5 ms·

Euclidea – Geometric construction game with straightedge and compass

129 points by elasolova 8y ago

dang 8y ago
Discussed in 2016: https://news.ycombinator.com/item?id=13259944 https://news.ycombinator.com/item?id=13259944
dandare 8y ago
I love this game, but I got stack at 1.7, unable to achieve the E star, unviling to give up or seek help :).
- awhitty 8y ago
  The solution will rattle you! At least it did me. I happened to blindly stumble upon it while trying various approaches, but I’d love to know what sort of intuition it takes to find the solution short of brute-forcing/lucky-guessing it.
- jonsen 8y ago
  Try a stucktrace :)
- danbruc 8y ago
  In case you eventually give up - as I just did - or somebody else is interested, here [1] ist the solution. It is definitely not a straight forward construction. [1] https://math.stackexchange.com/questions/1587861/inscribing-square-in-circle-in-just-seven-compass-and-straightedge-steps https://math.stackexchange.com/questions/1587861/inscribing-...
lordnacho 8y ago
This is brilliant! What I really want is a list of such mathy games for my 6 year old. I found him a logic gates (XOR, AND, etc) game that he also likes.
- sujeetb 8y ago
  I know of two other mathy game apps: Torus games (games like tic tac toe on a torus, Klein bottle etc.) and Pythagorea (which is about geometry)
- aidos 8y ago
  What’s the logic game? I’d also love to find more games like these for my kids (they love playing with Euclidea, but it’s too abstract for them to grasp). Another one they do manage to understand (and love) is Lightbot http://lightbot.com http://lightbot.com
  - lordnacho 8y ago
    Circuit Scramble https://play.google.com/store/apps/details?id=com.Suborbital.CircuitScramble https://play.google.com/store/apps/details?id=com.Suborbital... It's so good I managed to do all 135 puzzles in two days and another few hundred generated ones. The generator might need some work. A lot of the ones it makes are too simple, solvable in 1 or two moves.
- deleted 8y ago
  [deleted]
- hammerbrostime 8y ago
  DragonBox Algebra is tons of fun.
n4r9 8y ago
Looks very similar to Euclid the Game which I enjoyed working my way through many years ago: https://kasperpeulen.github.io https://kasperpeulen.github.io
Nursie 8y ago
This one is also fun, just challenges to create different shapes, and shapes-within shapes in under a certain number of moves - https://sciencevsmagic.net/geo/ https://sciencevsmagic.net/geo/
- spiralganglion 8y ago
  Came here to post this — it's one of my favourite math games. For a really nice introduction to the more advanced uses of geometric algebra in three dimensions, there's this fantastic chapter in a book by Rudy Rucker, which you can read here: http://www.rudyrucker.com/infinityandthemind/#calibre_link-318 http://www.rudyrucker.com/infinityandthemind/#calibre_link-3...
Nursie 8y ago
Am I being stupid? I can't see how to move on past the first puzzle when it's complete.
- _Microft 8y ago
  The box with the blue arrow to the right does that.
infocollector 8y ago
Is the source code for this game available somewhere to look at?
- mihaifm 8y ago
  It's not open source from the looks of it. It's a freemium game, they have in-app purchases on mobile where you can unlock all levels without completing the previous ones. Some of those levels are insanely difficult, so you have to either lookup the solutions online or pay for unlocking, otherwise it's pretty much impossible to advance.
aidos 8y ago
I’ve spent a lot of hours toiling away on this game. It’s really nicely made.
xtiansimon 8y ago
Constructing '1.2 Perpendicular Bisector', I got stuck trying to use the hot key T. I switched to 'explore mode' to see the hint and realized I could complete the task using a compass. Then, on the next screen I 'discovered the Perpendicular Bisector tool'. Maybe greying out the different tools at the bottom would make the locked tool more apparent during the tutorial--I almost abandoned the site, but stubbornness compelled me to try again. hehe.
obastani 8y ago
Does anyone know what are the algorithms behind this game, i.e., how does the game decide whether a given construction is valid? I'd appreciate any pointers!
- mihaifm 8y ago
  I am intrigued by this as well. I think they check for the existence of certain primitives and a sequence in which they are drawn. For example for level 1.1 where you need the 60 degree angle, if you use Explorer mode to view the solution and then you draw a "cheated" line on top of it, it won't give you a completed level because you don't have the sequence (2 circles and an intersection point). It also doesn't allow you to draw another line on top of an existing line, so you'd have to restart the level in this case.
  - MauranKilom 8y ago
    It won't give you a completed level because you're in explorer mode, not because the step sequence is wrong. Also, you don't have to restart to leave explorer mode (at least in the web version).
- 4rgento 8y ago
  My guess is that it uses analytical geometry to compute the equations of the drawn items. This also may includes a mapping to some canonical dimension(size) and orientation(rotations).
- lifthrasiir 8y ago
  My cursory analysis suggests that there are hidden constructions invisible in the game but used for the verification (you can see a base64-encoded task file flying through the network). The actual verification happens in an Emscripten-powered C++ engine and it is pretty opaque to me---the only thing I can identify is a parser for the task file. My best guess without the actual source code is as follows: The perfect algorithm would involve the equality between two functions returning constructible numbers [1], where each function would map from unspecified points (that you can move around with the hand tool) to the result points. As far as I concerned comparing two constructible numbers is possible but inefficient [2], and comparing two functions is probably much harder. However for the purpose of game, we can approximate the equality by randomly evaluating a difference between two functions to the reasonable accuracy and checking if it is close to zero. Theoretically exact real arithmetic would be preferable, but adaptive fixed-precision real arithmetic may be also possible as long as rounding errors are tracked. [1] https://en.wikipedia.org/wiki/Constructible_number https://en.wikipedia.org/wiki/Constructible_number [2] https://mathoverflow.net/a/211556 https://mathoverflow.net/a/211556

129 points by elasolova 8y ago

dang 8y ago

Discussed in 2016: https://news.ycombinator.com/item?id=13259944 https://news.ycombinator.com/item?id=13259944

dandare 8y ago

I love this game, but I got stack at 1.7, unable to achieve the E star, unviling to give up or seek help :).

awhitty 8y ago
The solution will rattle you! At least it did me. I happened to blindly stumble upon it while trying various approaches, but I’d love to know what sort of intuition it takes to find the solution short of brute-forcing/lucky-guessing it.
jonsen 8y ago
Try a stucktrace :)
danbruc 8y ago
In case you eventually give up - as I just did - or somebody else is interested, here [1] ist the solution. It is definitely not a straight forward construction. [1] https://math.stackexchange.com/questions/1587861/inscribing-square-in-circle-in-just-seven-compass-and-straightedge-steps https://math.stackexchange.com/questions/1587861/inscribing-...

lordnacho 8y ago

This is brilliant! What I really want is a list of such mathy games for my 6 year old. I found him a logic gates (XOR, AND, etc) game that he also likes.

sujeetb 8y ago
I know of two other mathy game apps: Torus games (games like tic tac toe on a torus, Klein bottle etc.) and Pythagorea (which is about geometry)
aidos 8y ago
What’s the logic game? I’d also love to find more games like these for my kids (they love playing with Euclidea, but it’s too abstract for them to grasp). Another one they do manage to understand (and love) is Lightbot http://lightbot.com http://lightbot.com
- lordnacho 8y ago
  Circuit Scramble https://play.google.com/store/apps/details?id=com.Suborbital.CircuitScramble https://play.google.com/store/apps/details?id=com.Suborbital... It's so good I managed to do all 135 puzzles in two days and another few hundred generated ones. The generator might need some work. A lot of the ones it makes are too simple, solvable in 1 or two moves.
deleted 8y ago
[deleted]
hammerbrostime 8y ago
DragonBox Algebra is tons of fun.

n4r9 8y ago

Looks very similar to Euclid the Game which I enjoyed working my way through many years ago: https://kasperpeulen.github.io https://kasperpeulen.github.io

Nursie 8y ago

This one is also fun, just challenges to create different shapes, and shapes-within shapes in under a certain number of moves - https://sciencevsmagic.net/geo/ https://sciencevsmagic.net/geo/

spiralganglion 8y ago
Came here to post this — it's one of my favourite math games. For a really nice introduction to the more advanced uses of geometric algebra in three dimensions, there's this fantastic chapter in a book by Rudy Rucker, which you can read here: http://www.rudyrucker.com/infinityandthemind/#calibre_link-318 http://www.rudyrucker.com/infinityandthemind/#calibre_link-3...

Nursie 8y ago

Am I being stupid? I can't see how to move on past the first puzzle when it's complete.

_Microft 8y ago
The box with the blue arrow to the right does that.

infocollector 8y ago

Is the source code for this game available somewhere to look at?

mihaifm 8y ago
It's not open source from the looks of it. It's a freemium game, they have in-app purchases on mobile where you can unlock all levels without completing the previous ones. Some of those levels are insanely difficult, so you have to either lookup the solutions online or pay for unlocking, otherwise it's pretty much impossible to advance.

aidos 8y ago

I’ve spent a lot of hours toiling away on this game. It’s really nicely made.

xtiansimon 8y ago

Constructing '1.2 Perpendicular Bisector', I got stuck trying to use the hot key T. I switched to 'explore mode' to see the hint and realized I could complete the task using a compass. Then, on the next screen I 'discovered the Perpendicular Bisector tool'. Maybe greying out the different tools at the bottom would make the locked tool more apparent during the tutorial--I almost abandoned the site, but stubbornness compelled me to try again. hehe.

obastani 8y ago

Does anyone know what are the algorithms behind this game, i.e., how does the game decide whether a given construction is valid? I'd appreciate any pointers!

mihaifm 8y ago
I am intrigued by this as well. I think they check for the existence of certain primitives and a sequence in which they are drawn. For example for level 1.1 where you need the 60 degree angle, if you use Explorer mode to view the solution and then you draw a "cheated" line on top of it, it won't give you a completed level because you don't have the sequence (2 circles and an intersection point). It also doesn't allow you to draw another line on top of an existing line, so you'd have to restart the level in this case.
- MauranKilom 8y ago
  It won't give you a completed level because you're in explorer mode, not because the step sequence is wrong. Also, you don't have to restart to leave explorer mode (at least in the web version).
4rgento 8y ago
My guess is that it uses analytical geometry to compute the equations of the drawn items. This also may includes a mapping to some canonical dimension(size) and orientation(rotations).
lifthrasiir 8y ago
My cursory analysis suggests that there are hidden constructions invisible in the game but used for the verification (you can see a base64-encoded task file flying through the network). The actual verification happens in an Emscripten-powered C++ engine and it is pretty opaque to me---the only thing I can identify is a parser for the task file. My best guess without the actual source code is as follows: The perfect algorithm would involve the equality between two functions returning constructible numbers [1], where each function would map from unspecified points (that you can move around with the hand tool) to the result points. As far as I concerned comparing two constructible numbers is possible but inefficient [2], and comparing two functions is probably much harder. However for the purpose of game, we can approximate the equality by randomly evaluating a difference between two functions to the reasonable accuracy and checking if it is close to zero. Theoretically exact real arithmetic would be preferable, but adaptive fixed-precision real arithmetic may be also possible as long as rounding errors are tracked. [1] https://en.wikipedia.org/wiki/Constructible_number https://en.wikipedia.org/wiki/Constructible_number [2] https://mathoverflow.net/a/211556 https://mathoverflow.net/a/211556