraordinarily risky. It's assumed that the research team knows their material well and are very comfortable about speaking about it. This poster does not speak for itself. It helps you with the eye flow with the way that the different images are connected, but having a poster like this likely really depends on your audience. It's great for encouraging a reader to interact with the presenter. Doing something like this really comes down to personal preference. Okay. And those are the examples that I had. This is our example. This is our template. What did it look like? You can download it. You can download it on our website. So it's just bit.ly slash underscore templates. And that's where you can find our poster template as well as our PowerPoint template if you'd like to use that as well. So thank you very much. And I hope you enjoyed this little presentation. And I hope to hear from you soon.


When a narcissist hits on you when they ask you out on a date When they show romantic or sexual interest in you, they might try to get your attention or interest They might give you praise or compliments and This could be quite flattering to you. We all like positive attention We all want to feel and feel admired But there is a big difference between being attended to and admired by a regular person and a narcissist When a narcissist hits on you It's only because they see you as something impressive or attractive They only see the outer shell It doesn't go any deeper than that But with a regular person They will be more curious about you They will be asking questions They will be eager to know more about you Because their standards or expectations are more than something superficial They're more than something existing on the surface But all the narcissist really wants Is something that looks good and makes them look good They don't care about anything else It's all about their image or reputation That's all that really matters to them There is nothing flattering About being hit on by a narcissist It's the same thing as someone renting a luxury car for the weekend They like the car. It looks good It's fast It's powerful and when they take it out They have a lot of fun with it It makes them feel good about themselves But they don't really care about that car They don't really respect it They love what it can do for them They love how it makes them look good They love how it makes them feel But once they've had their fun It's over And when they return the car It's never in the same condition As when they picked it up By the time they're finished with it It's probably got all kinds of damage There's probably loads of rubbish left inside it Maybe it's out of fuel But the narcissist doesn't care about any of that They were looking for something temporary They were looking for something That they could use for a few days Without any worries or consequences Something to make them feel better about themselves And when they're done They leave it for someone else To pick up the pieces And it's the same thing when you deal with these narcissists They don't care about you They don't respect you And when they hit on you It really has nothing to do with you It's just this fantasy That they've created in their own minds Of what they think you are And of what you're going to do for them And how you're going to make them feel It has nothing to do with Giving you the proper care And respect that you deserve You won't get that from a narcissist Because it's all about them They don't come into your life to give you anything They're only there because they're deficient in something And they want to take something from you They just want to use you for their own selfish desires or needs And when you accept their advances They don't see it as though you're on the same page They just see you as another fool That has fallen for their manipulative game They just see you as another fool That they're going to take advantage of And then dispose of Whenever you start to realise what's really happening When a narcissist hits on you It's not because they care for you or respect you It's not because they want to take you out or treat you right It's all about them And what they think they're going to get out of it They might like what they see They might find you attractive But they don't know how to treat you They wouldn't know how to deal with a respectable man or woman They wouldn't know how to give you the proper care and attention that you deserve They wouldn't know how to treat you right And they have no desire to learn how you want to be treated Because it's all about them It's all about what they take from you You won't find anything good from dealing with these narcissists All they're going to do is take everything from you Without giving you anything in return And then they're just going to leave you broken and confused Wondering what just happened So when a narcissist hits on you Don't let yourself become another one of their fools Don't let them trick or deceive you Respect yourself enough To walk away and realise that you deserve better Respect yourself enough To realise that you deserve someone who knows what you want Someone who knows how you deserve to be treated And then you will find yourself Involved in something that is mutually beneficial Where there is an equal exchange Thank you for watching I hope this video has a note of you Please like, comment, share and subscribe Click the bell icon to receive notifications For more videos If you would like to donate My paypal link is in the video description Coaching and Choirs, you can email me at Thanks for watching and I'll talk to you soon


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Alrighty there is sound let's watch as the full first But we let her live because that's what heroes do they show mercy these Are not the cookies, right? Okay. I ordered oreos. All right. I've I've been working so hard keeping everything together, baby, and I can't even get the cookies that I want Sweetheart they look the same But all right, all right, let's go with this first one Let's bring this up a bit here But we let her live because that's what But we let her live. Okay, there's some technical things here and there. I think generally I don't know if you're gonna render this I'll be careful with too Many lines going on here where we start to lose the silhouette I'll probably take this out and take this chair away and just have one We're starting to have tangents and just kind of love Get busy backgrounds But we let her live because that's what heroes do Now from a technical point of view watch out your elbow on the right But we let her live right there.  I like that this goes down and the rest is influenced But it's a bit But you let her live just a bit strong there but But we let her live and for But for the but I think But this is very subjective but to me it's like that thought has already been formed in there That he wants to say but and right now it's just kind of stuck in that pose and goes but But and you could do something where he goes And he's already compressing the lips and then maybe two three frames earlier that chain would already go down While the lips are still closed It's kind of but like it's already mouthing it and then the mouth opens like the lips separate for the but And I don't think you need to go back into a close It has a bit of a Default feeling whenever a word is being spoken afterwards that the mouth goes back to close you can do but But we later there's a but and then you stay maybe within like this range half of that We let her live we let her live, you know, it could be but And that open we let her live and then you really go When you move that which you have here So imagine you're going from a somewhat open between these two frames into This but this is more like having a straw in there like a whistle versus We we I don't feel good that strong. It could almost be here. Let her live because that Same thing here.  Hold on. Let's do some scrubbing here Like there's no need to close that I don't this might be subjective But I'll just be careful in terms of always going back into this kind of default close Because that's what heroes do they show I don't mind here because he made points where he was do They show mercy And even he at the end mercy Kind of within this range. I would stay Turn that scrubbing off instead of going Back into a close like that's my main thing for the mouth But let her live because that's what heroes do. They show mercy I do like your accents though, especially here. They show mercy Right, I like that a lot Maybe now then it's a bit ik I see like a lot of movement in the body and this going back and then you can see here This is completely frozen I mean, you know, there might be some pixel movement, but it's fairly frozen Even on that pullback here like on something like this It just feels like a translate in his arm versus a little bit of move in a bit of slight rotation over at the wrist Just giving this a bit more complexity there And maybe here that's what heroes do Do gets a lot more tense do and at that point you can maybe Go back in with the fingers a little bit tense the cup holding here a little bit Not like a squeeze, but you want to feel like This fans out and it still has an influence everywhere like shoulders or elbows can go in a little bit Is that's what heroes do just a bit show mercy And in that way you have a release when you do this right and then you can open this up a bit You can almost relax that pinky here a little bit show mercy But we let her live because that's what heroes do they show mercy The only I would say is it's almost a bit of a default I know that I see the eyebrow higher here, but it's almost like a default expression Like when he says do they show mercy They show mercy Like how does he feel when he says that like what's if you say They show mercy How is he you know, is he just teaching is he condescending is he forceful? Is he disappointed in having to say this like what is he really thinking as he says this and what is The face telling us in that aspect like this feels a bit too default and almost neutral I'm not quite sure what he feels right there. This is almost like pity neutral pity And then I be careful. I know there's there's good stuff there in terms of movement How you go from this right to this like there's good stuff there, but he does have a general I'm always leaning against this and I wondered he gets very subjective But I wonder if is there a point where he says all of this right would it be something where I was almost almost gonna say he ends with this right imagine he starts like this is in his lecturing mode But then imagine he would say They show mercy and he wants to teach he wants to be friendly He wants to engage with whoever's in front of him Then he would almost end in this position because he's closer Right arms are closer. The body is closer to the person. He's engaging and then now he disengages I don't like I would think in those terms as well. I don't know how far I don't want to dictate you acting Like you got a you got to tell me what you want to have him come across as I don't know if that was English or what I just said, but you know, is he He's straight leaning not leaning forward. It's fairly straight and then he leans back Why like why do you want him to do that? And why do you keep him that way? Is that okay? Do you want that distance? Do you want that further distance from who is he talking to and so on? um I would think about that But before I go more into this I don't want to know what you think so You can always email about this and then I can give you some more pointers And the biggest thing for this shot The voice in him is I guess a lot of energy. There's a lot of stuff happening, but if I turn over the sound There's some accents with the hands, right? But then he is more like, okay. All right. Do this today. Yeah But if you listen to what is he saying here been working so hard keeping everything together, baby And I know he says I'm trying to keep everything together. Maybe that's why you want him so tense while he Explodes internally. I'm not saying he has to do some crazy gestures But I would amp up a bit more in terms of like this line to hear like some more Head accents where it's like you want to feel the tension basically what what I'm hearing in the voice is He's about to explode and he's trying to contain this And looking at the animation it almost feels a bit too clean There are some accents every now and then but then to me it's more like Okay, he's just forceful about something, but I don't feel the The tremor it's almost like it has already exploded And the shockwave is now going through his body and he's trying to keep that in He's trying to keep that shockwave in but he's already exploded like that's kind of how I see that part So like doing something like this right there when I just play this without sound This is more like okay Do you want this or not like this is more like a threatening creepy thing versus Let's go back to the audio Working so hard keeping everything that to me. It's just just like there should be Tremors he's shaking again not crazy overactive But there's an overall layer of tremors of I already exploded internally and I just I don't want to I don't want to kill this person I just uh And then that's the thing that last comment That's okay because now he does explode Sweetheart they look the same and for her it's a bit I like that she has that slight lean over Where visually she gets closer to the person but I think she wants to help him maybe they're kind of the same She's not making fun of him or anything So I think I would push that where I would have her lean forward or take a step forward a bit more to kind of Close that gap just go empathy change there in terms of distance and then loosen up the whole thing if you Just watch her I see mostly movement in the jaw and a drift in the body here. I suppose again watch this line She's just kind of drifting. It doesn't feel like she's saying something with with like a lean forward with head accents That come through because of the energy and the voice and what the jaw is is doing It feels very very isolated in here with a drift So I would think in terms of if she's like this Which she then opened up her arm which she let go of this and like how could you Not not to force animation into this but could you potentially have a post change? So it's not just this suddenly maybe a slightly bigger. This is to me more like a pose in a sub pose Is there something to be slightly bigger to me? It could just be maybe you keep all this But you do take a step forward or she brings that arm down And maybe relaxes this arm out into the open with a step forward or maybe a lean forward Like something where like I want to help you Get through this and of course he misunderstands because he's already raging and he already exploded If that makes sense, I don't know. I'm gonna leave it at that I'm curious how that works for you that type of feedback And if you want to take that and run with it or You want to give me some more information about what you're intending to do with them And then I can give you more pointers and be more more specific again to me It's always I want to I want to avoid Dictating acting choices because it's then it's not your shot anymore if that makes sense. Alrighty I'll leave it at that. Thank you All right, there's an email you can sign up you can start whenever you want you can submit whatever you want You get 16 submissions either way a like and subscribe would be awesome. All right. Thank you


In his method of finding maximum and minimum values, 1636, Fermat outlined a general procedure for solving two types of problems. Today, we'd call them the optimization problem and the tangency problem. They are two of the central problems of differential calculus. Fermat illustrated his method with the problem to divide a given line into two parts, so the area of the rectangle formed by the parts is the greatest possible. Fermat's procedure went like this. Let B be the length of the line, partition it into segments of length A and B minus A. Then the area of the rectangle will be A times B minus A, which we can expand. Now consider a second partition into lengths of A plus E and B minus A minus E. The area will be, at this point Fermat does something that has caused a lot of debate among historians of mathematics. He pulls a term from Diathontis and says, adequate the two expressions for the area of the rectangle. Now if we treat this squiggle as an equals, these two expressions can be simplified and we can divide by E to get. And then Fermat says the following, we'll diminish E and so B is equal to 2A, which gives us the solution A equals B over 2. Fermat also solves the tangent problem in the same way. In Fermat's terminology, the problem is to find the sub-tangent to the parabola y squared equals x. This term sub-tangent might not be familiar, but we can view this as the line below the tangent. So Fermat proceeds as follows. Let C E equal A, the sub-tangent, B E, the actual tangent line, C I equal to E, O, a point on the tangent, and C D equal D. Let I O equal y2 and C B equal y1. By the equation of the parabola, we have D is to D minus E as y1 squared is to y2 squared. Now since this line is tangent, O has to be exterior to the parabola, so O I must be greater than y2, and so that says D over D minus E is greater than y1 squared over O I squared. Now by similar triangles, C B is to O I as E C is to E I. Well C B is just y1, so we have y1 is to O I as A is to A minus E, or squaring both sides. And so D is to D minus E is greater than A squared is to A squared minus 2AE plus E squared. Or we can cross-multiply to obtain the inequality. And we have an inequality, but if we adequate the two sides, simplify, then divide by E, then diminish E, which we can simplify to A equals to D, which gives us the length of the sub-tangent. There's a lot of debate over exactly what Fermat meant by adequate and diminish. Let's take a look at Fermat's work again. Now viewed from the perspective of calculus, it appears Fermat obtains the solution by the following reasoning. If x equals A maximizes our objective function, then x equals A plus E will be very nearly equal to the maximum value. And that's one of the meanings of this word adequate in Diathontis. And so the two values can be equated when E is equal to zero. And so it's possible to view Fermat's work as a precursor to calculus. However, this interpretation relies on what Fermat means by adequate. While he takes the term from Diathontis, it's unclear what Fermat really means by it. Now this led to a series of letters back and forth among French mathematicians that it's convenient to refer to as the Descartes-Fermat correspondence. Although Descartes and Fermat only rarely wrote directly to each other. What's important is that the Descartes-Fermat correspondence makes clear that the theory of equations was the basis for the methods of both Fermat and Descartes. In somewhat modern terms, we can describe their approach as follows. For finding extreme values, in general there are two values A and A plus E that give the same value of the objective function. But at a local extreme value, stop me if this sounds familiar, the two values are the same. And so what that says is that we can find the extreme value by requiring our objective function equal to some value. f of x equals m and otherwise have a repeated root. Similarly, we can view a secant line as intersecting the curve in two places. But as we change where the line meets the axis, those two places become one. And the system of equations giving the tangent line and the curve have a double root at the point of tangency. And so again it appears that Fermat is basing his work on the theory of equations. A non-tangent line will cross the curve at two points, but the two points will coincide if the line is tangent. So we can find the tangent line by requiring the curve and the tangent line have a double solution. This leads to a rather remarkable result. This means we can find tangents and solve optimization problems without resorting to limits. Instead, we can rely on the theory of equations. None of this messing around with things going to zero that aren't actually zero. Except there's one problem. Given an equation, what condition corresponds to a double root? In general, we require that our equation will be of the form x minus a squared times something, where our something could be a polynomial of arbitrary degree. And so now we have the problem. How can we identify the required condition?


I Shopping because I said yes for a Disney hall Are you excited? How much can I spend? We'll see as it goes. Oh, okay. All right. Let's go do this And I guess our first stop Disney and company I want to play something now. Oh, yeah, what's that? I just noticed that this sign right here is supposed to be a Mickey watch nifty So very ironically every time we start to film something and talk about like a certain merchandise The March of the first order song comes on and just cancels out everything because it's so loud So it's definitely becoming a nuisance in this. Oh Yes They've given away the pass holder magnets right at the door Haha We're not only gonna show you what yep's getting today But we're gonna show you some of the other things that are actually for sale in the stores at the parks at the moment Hopefully some new stuff and some other stuff that we think are just real pretty nice. Oh, you already got things lined up Oh, wow, I think I'm in trouble Look at this nifty shirt Magic Kingdom Lake Bonavista and then it's got all the parts of some of the rides But on the inside that's the cool part. That is the cool part. It was reverse. I would so want this Why can't it be reversible? Oh, it's on the back. Oh, no, well, it's see-through. Oh, well, it's still pretty cool shirt And it's 3699 And basically this whole entire wall is dedicated to the new line of stuff that they just put it on the parks kind of cool This frame is pretty nifty The magic king the manual kingdom Hollywood Studios Epcot, and I wonder I mean you can just kind of like well, oh wait No, you can't I feel like a fool, but it is 2999 And it looks like we have a new pair of ears. I haven't seen before Huh pretty awesome And I think there you are 2499 just like all the other ears Hello, I Find it funny how we're doing a shopping haul video and I'm the one that's doing all the filming and talking about the Mertz vests Because she is in shopping mode and I don't see anything here. So we've got to move it along. Oh, we're leaving Disney Company. All right, I Guess it's Keystone Clothers where we're headed next right across from Disney Company in the crosswalk. Oh, yes. Thank you Some nifty new jerseys here. This is like acid wash from the 90s denim. Oh 5999 This is something I think is really cool. It's a coaster set. It's got big Al the orange bird Liberty tree Louise Casey's and a ventures club congelouche 1499 this is a cute little mini shirt the only thing is is that it's summer here and It would not be comfortable. It's 54 99 You know, I try to tell you it all the time. She should wear bows in our hair They are always in style and this shirt just proves it 3999 What you got there?  It's a lot of pressure. Oh Will you buy me this? Oh I think that might be a little bit too much an orange Really no price for love. No price for love, huh? She went to the glass case Pandora's Alex and Annie's They got a whole bunch of them Two shops down and she still has not picked one thing out. I'm impressed. I have all you have Oh, man the orange board. Oh, haha So I guess our next stop is real vogue. I only know the name of these Stores because I'm reading the sign before that but Real vogue Well, they got rid of all the Wally stuff and the up stuff Yeah, just put toy story stuff getting pumped about toy story land, but check out this talking slinky dog Here Wow No, I don't know but it's 2499. This is a pretty nifty mug And you got the castle and the fireworks 1399 got a little toy story Oh Look at that and the back's pretty cool. Yeah Walt Disney World Yeah, oh, I like it $50. Yeah Is it me or does buzz kind of have like a smug look on his face? This is pretty interesting they have a bucket full of little green men from toy story What green aliens? I know it says men, but you can be the claw So like they're all in there. You can just like reach your hand down be like the claw It has chosen me 1799 the claw is our master. I have been chosen We're jumping stores again heading over to the Sunset Club Couture There wasn't as much in there as there was the other day. Yeah missing the up stuff because that was cool And they got miss Piggy ears yeah 2499 yes, and they also have little mermaid ears aerial ears and Alice in Wonderland ears Well, yeah, Chester cat. That is awesome.  You know, I really think you've been acting like you have a chip on your shoulder, and I think that's unacceptable Strange I'm almost about to start calling this the stitch store stitch stitch stitch stitch Stitch I Was trying to talk her into maybe getting a board game like you know, Disney World Monopoly The Tower of Terror crew the Haunted Mansion life or battleship Pirates of the Caribbean edition We can play with just me and you I went oh So you've just informed me that she did have something in mind that she wanted to get a Tower of Terror shirt And I said what's wrong with the one you're wearing right now? It's oh, oh, so I guess we're heading to the Tower of Terror gift shop I might as well point out that the crowds are not that bad today.  I don't think they're that bad I mean Tower of Terror. It's at a 35 minute wait. I mean, that's like an average wait time for that I checked out before Rock and Roller coaster was at 50 minutes That's not bad at all So the Tower of Terror gift shop Here we come And don't you think like if you were to loud up there to look over there be some good photo spots, right? We did that before I know we were allowed we were allowed, but I want to do it again See when it comes to shopping at Disney World, I don't like to get clothing and stuff But these keys to the kingdom is definitely something I would want to buy Look they got hot box ghost key the hot mansion key. It's a smart world key Alice in Wonderland key These are awesome and all the prices. I mean they're all soon about 34.95 But a nifty Tower and Terror bathrobe That's what you came here for it's 74.95 Well, huh So this is the Tower of Terror shirt that you've wanted to get 54.99 I honestly have decided I don't want this anymore because I feel like it's too hot So who would to be hooked to my shirt? I honestly you can't be serious in my head. I So I guess nothing at the Tower of Terror Oh my lord carry on then That's nifty, that's only 7.99 Oh, no, I'm starting to think she's just having fun dragging me in and out of all these gift shops So where to next there miss Daisy Daisy well because you're just taking me on this Grand tour of souvenir shop. So where we going next? Oh the five and ten or head to toe Okay, I Love the inside of head to toe because they have all the classic Disney posters up on the wall. It's not awesome And it's actually very tall ceilings in here. I've never noticed that And now we're in five to ten if anything I'm gonna bet she's gonna find something in here that she wants She loves home goods and stuff like that. So watch something's gonna come about this is the one This is the one Marv What you got there Ooh Nice set of whisk and matches my silverware. Oh for kids and adults It says that on there for kids and adults. Yes, how much is this? Oh, it's only 14.99 I think we made progress here. We found something she may have wanted It's a hook for the Gracie's leash and the first order March out there is messing up everything as always You love the first order don't lie I Look at this new fresh set of coffee mugs they got here. This is pretty awesome Peter Pan while Captain Hook Wow Alice in Wonderland Robin Hood I like that one and they're all 1599 Looking at these nifty magnet sets name a whole entire set of magnets dedicated to Park's food And that's pretty awesome But This is something that caught my eye A Hollywood Studios theme park magnet set And they have like Star Tours, Tower of Terror, Rock and Roller Coaster, Fantasmic Buzz Lightyear for Toy Story Mania And they're 14.95, but I'm wondering do they have a set like this for every park Because that would be a cool fridge Well, I think Yip has decided on something finally She's gonna get the Mickey glove wall hook to hang Gracie's leashes on Yeah, it's like Mickey's hand like this and it hangs on the wall and then he could put the leash on it And uh, it's like he's holding it as we get home so we can show you. Oh, I guess so Well, I think that's about it. We gotta go to work and school Right, you have to go to school. I gotta go to work But I hope you guys enjoyed our little souvenir shop Disney shop thing. I don't know. You only got one thing, which I'm very shocked and very proud of you Good job. Yes. We didn't even go to Disney Springs. Oh boy. I guess that's next So love the life you live with the life you love and if it's your first time watching our channel subscribe Because you might like it And the Mickey hook is officially hung. Isn't it perfect? I hope Gracie likes her new leash holder You like your new leash holder She loves it. She loves it even though she doesn't know what it is. She doesn't even know what it is, but she loves it