Interactive explorable websites - looking for mathematical ideas or interface designers

explanaria commented 2 years ago

About the Author

I make interactive, animated math explanations in a web browser, using 3D graphics and webGL to make the intangible tangible. You can see some of my work here at The Case of the Impossible Triangles and How Mathematicians Think About Four Dimensions. It's especially well suited for making things which are 3D and interactive, letting people get their hands dirty directly and learn!

I'm looking for help in two different areas: first, coming up with new mathematical concepts to bring to life interactively; and second, creating engaging interactive user interface design for these mathematical concepts.

Topic ideas

Here are some potential ideas I have for topics to visualize:

Abstract algebra, visually

Mathematicians care a lot about abstract algebra, and groups have many interesting niches to study. However, I'm looking for a good problem which is hard to solve without groups, to answer the question "why do mathematicians think groups and symmetry are worth studying in the first place?".

One idea for such a problem is solving Rubik's cubes.
Another problem was crystals, which are very symmetric and can be classified using groups. I found a paper by John Conway (of Conway's game of life fame) which calculates that there are around 230 possibilities, but it was very dense and I wish there were visuals.
Another possibility is molecules, and figuring out whether they have a magnetic dipole or not by what type of symmetry they have.

For groups, there is a book called Visual Abstract Algebra featuring diagrams of cayley graphs, which feel like they're begging to be made interactive.

Tensors

Tensors are a mathematical object which generalize matrices and vectors, but also show up in geometry and cohomology as differential forms. They can be visualized using changing coordinates, and it would be interesting to connect this definition of tensor to visualize differential forms and more.

Knot theory?

I experimented with visualizing knot theory here, and it would be interesting to partner with someone excited about knot theory to explore this further.

Target medium

My preferred medium is interactive websites. Videos are great, but it's even better to interact with the amazing ideas!

Contact details

If you're interested, email me at explanaria @gmail.com or comment here!

electrineer1 commented 2 years ago

Hello, my topic post # 173 combines matrix transformations from Discrete Fourier transforms and connects them back to geometry, all related to a poorly taught math topic taught to power grid engineers. It aligns well with your triangle simulator and interest in Tensor transformations.

nacochran commented 2 years ago

@explanaria I think you have great ideas! I am actually interested in much of the same concepts. I played around with WeBGL last year but I plan to learn it in depth sometime this year.

But in my thoughts about how to teach best, I think that simulations, and especially interactive 3D models are very helpful for the student learning. After all, we do live in a 3D world so when we are talking about anything that has 3D implications I think that is very important. I have thought about many other pedagogy ideas as well, as I am interested in the most efficient ways to teach both myself and others a new topic.

You talked about crystals and molecules and that is definitely up my alley as well! I am currently spending a good deal of time studying Chemistry right now and although 3D simulations do exist (ChemDoodle, etc), I've thought of more advanced ideas that I want to implement sometime. (Such as trying to find dipole moments, etc.)

Speaking of which, I have found some pretty amazing Chemistry videos that implement some of these 3D simulations and I think they do a really good job like 3blue1brown does for math.

Anyway, keep it up! Unfortunately I have not studied knot theory yet (I plan to study topology, knot theory and related fields sometime when I have more free time), but I look forward to see what you come up with.

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