NOVA

(door knock) Oh. Wonder who that is. Yeah, yeah, yeah, what's up? What, oh, no - (man screaming) (zombie growling) (upbeat music) (man screaming) (zombie growling) (zombie screaming) No. (door thud) Ah, too close. Too close. Uh. (upbeat music) Wish me luck. (zombie growling) Ah, who isn't (indistinct) this calculus book would come in handy? (upbeat music) (door squeak) (upbeat music) (footsteps pattering) (Zombies growling) Typical. Typical zombie behavior. Instead of running across the front and up the stairs like any rational human being would do, they don't have the brains in their head to do it that way. Instead they have to come straight for me straight up the chairs. It's gonna take them a half hour to get here. (zombies growling) All right. well, we better get going. (upbeat music) Okay. We are up here on the roof of the Science Center. I think we're safe from zombies up here. And you might've noticed what happened down there in the auditorium. A little bit scary, but it worked out okay because zombies head straight for their target which in this case was me. So therefore that's gonna bring them straight over the chairs, which was one of the worst things that they could do for their sake. Now, we can describe that using one of the concepts from calculus called the tangent factor. The idea is very simple. If you have any object that's moving along a curve in space the tangent vector will be an arrow that is just touching the curve and it's what we call tangent to the curve pointed in the direction of motion at a given instant. And as that particular object moves through space that tangent vector moves along with it always pointing in the direction of motion. In the case of the zombies, that vector, that arrow was always pointed toward the person that the zombie is chasing. Then that completely determines the path of the zombie. (man screaming) In fact, if you look down here right now you can see a case. There is somebody running from a zombie right there and you'll notice that the zombie is always heading straight toward the person. So if you think of that zombie moving along a curve that is the path that it's taking then it's tangent vector, that arrow was always pointed toward the person that the zombie is chasing. And the zombie's never gonna catch the person but it's always pointed towards where the person just was not where the person's going to be by the time the zombie gets there. And the zombie never knows to cut them off. And you can use that to your advantage just as I did down in the auditorium. Good, it looks like they're gonna be safe. -

Man

Go away zombie Maggie. Now this idea of tangent vectors turns out to be very useful in a lot of contexts. For instance, if we're looking at the space shuttle and trying to get it to dock with the space station, you use it when you're trying to get satellites to a particular orbit. This turns out to be a very useful concept. (zombies growling) (woman screaming) Oh, I see some people run down there look like they're in trouble. Look, I'm gonna see if I can go help 'em. (people screaming) (zombies growling) So I'm gonna ride my bike and see if I can help 'em. So let's see what we can do here. Of course, safety first. Get the helmet on. All right, I'm going to try to attract the zombies to me. Here we go. Wish me luck. Let's see what happens. All right, you zombies. Hey, follow me. Come on, you zombies, follow me over here. Come on, you're not so smart anymore you used to be academics (indistinct) not anymore. Oh, yeah That's good. Good zombies. Come on. Working like a charm. Nothing like an afternoon bike ride with a bunch of zombies behind you in a park. I'm riding in a big circle around the quad right now. So you notice they've started to follow me. They're starting to group together. And the idea is that the zombies are always gonna head towards where I am. And what that means is their tangent vectors are always pointed straight at me. Now, because of that it turns out that no matter where they start, they end up actually grouping in a clop and they end up following me on a circle that has a smaller radius than my circle. So my circle is bigger than theirs cause I'm riding faster than they're moving. But I end up getting all of them to follow me. So eventually they'll be all together in which case these people can escape. All right, the zombies are following me. Okay. You folks, I think you're clear. You can get out of there and get to safety as quickly as possible. All right, it looks like they're good. Now I just got to get to safety. So hang on just a second. I'm going to bring it around. Come on, you zombies. Okay. So this is the end of my video. I hope you've learned some things that you'll find useful. Maybe math will save your life and I wish you good luck. I gotta get inside. Drop the bike, we're outta here. (upbeat music) (footsteps pattering) (upbeat music) (zombie growling) (upbeat music)