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Autograph spreadsheet

welcome to a quick tour of some of the exciting features of the new free auto car 5 it would also be very useful for you to watch the summary video of version 4 as all the topics covered in that video apply equally to version 5 when version 5 starts up there's a bit more detail now about the two standard and advanced levels of autograph standard has no radiant and no calculus now when it starts up now you get the opportunity to log in to your autograph or complete mass account complete mass is the new home of autograph and in time this will be a way to get through to lots of resources for now I'll just log in and ami go and what you get now is a nice summary of the various pages of autograph you've got the stats page here a 2d graphing page the 3d page and complex numbers page so let's give you a quick tour now of some of the facilities these are the different page types we've mentioned and let's have a look at a 2d page and everything is done through the right-click so you've got whatever you've got selected nothing in this case these are the top-level objects it's enter an equation and type away so y equals x X X with X cubed minus 3x minus 1 I may notice that the slope lot is on and that's very important it means it's going to creep across here and you can stop and talk about it and discuss where it's going to hit the x axis and y axis and so on that's the autograph way of plotting graphs all right let's put some points on these points remember you keep putting points on including on objects until you go back to select mode the point mode has been extended you have the intersections mode now which is always looking at wait for the little circle and the line segment and also vectors they're quite nice so let's go vector from here to here here to here and here to here and let's summarize some that Plus that Plus that and put it here and right click vector add vectors and you can see that the sum is the same whatever your disease that's quite nice so a point on a curve point options line options including tangents and so on create newton-raphson that's a nice one just see how that works and it goes and the point is of course you can move this around and see that it's not always clear which we're just going to end up looking at and don't forget always zoom let's outlook some geometry now and you'll notice that I've got a finished solution here of this particular theorem to do the circles just quite nice and I have another file here which is the beginnings of it now they're going to show you how it all works quite nice to have these two side-by-side I can do that in the window menu windows and select circle one you have to press the ctrl key to do a multiple selection and we want our vertical and there they are next to each other which is really nice now this is the file I want to start off with so I'm just going to put it together for you first of all on the axes menu there is the option to turn labels on or off and there's lots of times when you don't really want the diagram littered with labels but on this occasion we certainly do so I'm going to click that on first thing I want to do is find the tangent from this point to the circle so the logic of autograph is select the objects you're interested in and then right click line tenth now there are two possible tangents so we just want the 1 now I want to go to a point mode and do a line segment from P to B and also from P to this point up here which we haven't actually established yet so let's do that next intersection wait for a little circle I don't want to call it a I want to call it t so double-click on the a and change it to T so P and we want this point here this is an another intersection point wait for little circle select and drag a over there we also want this line segment as an item so we go again to here and go from here to here and we want to go from P to T notice if that is called e if we can grab it yes we can that's called D and that's called B we're gonna need all these in the calculator now we're going to use the calculator and I noticed that what we're going to need is the squared symbol so if we winter need the on-screen keyboard wonderful invention here it is and here you can put in all sorts of things to do with data or this side a lot of mathematical notation and here's the squared symbol what we want so let's pop that up there and open up the calculator which is this one getting the way there we go okay now we want PT squared so I'm going to write in here and the PT is the object YZ I'm going to click on that and YZ distance there it is and I wanted two squared raised to the power two but the text before would make it look nice I want to do PT now we want the squared which is this one here the space equals space seven point nine there it goes so that's how you put that information on and obviously you can do something similar for PA times PB equals 622 here's an example of velocity time situation and showing that the area under the velocity time graph is the distance traveled and we've got a variable and point here which is showing you the area under the velocity time situation and up here we've got a point that has been generated from the x value of this and the value of the area so let's show how this works first of all this is a piecewise expression V is equal to zero up to here 2t up to here for constant then eight minus T down to here so typical alton back for lost your time graph if you double-click on this you can see from the equation entry how it works you just put commas between each of the values and then the startup options because it knows it's a piecewise equation it's giving the options as to where the first one begins and each intersection is followed by the last one so it finishes at 10 good thing about this piecewise function is that it is a function so you can do things like work out areas and so on just need to put a point somewhere along here and then select deselect the first one point then this point now right click it's quite a big menu Sun plant it's off the bottom so don't forget the right-click menu is duplicated in the object menu it's quite useful when making videos like this so go to create because it doesn't fall into any of the other categories create area and the area dialogue the one that produces a nice pretty pattern like this is Simpsons rule but there's a general one as well rectangles midpoint trapezium Simpsons The Simpsons with say 15 divisions enough so that definitely is an object in its own right it has a value and so does this have a value as well so I'm going to select this point here and the area and then I'm going to use this feature here which produces a new point based on attributes of objects that have been selected and you can see that the x value of this point here is the x value of the end of the new point and the area itself once at the air at the moment but two or three so it's going to be a point up here somewhere and there it is and the lovely thing about this is that as it moves around so you can see that it takes characteristic shape when the velocity is a linear function the displacement is a quadratic when this is constant that's going to be a straight line now if you select this point and this point we've got two points one of which is constrained in a particular way and the other one is a consequence of that and that is perfect for create a locus off the bottom again so object create a locus perfect already and then it's offering us from - there - that'll do fine but you can do change that right and obviously putting on these extra lines isn't it extra little bonus but that's a lovely way of just looking at how area and displacement and velocity and time are all linked up now a little exercise in introducing the concept of a scatter diagram and you can see that I can move these points around and whatever happens the line of best fit which by the way it's not supposed to extend beyond its natural limits extrapolation is something you do great care but it shows the mean as well and it shows that the line of best fit always includes the mean so how do we do that first of all grab the hand and move it down here we don't need this a photo so exes don't share the key all right now we get to point mode and we stick some points on I'm gonna hold the shift key down as I do so and so they're all selected don't put many on just enough to prove the point right click line y on X regression line there you can see that it shows that quite nicely and you can move it around but it's very very important I think to show at this stage that the mean lies on that line so right click point mean and sure enough it does what you can also do with these points selected is right-click convert those to a data set now they've changed they're just a single object one click and they all wake up double click and you can see this is the data you have created and that's where you can paste data in across from a spreadsheet to do more analysis well let's do just that here's some data from the TSM resources I'm very careful when I put data up there to be sure that I know what the source of the data is and here all the links to Berkeley University in the states that have done this research into baby weights and mother's age and so on so I'm going to select two columns birth weight and gestation days the feeling is that the longer the babies in the womb the heavier it's going to be so there should be some relationship there so right click copy there we go into autograph this time of course it's 2d right click enter XY data right click paste notice the column headers have come through that's where you spoke they will then become the X and y axis labels uh-huh well is this the right way around is the gestation day or the birth weight the independent variable I suggests it's this one so double-click you can swap the X each four years for you and you can also show the statistics now look at it finally on the different aspect ratio but that's what's happening there you could transfer that to the results box which is just sitting on the right hand side you could view results box and here's all the stuff we've been doing in this session that's all there is text which you can just copy and paste it but somewhere else let's go and find some data that's well illustrated using the concept of a box plot here we've got male and female life expectancy at Birth for all the London boroughs so it's quite it one two three four five six sets of data let's just choose one to start su so how it works I'm just gonna grab female all the way down to the last one hundred eighty two point six notice the column header has gone through but not the bit at the very top so copy that and we'll have a look at autographs now with a stats page so it's got frequency up here it's only one variable along here as opposed to the two dimension which there's two variables okay so right click we've got all that data sitting on my clipboard I got an end to raw data and right click pace simple as that to put it in and click ok may be out there it is and it's taken the column header and told you that so let's have a look at what we can do with it so the boxer whisker diagram is the one that was looking at and from from raw data that's correct and there it is there's an outlier which is interesting the usual rule of course one and a half times the interquartile range it's more than that which is why it is it out if you want to you can draw a dot plot as well underneath it which is quite good to be able to show how that all fits we just need to rescale with the red tick there it is you can move this up and down if you want to so there's the raw data and there's our outlier or possible outlier and notice the column header is now the label of this diagram here which is why it's possible to do this many times and show comparative box plots well that's probably about enough for part one of this video so we'll just run through the tabs gain to remind of what we've been through these multiple box plots individual box plots with dot plot underneath scatter diagram from large data scatter diagram from just a few points of data to make a good teaching point floss your time graph showing that area underneath the frosty time is displacement and a nice bit of fit and I'm at work on circle theorems and we've started off with messing around with some points and universities