Making Math

This course should empower you to create your own instances of making math material. The only way to acquire a skill is to practice it. We have now been through several cycles of discussing a mathematical topic and brainstorming things we might build related to it, modeling possible structures to build, and then choosing and constructing physical objects that embody some aspect of the initial topic.

This second major assignment "Making Math" is your opportunity to pursue a full cycle of this type on your own, under your own direction, and exploring ideas and methods of interest to you. Thus if there's a mathematical topic you were hoping would be on the syllabus but isn't, you can choose that topic. Or if there's modeling software that you are comfortable with, or have been wanting to try, you can use that software. Or if there is a construction technique you want to experiment with, you can find a topic that will lend itself to that technique, as we did with the cube-and-pipe-cleaner constructions.

None of the above is required; that is to say, you are welcome to explore a different aspect of a topic we have covered in class, using modeling software that we've used for other projects, and then build your result using construction techniques we have tried in class. All that is required is that this be a new construction, not the same as any other construction that has been submitted for this class (by any student). Of course, as a major assignment, you are in any case expected to go beyond the level and polish that would be appropriate for a weekly submission. So just doing another new construction that would have been a reasonable response to exactly one of the weekly assignments in the class would be less likely to receive full marks, unless it excels in conception or execution. You're encouraged to strike out in new directions, but don't let that be a limitation on your creativity.

On the other hand, a certain amount of structure fosters creativity. So there is a theme to Making Math: the beauty of mathematics. Your project should somehow evoke the inherent beauty of mathematics. That could mean that you choose a topic that for you embodies the beauty of mathematics. Maybe there is a proof that so struck you with its elegance that you still remember it; then perhaps you can find a way to make a physical construction that illustrates or illuminates that proof, or the ideas and mathematical structures used in that proof.

Or it could mean that you produce an end result that you find visually beautiful. It might be beautiful for its symmetry, or its use of color, or its intricate detail, or other aspects that appeal to you.

Or the beauty of your project could lie in a surprise or a paradox that it embodies. Perhaps you can create something that seems as though it will behave in some particular way, but then actually behaves very differently. I personally would say the construction produced from multiple copies of the square orthobicupola, which contracted in other directions both when compressed and when stretched along one particular axis, exhibits this type of beauty.

The bottom line is that the aspect of beauty is up to you; create an object that helps to reveal that aspect.

Mechanics

You should submit three written items, one digital item, and one physical item for this assignment:

1.  A discussion of your mathematical topic. This should be an essay at least three pages long (you are welcome to use more if you like) which introduces your topic, gives an exposition of a few central ideas, structures, or theorems of your topic for a general audience, and then discusses the questions, structures, or proofs that you think might provide a fruitful source of objects to build.
2. A software model of the object you plan to build. As always, submit the internal fully-structured files of the application you use, rather than just images.
3. A written inventory of materials and build plan for your object. Remember, even though you're going to build this item yourself, your instructions should be clear and complete enough to allow a third party to build the object.
4. Your executed construction. Bring it to section on November 7th, which I will attend, and where you will get a chance to enjoy each others' projects. Be ready to briefly introduce what you've built (you won't need to go in depth), explore what others have built, and share the thoughts and questions that other projects inspire in you.
5. A brief essay (three paragraphs may suffice, but again you may use more) describing how your project fits the theme of the assignment.

Choosing a topic

You should expect to have to contemplate multiple possible topics to find one that you want to pursue for this project. Think about the areas of math that most excite you, and then think about something that you've read about or heard in class in those areas that you'd love to see in real life. Or use this as an excuse to read up on an area that piqued your curiosity at some point. You may or may not find something that you think you can actually construct, but you'll broaden your mathematical horizons.

As mentioned in class, one section of your assignment due Friday (Oct 19) will be to brainstorm at least two different possible topics for your project. Once that's due, I will post a list of more concrete possible projects or project areas, any of which you'll be welcome to use; but you're at least as welcome to do a project not on that list. After that point (or in fact, even before that point, if you feel ready), you should as soon as possible (informally and not as an assignment) bounce the idea you're most leaning toward off of me, either in office hours, or after class, or make an appointment to speak with me in person or by phone, or via email. (I list email last just because it's the least efficient of those means of communication.) You should aim to be pretty well settled on your topic by Oct 24 so that you have two full weeks to design and execute it; you'll need that much time. Note that you don't need to wait for the suggested topic list to come out to start exploring your ideas more in depth, since you are welcome to pursue whatever topic you like.

Basis for grading

The following aspects of your project will be considered/evaluated in determining your overall grade on this assignment:

• Writing mechanics of all of the written portions of the assignment.
• Style and effectiveness of communication in items 1 and 5.
• Clarity and thoroughness in item 3.
• Correctness, significance, and clarity of mathematical exposition in item 1 (and to the extent relevant in item 5).
• Organization, relevance, and correctness of software model in item 2.
• Quality of the mathematical connection between the topic and the built item, and the degree to which the built item illuminates the mathematical topic or a specific idea relevant to the topic.
• The quality of the construction submitted for item 4. (I understand that you may not be experienced in the construction technique you choose. This does not need to be master craftsmanship. However, your item needs to be reasonably sturdy and not appear to be sloppy work to convey the underlying mathematical ideas successfully.)