Name: Zombies and Calculus, Part 2
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<div class="rich-text">A zombie will head toward where you are at any given moment and not where you will be in the future. Mathematician Colin Adams explains that you can use this, combined with knowledge about tangent vectors, to escape a zombie in hot pursuit and to help friends trapped by a zombie hoard. And don't forget your bicycle.
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You're being chased by zombies, and understanding tangent vectors may save your life.

<div class="rich-text">You're being chased by zombies, and understanding tangent vectors may save your life.</div>

Zombies and Calculus, Part 2

Physics & Math

<div class="rich-text">

 Colin Adams
 
 : Oh, I wonder who that is?


 Yeah, yeah, yeah, what’s up? Oh no!


 Oh, too close. Too close. Whew.


 Wish me luck.


 Whew, always knew this calculus book would come in handy.


 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 heads to do 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.


 Alright, well, we better get going.


 OK, 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. Little bit scary, but it worked out OK because zombies head straight for their target, which in this case was me. And so therefore that’s gonna bring them straight over the chairs, which is one of the worse things that they can do for their sake.


 Now we can describe that using one of the concepts from calculus called the tangent vector. 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 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—is always pointed toward the person that the zombie is chasing, and that completely determines the path of the zombie.


 And in fact, if you look down here right now, you can see a case—there’s 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 its tangent vector—that arrow—is always pointed toward the person that the zombie is chasing. And the zombie’s never gonna catch the person because 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.



 Human
 
 : Get away, zombie maggot!



 Colin
 
 : 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.


 Oh! I see some people down there that look like they’re in trouble. Look, I’m gonna see if I can go help them.



 People
 
 : Oh, no, zombies! Zombies! On top of the table!



 Colin
 
 : So I’m gonna ride my bike, and see if I can help them. So let’s see what we can do here. Of course, safety first. Get the helmet on. Alright, I’m gonna try and attract the zombies to me. Here we go! Wish me luck. Let’s see what happens.


 Alright, you zombies! Hey, follow me, come on, you zombies! Follow me, over here! Come on, you’re not so smart anymore, are you? You used to be academics—you’re not anymore, are you? 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 pack.


 I’m riding in a big circle around the quad right now, so you notice—they’re starting 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 clump, and they end up following me on a circle that has a smaller radius than my circle. So my circle’s 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.


 Alright, the zombies are following me.


 OK, you folks, I think you’re clear. You can get outta there. Get to safety as quickly as possible!


 Alright, it looks like they’re good. Now I just gotta get to safety. So hang on just a second. I’m gonna bring it around. Come on, you zombies!


 OK, 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.
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