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Just gave it a go. Quite a fun game actually. My compliments to the author. Some feedback that may be of use :

1) Use thicker lines, preferably in a color that contrasts better with white (although it'll be fine if the segment width is 2-4 pixels)

2) Support for drag + snap-to-intersect/vertex UX rather than click only. I instinctively tried this first.

3) Some sort of progress tracking (local storage or user accounts even perhaps)

Anyway, great idea and a promising start!

One more UI request: Given two points, there are two possible third points on an equilateral triangle, and no clear way to choose between them.

Great game, though. I'm on level 5 and having a lot of fun.

seems like the third point will follow the anticlockwise norm
Hey, you're right. Maybe clearer messaging is the answer. I had no idea that that was the norm.
An eraser to remove lines and segments would be useful too.
Yeah, some of the later ones just get cluttered and it can become difficult to click on the intended point.
Nice game! I think it could make geometry more fun for students.
Reminds me of this game: http://www.sciencevsmagic.net/geo/# which seems to be a lot less buggy.
thanks for the link. I had lost this game in the mists of time.

I'll give credit to OP's game however, giving you new tools once you have proved how to do something is great!

Cool game, well made, but it's driving me nuts. I'm stuck on 3/40 - I've created the enclosing circle for "in origin circle" but game doesn't want to acknowledge it. Clearly I'm doing something wrong....
"in origin circle" means that it has to be circumscribed by a circle with a center on one of the two starting points

Edit: It actually has to be inside of the circle made centered on one of the starting points and with the other starting point on the circle.

(comment deleted)
I wonder what other mathematical axiom sets can be pretty much directly translated in a game like that. Maybe something from calculus, topology or knot theory.
Deontic logic! "Prove that killing Mr. A is incompatible with the categorical imperative. Also supports undo and redo."
RollerCoaster Tycoon: Trolley Problem Edition
That's fun and educational.

Minor UI feedback:

The undo button moves when you click it which is annoying if you intend to step back 2 or more steps.

Another minor UI feedback: the yellow against white is very low contrast and difficult to see on my display.
Also if you do a partial action and press undo it undoes the partial action and the previous one.

It looks like Esc is the intended "nevermind" button, but it isn't obvious.

That reminds me of google/trimble sketchup. It always annoyed me.
I recently bought a copy of Euclid and it's been sitting on my bookshelf, waiting for that ever-receding "when I have the time." It's like the author set out to give me the most perfect and thoughtful birthday present. :)
This game is very similar to my first year of college mathematics -- studying Euclid's Elements and working through the proofs. I look forward to the game version of my sophomore year -- Apollonius' conic sections and Ptolemy's astronomy.
I was thinking the same thing... But Newton and Lobachevsky make for a much more challenging 3rd and 4th edition.
dammit, I'm stuck on 11. Has anyone got a solution?
Compass2 is your friend.
Ahhh, I hadn't ever used Compass2 yet, I'll have to check it out, thanks.
Wow, totally did not notice when Compass2 appeared, probably complicated several of my solutions quite a bit...
I'm struggling on 17. There is no circle that intersects both A and B that is tangential to the line. That's how I interpret the instructions for that level, anyway. However, it seems there should be an infinite amount of circles that are tangential to the line that can intersect A.
The circle is supposed to be tangent to the line at B.
Is that to mean tangential to anywhere on the line that intersects B, or B is the point at which the circle is tangential to the line that intersects B?
I figured it out. I was a bit confused in my assumption.
I'm not sure about you guys, but I'm not getting any feedback whatsoever. I've measured it with all the tools I can find, but I'm not getting any "Well done" or any link to the next level. Any thoughts?
It is important to not guess.

You need to use the tools provided to create something that is guaranteed to be what is asked for.

For instance in the first level you aren't given a ruler, so you need to figure out how to do the level without using one.

Well, no shit. But I'm saying I constructed an equilateral triangle but the game wasn't recognizing it. After reloading the page a few times it finally started giving feedback, like thickening the line when moving over it (which wasn't happening before), letting me actually place the dot on the intersection between the two circles
Really cool game and great idea, there's some good educational potential here. I'm looking forward to exploring Euclid's proofs again in this digital format. This easily beats dilly-dallying with a real-life compass.
Looks cool! I think math needs to be taught in that kind of style, where people learn by doing it. I would be interested in having something similar to that on my site, Learneroo.com. One suggestion: start people off by walking them through easy challenge so they learn the interface.
I went through couple levels before I realized I got more tools as I go on. Was using just intersect, segment,and compass and things were getting crowded.
If it was good enough for the ancient Greeks, it should be good enough for you.
Time to crack out the papyrus and stylus and turn off the computer?
Awesome. Definitely forwarding to all the teachers I know.
Great game! I'd love to see other peoples' solutions once I finish mine.
I love this stuff. If this is "thinking geometrically" how does that compare to other forms of problem solving?
Warning: if you are stuck on #19, there is a bug. For some reason it won't let you make points at the intersections you need to complete it.
well thanks for the tip... but I'm stuck on #19

... because I'm stuck on #19

T.T

There is a bug, but you can hack your way around it and still solve it. It's like 2 problems in one!
Maybe I'm blind, but I can't find the link to level 2 when I solve level 1.
Ah, so "Well done" doesn't mean you're actually done. I needed to actually draw the lines between the three points to get to the next level.
Very nice game.

One problem for me is that by default the comments from other users are shown, sometimes with the solution for the level.

I think dashed lines for rays would reduce a lot of visual clutter.

Anyway, I long for the day when someone writes a similar toy for a non-Euclidean plane.