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Show HN: Compass and Ruler construction problems as puzzle game (sdkgames.itch.io)

125 points by sdkgames ↗ HN
Ecocoru is a puzzle game where you have to solve compass and ruler construction problems. The game mimics compass and ruler and let you draw straight lines/segments and circles/arcs. You can also view and explore a solution for each problem. A basic knowledge of well-known results of Euclidean geometry is needed to play the game. The game has over 70 problems.The game is designed for full-screen mode and the use of the mouse.

27 comments

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jstrieb
This looks very fun! It reminds me of a game called Euclidea that I played and enjoyed a while back, though the interface for this looks pretty different.

https://www.euclidea.xyz/

Congrats on the release!

jbaber
Second Euclidea. It's a shockingly intuitive interface for geometric constructions on a phone.
sdkgames
Thank you! While Euclidea and my game explore the same theme, the approaches are different. It seems Euclidea uses some kind of automated theorem prover to verify a solution. I use numerical verifiers. There are pros and cons for both approaches. The tools are different. I think some choices in Euclidea are too restrictive (e.g. collapsible compass, inability to draw arcs). Their monetization model affects the gameplay (grinding, solution hiding).
JadeNB
> I think some choices in Euclidea are too restrictive (e.g. collapsible compass, inability to draw arcs).

Collapsible compass is not a choice of Euclidea, but a choice of Euclid. (Although, of course, one of the first things Euclid proves is that you can simulate a rigid compass with a collapsible compass: https://en.wikipedia.org/wiki/Compass_equivalence_theorem.)

gilleain
Interesting to me is how complex some of the 'traditional' or, perhaps, formal construction methods can be.

I've been trying to draw Islamic designs, and the strict methods are very involved. For example this shows a very simple design, with construction lines then the final pattern:

https://ibb.co/RN8vJKN

amenghra
Euclidea’s solutions are a YouTube search away.

I personally prefer the satisfaction of finding the solutions myself, even if it sometimes takes me months to solve a given puzzle (I usually end up putting it on hold for weeks and then revisiting with a fresh perspective).

Over the years, I amassed 430/535 stars, not bad but still quite some stars to go.

I always wondered how they came up with the minimal constructions and if they ever got them wrong?

alanbernstein
Whenever I play a puzzle game, I wonder about the construction of the puzzles and solutions. Who is responsible for it? Do they have a systematic method? Or does a solo indie game author just become so familiar with the mechanics of their game that most of the solutions become obvious?

I definitely had these questions about euclidea.

I like their other games as well, Pythagorea and x section.

gilleain
At least one person simply asks on Math Stack Exchange ...

https://math.stackexchange.com/users/11955/ed-pegg

but yes, I suspect that when you get very familiar with the mechanics of the game, solutions become obvious. Or they construct 'backwards' from the solution to a problem, maybe.

ComplexSystems
How can you be sure that your numerical algorithm gives the right answer? There are pairs of constructible numbers that are arbitrarily close to one another.
Waterluvian
Euclidea, in my opinion, has genius game design where you have to use the existing tools to make new ones. It basically teaches you, “you can do all this with just a few basic functions. The rest are just time-saving aggregates.”

I learned a lot from the game.

quyleanh
I can see the students could take the advantages of this game to geometry lecture. Not only fun but also educational. Thank you.
mnorris
Thanks for sharing this!

This is a cool game concept and I feel like it compressed a lot of geometry intuition into a short period of time. I have a math degree but managed to never take a geometry class in college or high school, so this was the first time I've had my (non-existent) knowledge of geometry "graded."

I hope more games like this can be incorporated into the formal educational process in the future; I feel like my childhood video game addiction could have been exploited by the education system just as much as the gaming companies, but with a better outcome.

Maybe the same type of game could be made for other subjects, too.

I'd like to see the concept extended in 3d with augmented reality with a limited set of construction tools. Maybe I'll try to do that if I get the time.

Also, I just realized that I only played the tutorial! There goes my morning.

blakesley
Nice! I was having fun with it, but then I got to "divide the segment in half". It's super easy, but it's too zoomed in for me to click on the snaps I want, and I can't find a way to zoom out. Clicking "full screen" gives the same level of zoom. What am I missing?

Edit: I just now tried Euclidea for the 1st time, and even tho its UX is a lot more polished, it starts off with lots of lines & midpoints. I appreciate that Ecocoru starts off with more circle-oriented problems, so that we can get a taste of using a compass. The 1st hexagon problem, though easy, was a joy to discover!

matsemann
I assume you're trying to find the half-point by making a circle with center in each end of the line, with radius spanning to the other end. Which is too big for the game area.

However, what you need is to equal circles from each end point, no matter the size as long as they overlap. So the solution here is to make a smaller circle on one point, and using the compass make a "copy" of that circle with the same radius at the other point.

yayachiken
The detection of solutions seems a bit buggy.

In the fourth task "Add the angles BAC and EDF on the given line GH", I drew the circles DF and EF in, then connected E and F with a line segment, and it told me that I solved the problem without touching the points GH at all...

Edit: In fact, simply drawing the line from E to F is already enough.

Edit 2: Similar when doing the "Perpendicular to line in a point not on a line": Drawing any perpendicular is enough, even if it is not going through that point.

sdkgames
Thanks for the feedback. I will check the win conditions.
gilleain
Very nice. A small suggestion would be to have a list of the steps shown on screen - like 1) draw circle centered on A, 2) extend line A-B (or whatever).
brianjacobs
On Firefox ESR 102 on Debian testing, I could not complete part 3 of the tutorial where I had to make arcs of a circle. I even eventually filled in the circle entirely, but it won't recognize it as completed.
sdkgames
That's strange. I have no errors on Firefox 104.
kentbrew
The thing where Escape is supposed to get you out of the arc tool but instead drops you out of full-screen mode is super annoying.
kapildev
How does the game check whether the solution has been made? Genuinely curious.

Also, I had found some bugs. Like when we are asked to create a perpendicular, any line that starts properly and is almost done but isn't done fully is treated as solution. Also, when it asks to create a triangle, but the solution is complete, it still passes. Although one could argue that the solution would be reached either way, in future cases where a person is nowhere near the full solution might be confused when the game marks the puzzle as solved.

sdkgames
Using analytic geometry methods, I test every new figure, whether it gives a solution.

Thank you for the feedback. I will check that.

vintermann
There was a nice educational game for mobile devices called Dragonbox Elements that also did this, in a very kid-friendly way. But I always thought Dragonbox's interfaces (they had an algebra game too) were almost too nice for kids' games, I wanted something more useful as a proof assistant. So very happy someone is exploring this space further!

logitext.mit.edu/tutorial was also something similar, an interactive, puzzle-game like interface for proving statements in the sequent calculus. Maybe that can be an inspiration too?

FunnyBadger
Very cool.

If you do machining, carpentry, construction, etc. you find this kind of stuff is surprisingly central to everyday work - you'll use either geometry constructions or the concepts behind them CONSTANTLY. Very useful to peak your skills at doing drills like this.

Bravo!