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Course: Math for fun and glory > Unit 1
Lesson 7: Thanksgiving mathGreen bean matherole
This Thanksgiving, make sure your table isn't missing the all-important green bean matherole. Pick your favorite vector field and have at it!
Mathed Potatoes: http://youtu.be/F5RyVWI4Onk
Borromean Onion Rings: http://youtu.be/4tsjCND2ZfM
Turduckenen-duckenen: http://youtu.be/pjrI91J6jOw. Created by Vi Hart.
Want to join the conversation?
- What's a vector?(26 votes)
- An amount having direction. Also determining the position of one point.(3 votes)
- how are string beans affected by electro-magnetic force?(6 votes)
- All matter is affected by it, since everything consists of atoms, and atoms consist of Protons, that attract Electrons.
In fact, it's pretty much the only reason we don't fall through the floor or can touch and eat string-beans.(8 votes)
- Does anybody know how to make that "goopy stuff "?(6 votes)
- lol.. That "goopy stuff" is the sauce or wet part of a casserole. You can make your own but most people just use canned.(4 votes)
- Does a bar magnet have a magnetic pull at each end?(4 votes)
- Yes it does because when you take two ligitiment magnents they will pull from each other because they are attracted to different forces.(2 votes)
- Around2:35, did anyone else notice the vague thump-thump noises in the background, like someone listening to heavy metal music?(2 votes)
- Thank you for making this videos they helped me understand math and how this videos relate to the world and how the world of math is the best wich relates to the real world.(3 votes)
- Who takes the video? It can't be Vi hart because sometimes you see both of her hands.(2 votes)
- As far as I know, she usually has the camera on a tripod looking over her shoulder. And sometimes other help to create a hundred dozen hexaflexagons for example.(3 votes)
- Is she talking about a PVector like in JavaScript?(3 votes)
- Where is Sal Khan in this video?(1 vote)
- Sal is not in this video. This video was made independently by Vi Hart.(3 votes)
- What does she say at2:18?(1 vote)
- "If you are cooking at a high altitude, be sure to cut you beans shorter by a negligible amount"(2 votes)
Video transcript
OK, I know some people aren't
into green bean casseroles, but I like them. Plus, they remind
me of vector fields. Each green bean is
like a little arrow, and I just have the
urge to line them all up so they flow
in the same direction. Maybe a little wavy,
representing the vectors of flow in a river or something. Maybe complete little eddies. Or maybe the beans could
represent wind vectors. Long beans would be
high-magnitude vectors saying there's a strong wind
in that direction, and short, low-magnitude beans
would mean low wind speed. You could have a hurricane
in your casserole dish with the long beans of high wind
speed flowing counterclockwise near the center, mellowing
out towards the outer edges of the storm. The center would have the
shortest beans of all, showing the calm
eye of the storm. Oh, and if you're wondering why
I'm not curving the beans like this is because while vector
fields might have a shape or flow to them, the
vectors themselves don't. They're usually shown as
straight lines, or numbers, or both. But that's not because
they are straight lines. Vectors just represent what's
happening at a single point. It's like this tiny point
and this bit of wind can only travel in one
direction at a time, so the bean points
in that direction. And that tiny bit of
wind has a certain speed, which is represented by
the length of the bean. But the bean itself
is just notation. Vectors themselves don't have
a shape, just a direction and a magnitude, which means
a bean with a direction and magnitude is just as
legitimate a vector as an arrow plotted on a graph, or
as a set of two numbers, or as one complex number,
or as an orange slice cut with a certain
angle and thickness, or as shouting a
compass direction at a precise decibel level. North. East. I'll admit I'm not a huge fan
of individual vectors sitting by themselves without
meaning or context. One string bean does not make
a casserole or matherole, as the case may be. But fields of
vectors are awesome. They do have curves
and patterns, context, and real-world meaning. There are vectorizable fields
permeating this casserole dish right now-- the gravitational
field, for instance. Gravitational
forces are affecting all of my string beans, pulling
them down towards the earth. And so you could
use the string beans to create a vector-field
casserole that actually represents the gravitational
field they are currently in. Of course, this means
just lining up the beans so all point down. And since they're all affected
by basically the same amount of gravity, they should
all be the same length. If you are cooking
at a high altitude, be sure to cut your
string beans shorter by an negligible amount. Another favorite
vectorizable field of mine is also currently permeating
these string beans-- the electromagnetic field. And if I had a giant bar magnet
as a coaster-trivet thing, maybe I'd want my casserole to
show the magnetic field that is actually there. The points near the
poles of the magnet would have larger vectors,
and they'd curve around just like iron filings
do when you put them in a magnetic field. And the beans would show
how the force weakens as it gets further
from the magnet and goes from north to south. Or if you want to be true to
life and don't have a magnet, you could put
equal-sized string beans all pointing the
same way, and then make sure your casserole is
always pointing north, which might make it difficult
to pass around the table, but I think dish-passing
simplicity can be sacrificed for the sake of science, or
mathematics, whatever this is. Speaking of which, you can also
invent your own vector field by making up a rule for what the
vector will be at each point. Like if you just
said for any point you choose, you'll take
the coordinates x comma y, and give that point a
vector that's y comma x, so that this point, 0, 5,
has the vector 5, 0. And at negative 3, negative
1, you have negative 1, negative 3. And negative 4, 4
gets 4 and negative 4. It's so simple. But you get this
awesome vector field where the vectors kind of whoosh
in from the corners and crash and whoosh out. Anyway, there's lots of
other stuff you can do, but I'm going to go ahead and
pour some goopy stuff into here and get this thing
casserole-ing. It may not look very inspiring
yet, but it's far from done. The most essential
part of a matherole is an awesome oniony topping,
and I've got just the trick. I will even show it to
you in the next video.