
Euclidea – Geometric construction game with straightedge and compass - elasolova
https://www.euclidea.xyz/
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n4r9
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)

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obastani
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!

~~~
lifthrasiir
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)

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obastani
Thanks for the response! I think you're right that it's something along these
lines. I didn't find any further information about Euclidea, but for anyone
interested, I did find some information about open source engines that achieve
similar purposes [1,2]. Need to do some more digging...

[1]
[https://en.wikipedia.org/wiki/List_of_interactive_geometry_s...](https://en.wikipedia.org/wiki/List_of_interactive_geometry_software)

[2]
[https://dev.geogebra.org/trac/wiki/TheoremProving](https://dev.geogebra.org/trac/wiki/TheoremProving)

~~~
lifthrasiir
Thank you for the pointer to Geogebra, yeah, there ought to be someone already
dealing this :-) It seems that there are some shortcuts for many functions
(e.g. [1] only evaluates the function finite number of times).

[1] [http://ggb1.idm.jku.at/~kovzol/papers/Kovacs-Recio-
Weitzhofe...](http://ggb1.idm.jku.at/~kovzol/papers/Kovacs-Recio-
Weitzhofer-20120323.pdf)

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lordnacho
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.

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aidos
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
Circuit Scramble

[https://play.google.com/store/apps/details?id=com.Suborbital...](https://play.google.com/store/apps/details?id=com.Suborbital.CircuitScramble)

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.

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Nursie
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
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-3...](http://www.rudyrucker.com/infinityandthemind/#calibre_link-318)

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dang
Discussed in 2016:
[https://news.ycombinator.com/item?id=13259944](https://news.ycombinator.com/item?id=13259944)

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xtiansimon
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.

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

~~~
danbruc
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-...](https://math.stackexchange.com/questions/1587861/inscribing-
square-in-circle-in-just-seven-compass-and-straightedge-steps)

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

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

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

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

~~~
mihaifm
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.

