Kind: captions
Language: en
oh i wonder who that is
yeah yeah yeah what's up
ah too close
too close
wish me luck
i always knew this calculus book would
come in handy
ah
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 going to
take them a half hour to get here
all right well we better get going
okay we are up here on the roof of the
science center i think we're safe from
zombies up here and you might have
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 going to bring them
straight over the chairs which is 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 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 is 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 is always
pointed toward the person that the
zombie is chasing and that completely
determines the path of the zombie in
fact if you look down here right now you
can see a case there's somebody running
from a zombie right there 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 is
never going to 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
going to be safe get away zombie maggot
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 looks like
they're in trouble look i'm going to see
if i can go help
i'm gonna ride my bike
and see if i can help him so let's see
what we can do here of course uh safety
first
let's 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 zombaes hey follow me come
on you zombies follow me over here come
on you're not so smart anymore you used
to be academics or 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 going to 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 is bigger than theirs because 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 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
uh i gotta get inside
drop the bike we're out of here
do
hmm
you