 So I'm often asked Jeff how do you make those brilliant animations you do in your videos? I mean they should be winning awards All right truth to tell nobody has ever said that nobody's ever called any of my illustrations brilliant But it is a legitimate question How does one make a nice sequence of animations and I don't know how other people do it But here's an example of how you might do it most easily and the important thing here is to start with your final composite picture and In this particular case what I want to do is I want to draw a graph of y equals log of x and I want to shade the area Under the curve above the x-axis between x equals 1 and x equals 4 and at the end I have this picture here and I produce this in a fairly standard drawing program Microsoft has a version of it open office has a version of it if you want to get really sophisticated There's other things you can do but the important thing here is I have my final picture Now the secret is that animation consists of showing a sequence of pictures that differ from each other very slightly and So here's the important thing if you don't want your animation to be choppy What you're going to want to do is you're going to want to make that difference as small as possible And so a good way of doing that is to start with again the final picture this is where I know I want to end up and I'm going to produce the preceding pictures by Successively deleting elements from this picture so if I know I want to illustrate the process of finding the Area under the graph of y equals log of x under the graph above the x-axis from x equals 1 to x equals 4 then Mentally the picture that I have is I'm going to want to draw the graph of y equals x I want well first of all I'm going to draw the x and y axes I'm going to draw the graph of y equals log of x I'm going to place my x equals 1 place my x equals 4 then shade the region and So the last thing I put into this picture is going to be shading the region And so the picture before the final one is going to have the same region Everything being the same except this shaded region is not going to be there. So first thing I'm going to do So the first thing I'm going to do is I'm going to select the region and I'm going to copy it This is an important step. I want to copy this and I'm going to Insert a new slide. I'm going to now paste the picture there And so now I have this picture here This is my copy of the picture my previous picture still exists You can't tell but I've just switched back and forth between the two pages But now what I'm going to do is I'm going to Select the region that I want to get rid of So I'll click in the region and at this point I will now just cut that region out and that's gone and now what I have is I have my Next frame or really my preceding frame and now if I go back to the original I have the original I have the frame minus one particular picture and if I flash this then this it looks like I've filled in the region and Most importantly things haven't moved very far All right, well, what if I wanted to do the next thing well I can also so here I'm going to do something a little bit different You can't see it because it's taking place off-screen, but I'll use my software. I'll insert a duplicate slide So now this is actually a copy so Nothing up my sleeve. Here's the copy. Here's the second picture. We did here's our original So again, I'm now working on the copy of the second frame And I want to get rid of this terminal line x equals 4 so I'll delete it I'll delete this And those are gone and there's my new picture and again, I'll do the same thing. I'll make another copy of the slide So nothing up my sleeve. I'm going to copy. I'm going to open up a new page here. I'm going to paste That new picture and then the last thing I'll do is I'll get rid of this line here and There's my final graph. So again in the sequence of animations This is actually the first graph I'm going to show followed by the next graph There's my x equals one followed by the next graph x equals four followed by the last graph Which includes everything And there's the secret of animation and now you can go on to produce your own animated versions of anything you want to