Show HN: I made a puzzle game that gently introduces my favorite math mysteries

This is the first iteration of a short game I’m making that tries to interactively explain some of my favorite math questions / ideas. My goal is mostly to get the player curious and not necessarily to explain absolutely everything.

There were a lot of fun technical parts to building this:

- For implementation reasons, it’s much easier if the lines all have integer intersection points with each other. To do this, when a new line is added I “cheat” by rounding intersections to integers and then splitting the old lines at the intersection into new linds (with potentially different slopes) going through the rounded point

- I had to draw semi accurate maps of actual places (UK, South America, US west coast) in the HTML canvas using just line segments. I tried a few different solutions, including using SVG data. I ended up using the topojson library to give nice line approximations to GeoJSON maps

- I use a simple backtracking algorithm to handle the live coloring of graphs

- I use turf.js’s polygonize function to handle finding polygons from line segments (very happy I didn’t have to implement this myself!)

- I wanted to make the game as mobile friendly as possible (don’t think I’ve nailed this quite yet)

There were also a few tradeoffs I made:

- I wanted give links earlier in the game for players to learn more, but I decided to wait until the end to maintain the flow of the game

- In order to make the game more mobile-friendly, I generally stuck to maps with a small number of regions (at least for maps people have to interact with them). So for the most part all of the instances in the game are “easy”

Show HN: I made a puzzle game that gently introduces my favorite math mysteries
rahulilango.com

Hi, my two cents; you claim "Although mathematicians believe their proof is correct, it is too complex to verify without computer assistance", but I'm not sure "believe" is the correct verb since the proof has been formally verified (see for instance https://github.com/coq-community/fourcolor for a formal verification in Coq).

I understand that you want to emphasize the fact that no human can understand the proof with a full overview, but I wonder whether the current sentence will not make people think mathematicians are not perfectly sure of the proof.

great work!

You do need to prove that you have assigned the colors before the choice of what to reveal is made, I think. Physically this is guaranteed by the presence of the colors under the post-its (barring dynamic e-paper or something).

I'm not sure how it works with the example of the primes, I lost the link to the later pages of the game so I can't read over it again, but I think it's guaranteed because there's just one number encoding all the assignments and you just get to unlock a single pair with the key given in response to your choice. There's an assumption that there isn't enough information in the key to fake any response, it has to reveal something that was already in there.

This was fun, I went into this thinking "Ha I already know this theorem" but came out learning something about zero knowledge proofs!