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Course: Math for fun and glory > Unit 1
Lesson 7: Thanksgiving mathOptimal potatoes
With Thanksgiving just around the corner here in the US, it is important to know how to arrange mathed potatoes on your plate for maximum gravy. Also shown are bread spheres, butter prism, and gelatinous cranberry cylinder.
Green Bean Matherole: http://youtu.be/XwIs1nlDQ2I
Borromean Onion Rings: http://youtu.be/4tsjCND2ZfM
Turduckenen-duckenen: http://youtu.be/pjrI91J6jOw. Created by Vi Hart.
Want to join the conversation?
- What is a brute force algorithm?
I even heard it in Brit's series.(36 votes)- A brute force algorithm is when you try every single combination (enumerate) in a series, until a value that works for your problem is found.(33 votes)
- at somewhere near1:00did anybody relieze that when she cut the second mathed potato it look like she cut one little bit the whoosh it all fell apart(6 votes)
- That's because she connected 2 different frames that were actually quite far apart, in real time.(5 votes)
- is there a video where she shows how to make the cranberry cylinder?(2 votes)
- yes. it is not here in Khan Academy, though. It is is YouTube(6 votes)
- Does she say Bennetarsky potatoes? I couldn't really understand that.(3 votes)
- she says banach-tarski potatoes.
they invented a paradox
see http://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox(3 votes)
- How would you make Banach-Tarski mathed potatoes? That would help if you wanted potatoes in powers of two. ;)
Thanks to anyone who answers.
Jack.(3 votes)- Cut a potato into five infinitely thin, infinitely precise pieces. Make sure to do it correctly, because it is the most important part of all. Rotate one of them by arccos(1/3) so that it becomes the equivalent of three of the four other pieces plus itself. Add the missing piece. What you end up with is the original potato. Take one of the three pieces that we haven't used and rotate it as well, so that it becomes the equivalent of the two pieces that we already used, plus itself. Add the final piece, and you are left with a second fully formed potato.(1 vote)
- How to make a cranberry cylinder?(2 votes)
- Most Americans will buy canned cranberry sauce for Thanksgiving. When served, the cranberry sauce will remain in the shape of the can containing it.(2 votes)
- Can you make the cranberry cylinder?(2 votes)
- Just by a can of Cranberry jelly and get it out of the can in one piece.(1 vote)
- what the heck is a hyperbolic plane?(2 votes)
- A hyperbolic plane is a surface that has a constant negative curvature. It appears very wavy. The interior angles of triangles will add up to less than 180° and pi would be greater than the familiar 3.14159.... Parallel lines diverge on a hyperbolic plane.(1 vote)
- Why didn't you skin the potato first? Does not doing so make it easier to cut??(2 votes)
- how do you make that with a potato??(2 votes)
Video transcript
At my house, no
Thanksgiving dinner is complete without
mathed potatoes. To make mathed potatoes,
start by boiling the potatoes until they're soft, which will
take about 15 to 20 minutes. After you drain them and
let them cool slightly, you're ready for the math. Take one potato
and divide evenly to get half a potato,
plus half a potato. Then divide the halves into
fourths and the fourths into eights and so on. Eventually, you will have
a completely mathed potato that looks like this. Once you have proven this
result for one potato, you can apply it
to other potatoes without going through
the entire process. That's how math works. While I prefer refined
and precise methods for mathing a
potato, many people just apply brute
force algorithms. You can also add other variables
like butter, cream, garlic, salt, and pepper. Place in a hemisphere
and garnish with an organic
hyperbolic plane, and your math potatoes
are ready for the table. Together with a cranberry
cylinder and a nice basket of bread spheres
with butter prism, you'll be well on
your way to creating a delicious and engaging
Thanksgiving meal. Here's a serving tip. When arranging mathed
potatoes on your plate, it is important to do it
in a way that holds gravy. If you just make a mound,
the gravy will fall off. It's best to create some
kind of trough or pool. But what shape will maximize
the amount of gravy it can hold? Due to the structural
properties of mathed potatoes, this can essentially be reduced
to a two-dimensional gravy pool problem, where you
want the most gravy area given a certain
potato perimeter. When I think of this
question, I like to think about inflating shapes. Say you inflated a triangle. It would add more area and
round out into a circle. And then, if the perimeter
can't change, it would pop. In fact, all 2D shapes
inflate into circles. And in 3D, it's spheres, which
is my bubbles like to be round. And turkeys are
spheroid, because that optimizes for maximum stuffing. The limited three-dimensional
capacity of mathed potatoes may confuse things a little. But since a mathed potato
sphere can't support itself, you're really stuck with
extrusions of 2D shapes. So what's better? A deep mathed potato cylinder
or a shallow but wider one? Well, think of it like this. If you slice the
deep version in half, you'll see it has equivalent
gravy-holding capacity to two separate shallow cylinders. And the perimeter
of two circles would be more efficient if combined
into one bigger circle. So the solution is to create
the biggest, roundest, shallowest gravy pool you can. In fact, maybe you should
just skip the mathed potatoes and get a bowl. Anyway, I hope
this simple recipe helps you have an optimal
Thanksgiving experience. Advanced
chef-amaticians may wish to try Banach-Tarski
potatoes, wherein after you cut a potato
in a particular way, you put the pieces back
together and get two potatoes. Stay tuned for more delicious
and extremely practical Thanksgiving recipes this week.