Introduction to Parametrics (1 of 3: Why Parameters Are Useful)

this is an imagined week in mr. woods like I said what give mister wearing funny clothes for Lydia an imagined week what you through plastic seven days of sales of a quarter store that's situated near the beach okay so what I happen to be selling these are these are sales of Pyro's cuz they need a beat okay is bottles of sunscreen and ice creams because see pastel because I made the beach right good boy so this is how an imagined week at my corners don't progressive these are the different kinds of sales that I made now I regardless of whether in a big advantage for this so clear structure to my sale of sunscreen and less no ice creams and in fact you can kind of see there must be linked in some way right for instance as I have more sales in sunscreen right I also have more sales in ice creams like my smallest day right for sales of sunscreen well obviously there's zero zero okay but here three that corresponds to the lowest number of ice creams and by the highest number of sales or cell phones on the sunscreen also corresponds to my highest number sales of ice cream so there's clearly some kind of relationship so if we call sunscreen s and we call ice creams by right how would we express this relationship that's not that hard to work out in this imagined week what kind of relationship we can fall for instance have a look at all of these sunscreen numbers what do they all have in common they are all yeah whose were three there are multiples of three okay so if I were to take the number of moles of sunscreen I solved right yes and if I were to divide that by three I would get a number right I'd get one three four seven two right so that's the number of moles in such been divided by three and those numbers they're related to these numbers right if I have it my head one three four seven two these numbers are also special right what kind of number love it they're all square numbers all right so says two reason I should like kind of take the square root here okay so I take the square root of all of these numbers the square root of R I'm going to get 2 4 5 8 3 right it's a look right divided by 3 square root divided by 3 to get 1 square root of 2/3 + 3 square root 4 divided by 3 that's 4 square root fine you can start to see a pattern right if I divide this by 3 it's really exactly the same thing as if I take the square root and I have to take off 1 right because the square root of this number is not exactly the same as this number by the battery but tada I have a relationship right I can say I can say if you like I could make the subject s and I could say well I can work out how many bottles of sunscreen I ought to expect to sell if I've already got a number about ice creams I've solved a square root take away one and then I multiply that number by three okay so what we have created it here yeah he's really put a bit of extra notation right it's sunscreen as a bless you as a function of ice cream does that make sense right it's sunscreen I have an expression for that in terms of ice cream okay and I can get a number out and at least in my favorite get years on if accurate okay now it's all fine it makes the miracle sense the only problem is it's ridiculous correct because there's no rule that says oh you know people are buying sunscreen I guess I'd better buy ice creams right there's not really up you know people people start is the sales of sunscreen to skyrocket quick quick buy ice cream or vice versa right that doesn't make sense okay as you can see by the way I didn't have to make sunscreen a function of ice cream I could have made how would I do it if I wanted to make ice cream a function of sunscreen what I do here I had one right so that would give me the spirit of my being S on three plus one and then I guess I'm swear right so that would give me this okay so what is what you the other what is the function y ella no big deal right it just doesn't make sense with reality okay in fact what's missing from is that both of these they're not related to each other but they're not related to each other it's that they're both rising and falling in response to some other information that's not on here some other piece of data of which next to the beach you might be able to guess is probably something like sunshine weather temperature something like that right so for instance if you take your table and precise if you add another color my suspicions okay now if for instance I sit beside all of these patients beside these months I have another measurement right let's for the sake of simplicity let's call it temperature okay and if I go ahead and I look up the actual you know recording time for each day suppose I get something like this okay so because I have this extra measurement right this extra metric if you like right but what actually happened to give the situation really as temperature rises that's what causes both of these two eyes okay it's not that sunscreen rising makes more sales of ice cream okay it's that when temperature rises both of these rise at the same time hey does that make sense so it's really this which is in control so even though I could say this and it would be accurately I would get the right job job it actually makes more sense to say I can write sunscreen as a function of temperature and I can write ice creams as a function of temperature right both of these things actually have a root cause right so we've seen this function notation before right you used to see f of X or whatever okay but you could use any letters you like and since my functions actually refer to objects on bodies what made my functions after my objects what would sunscreen be as a function of temperature you have a look okay for instance you saw there was division by 300 right okay now when you get one three four seven - how do they relate to these numbers it's a good question that's a very good question we will we will cover that in a second I just think that that's probably something realistic it's three two degrees I don't think it's any huge number of people you know oh I have a look right for instance I can see that these numbers here right are exactly it looks to be 25 a pot here right sorry when I divide this by three I'm gonna get one which is 27 pot whatever I this by three that's going to be 27 part to this and we're going to write this by three every 27 part do you see what's going on here okay so when I divide by three that's the same as taking 27 way for this yes okay so another way of saying that he is you can take the temperature subtract 27 and then if you multiply that by 3 that's how many moles of sunscreen others le yes good question we get it okay you can clearly see this URIs seem to be following a different kind of rule but then right they just like they just do it there okay okay so we'll we'll come to that in a second that's sunscreen now help me out with ice creams right something has to be squared the question is what you remember you told me there was an offset of 1 okay this one up here right yes instead of doing t minus 27 I think I should go to minus 26 right T most amazing so for instance here I will get 2 you scratch you get forward here I'm going to get 4 u squared you get 16 here I'm going to get when I say take my dream GTA 5 slightly at we fire okay so this makes sense tell you yeah that's right so you take this number as all settings and then you square it which is the equivalent of this square here

Channel: Eddie Woo

Views: 53,110

Rating: 4.9457011 out of 5

Keywords: math, maths, mathematics

Id: zBYs6ppuMSk

Length: 9min 19sec (559 seconds)

Published: Fri Sep 11 2015