Ancient Greek Geometry: The Game

July 3, 2013 9:04 AM

The regular polygons have been kidnapped by ninjas. Are you a bad enough dude/tte to construct the regular polygons with nothing but a virtual compass and straightedge?

(The five allowable moves of classic compass-and-straightedge construction are as follows:

1: You may create the line through two existing points
2: You may create the circle through one point with its center at another point
3: You may create the point which is the intersection of two existing, non-parallel lines.
4: You may create the one or two points at which a line and circle intersect.
5: You may creating the one or two points at which two circles intersect.)

posted by Iridic (67 comments total)

3: You may create the point which is the intersection of two existing, non-parallel lines.

But if you create the point which is the intersection of two existing, parallel lines, you win this game forever.
posted by Navelgazer at 9:07 AM on July 3, 2013 [5 favorites]

wow, this is great. thanks for this.
posted by yeoz at 9:11 AM on July 3, 2013

O
M
G

I've been waiting all my life for this app.
posted by DU at 9:11 AM on July 3, 2013 [2 favorites]

I did the triangle! The triangle is really easy.

I think I'll quit while I'm ahead.
posted by jeather at 9:11 AM on July 3, 2013 [5 favorites]

Is the bonus round a septagon? I hope so.
posted by boo_radley at 9:15 AM on July 3, 2013

I was thinking a heptadecagon or really any Fermat-prime-sided regular prime.

/pours out a 40 sided bottle for Gauss
posted by DU at 9:17 AM on July 3, 2013 [3 favorites]

In the new game +, you have to square the circle.
posted by Iridic at 9:18 AM on July 3, 2013

Due to some early inefficient moves I don't really want to re-do, I didn't make all of them under the move count, but I'm up through the 7 pack so far. Best game.
posted by DU at 9:21 AM on July 3, 2013

Are you a bad enough dude/tte to construct the regular polygons with nothing but a virtual compass and straightedge?

Look, I'm not going to conform to your geometric-normative attitudes, OKAY? WHo's to say what's REALLY a "regular" polygon?
posted by grubi at 9:32 AM on July 3, 2013 [3 favorites]

Look, I'm not going to conform to your geometric-normative attitudes, OKAY? WHo's to say what's REALLY a "regular" polygon?

Well, if you prefer bent lines, try hyperbolic or spherical geometry.
posted by eriko at 9:37 AM on July 3, 2013 [1 favorite]

Up until pentagon, it's just ringing a few changes on a couple ideas. It's a whole new ball game when you get to the next prime number.
posted by DU at 9:44 AM on July 3, 2013 [1 favorite]

Yay! Forwarding this already.
posted by carter at 9:47 AM on July 3, 2013

The only thing that could make this more perfect was some sort of Trapper Keeper interface to save my work.
posted by MCMikeNamara at 9:54 AM on July 3, 2013 [5 favorites]

Tip if you're having problems with Circle Pack 2 in 5 - extending a line does not count as an extra move.
posted by 0xFCAF at 9:59 AM on July 3, 2013

some sort of Trapper Keeper interface

Now I wish I was a programmer so I could make a Trapper Keeper app for tablets.
posted by grubi at 10:09 AM on July 3, 2013 [1 favorite]

The longer I play with this the more everything starts to look all Gallifreyan. This is not a bad thing.
posted by jeribus at 10:38 AM on July 3, 2013

i really wish I could selectively bold working lines other than by layering.
posted by leotrotsky at 11:10 AM on July 3, 2013

I also await the updated skeuomorphic edition with sticks on sand and hairy philosopher feet on the periphery
posted by leotrotsky at 11:14 AM on July 3, 2013 [1 favorite]

I don't get it. I can solve the first one, but I don't know how to even try the other ones. I've tried clicking on the hexagon and it does nothing (Chrome, if it matters, and it probably does).
posted by It's Never Lurgi at 11:14 AM on July 3, 2013

I don't get it. I can solve the first one, but I don't know how to even try the other ones. I've tried clicking on the hexagon and it does nothing (Chrome, if it matters, and it probably does).

You don't have to solve them in order or tell it what you're trying to construct; if you complete any construction it will credit you.
posted by Aquinas at 11:24 AM on July 3, 2013 [1 favorite]

awesome.
posted by mwhybark at 11:40 AM on July 3, 2013

I can't construct a triangle inscribed in a circle in fewer than nine moves :(
posted by kenko at 11:42 AM on July 3, 2013 [1 favorite]

Welp, there goes my day. 17/40 challenges so far, but I have no idea how to do most of these constructions in the smallest number of moves. And I'm just pretending that pentagon isn't there. I know I learned how to do it in elementary school, but hell if I can remember it now.
posted by duien at 11:43 AM on July 3, 2013

I wasn't paying too much attention the achievement box, so I didn't realized there were two constructions for each. I've only done some of the centered ones.
posted by DU at 11:48 AM on July 3, 2013

I've been listening to The Apocalypse Codex recently so I'm afraid of running this and summoning an Eldritch Horror.
posted by jclarkin at 12:42 PM on July 3, 2013 [1 favorite]

Damn!!! I have already wasted 3 hrs of office time and am sure I am going to waste a lot more.

This is amazing.
posted by TheLittlePrince at 1:26 PM on July 3, 2013

Dang it, I only know the multiples-of-threes and the square. I SHOULD be able to get past the square, but no.
posted by Madamina at 1:32 PM on July 3, 2013

Pythagoras would be so pissed off about us normals doing this stuff.
posted by roll truck roll at 1:58 PM on July 3, 2013

I'm up to the dodecagon and baffled.
posted by KathrynT at 2:16 PM on July 3, 2013 [1 favorite]

I can barely remember any geometry. Trying to figure these from scratch is tricky.
posted by BrotherCaine at 2:22 PM on July 3, 2013

WAHEY figured out the dodecagon!
posted by KathrynT at 2:28 PM on July 3, 2013 [1 favorite]

SQUEEEEEEE!

20/40... having trouble with the circles-within-circles. I also seem to only be able to get a 3-corner simultaneous day.
posted by Eideteker at 2:46 PM on July 3, 2013 [1 favorite]

Seriously, though, I was just talking about this in a bar on Saturday. "Straightedge; not even a ruler." Watching people get the impact of that difference is always a wonder.
posted by Eideteker at 2:48 PM on July 3, 2013

The 3-pack in origin circle is the last shape (I haven't done all the move less than X challenges yet either), and I think I'm giving up. I don't know why the 7 in one was a lot easier.
posted by BrotherCaine at 3:59 PM on July 3, 2013

This is fantastic, but I'll have a nightmare about the pentagon.
posted by springload at 4:50 PM on July 3, 2013 [1 favorite]

I found a cheat sheet for how to make a pentagon, written by euclid

maybe someone can just do it for me?
posted by rebent at 5:08 PM on July 3, 2013

The others felt like fairly straightforward geometry, but trying to figure out this pentagon feels like some sort of alchemy. I wish I could find a spoiler-free hint of what direction to go in. I made something that kind of looks like a fox but it's sadly not actually a pentagon.
posted by duien at 5:11 PM on July 3, 2013

Yeah, the pentagon is killing me. Damn my stupid degree-centric brain!
posted by DU at 5:18 PM on July 3, 2013

my stubborn video game habit of finishing everything on one level before i move on to the next is getting me stuck at the square. 8 moves? aaaa what am i missing
posted by a birds at 5:19 PM on July 3, 2013

oh here you go you just do it like this

fuck this game
posted by rebent at 5:31 PM on July 3, 2013 [1 favorite]

And imagine you're almost done when some soldier comes in and disturbs your circles. I'd get myself killed over that too.
posted by springload at 5:42 PM on July 3, 2013 [4 favorites]

Some of the "in origin circle" ones either don't make sense or are broken. I've done the two packed circles one about 167 times and it won't credit me with it.
posted by DU at 5:47 PM on July 3, 2013 [2 favorites]

I ran into some trouble with the packed circles snapping to a point that was almost but not quite the right one. If you zoom in really, really far you can see where the circles aren't quite tangent. I got bitten by that on the pack 4 and some helpful folks in the creator's blog post about the game got me straightened out.
posted by duien at 5:53 PM on July 3, 2013 [1 favorite]

They should totally teach this in school.
posted by leotrotsky at 5:54 PM on July 3, 2013

trying to figure out this pentagon feels like some sort of alchemy. I wish I could find a spoiler-free hint of what direction to go in.

The ratio between the side and diagonal of a regular pentagon is the golden ratio.
posted by stebulus at 8:18 PM on July 3, 2013 [1 favorite]

Some of the "in origin circle" ones either don't make sense or are broken. I've done the two packed circles one about 167 times and it won't credit me with it.

It reliably credits this straightforward Circle Pack 2 on my machine. Does it not on yours?
posted by stebulus at 8:21 PM on July 3, 2013

Here's a circle pack 7 that doesn't register. I think it's rather lovely.
posted by boo_radley at 8:23 PM on July 3, 2013 [1 favorite]

Thank you stebulus! That plus some golden ratio research (specifically this diagram of how to get the golden ratio from a triangle) got me there. But my solution is so, so hideous.
posted by duien at 8:48 PM on July 3, 2013

Here's a circle pack 7 that doesn't register. I think it's rather lovely.

It is lovely, but I don't think it's correct. The circles in the outer ring aren't tangent to each other, are they? If I compute correctly, their centres are 1/2 unit apart but their diameters are sqrt((25−14sqrt(3))/3) ≈ 0.50043.
posted by stebulus at 9:05 PM on July 3, 2013 [1 favorite]

(And this corrected variant is credited.)
posted by stebulus at 9:16 PM on July 3, 2013

I believe what it's looking for, for the origin circle ones, is that the circle in question have one of the original two points as the origin and the other point as the radius.
posted by rifflesby at 9:44 PM on July 3, 2013 [2 favorites]

I spent 3 hours trying to get the 8-move square. The feeling when I accomplished it (with some hints from a significant other, who was also trying to solve it) was uniquely satisfying.
posted by NMcCoy at 1:18 AM on July 4, 2013 [2 favorites]

OK - I made a picture of a Sombrero from above, but don't know what to do next?
posted by zoo at 1:45 AM on July 4, 2013

The ratio between the side and diagonal of a regular pentagon is the golden ratio.

So, I know this already. But I want to derive it for honesty's sake. It sure isn't obvious.
posted by DU at 2:27 AM on July 4, 2013

Fantastic ?game? ?puzzle? whatever.

The "in origin circle" thing was tripping me up. I think you have to take it literally - all of the required figures have to be packed in a circle which has as its center one of the original two points.

I think that's why boo_radley's solution won't register.
posted by etherist at 10:30 AM on July 4, 2013

I don't understand why this one doesn't count as being "in origin circle?"
posted by tickingclock at 11:43 AM on July 4, 2013

I think because the "origin circle" has to have one of the points as its center and the other on its circumference.
posted by KathrynT at 11:45 AM on July 4, 2013 [1 favorite]

Aha. Thanks.
posted by tickingclock at 11:49 AM on July 4, 2013

"I can't believe it. You actually found a practical use for geometry."
posted by Ned G at 5:44 PM on July 4, 2013

I think because the "origin circle" has to have one of the points as its center and the other on its circumference.

Put like that, it might seem like a bizarre restriction, but the effect is just that the circle is (or might as well be) among the givens, not for you to choose/construct, so the problem is effectively changed from, e.g., "construct an equilateral triangle" to "inscribe an equilateral triangle in a given circle". This is a very common type of problem in geometry, which (I'm guessing) is one reason the author didn't think it necessary to be very explicit about his meaning here.

Also, it should probably read "in original circle" (though it doesn't in fact have to be the first one you construct).
posted by stebulus at 1:18 AM on July 5, 2013

I made a pentagon! In 30 steps and a spaghetti of lines, but I did it!
posted by DU at 9:44 AM on July 8, 2013 [1 favorite]

I'm still trying to go through every challenge in order. Circle pack 3 was OK, but then "in origin circle" was insane. I can barely even understand my own solution.
posted by a birds at 11:13 PM on July 8, 2013 [1 favorite]

the 9-step on that is really a thing of beauty. I've been hacking away at 4-pack in 12 now for days.

another aspect of the site that is a thing of beauty? the whole UI and persistency of it. click a completed challenge icon, and it reloads. every time you get a new low-count on a challenge, it saves. If your derivations are horrifically spaghettinized, make a new layer. It works on phones, tablets, and actual computers. You don't have to login. There are no ads.

This thing, this tool, this toy: it is just about the best thing ever.
posted by mwhybark at 11:32 PM on July 8, 2013

the 9-step on that is really a thing of beauty.

Circle pack 3 in origin circle can be done in 9?! I got it down to 10 and was feeling so impressed with myself.
posted by stebulus at 11:56 AM on July 9, 2013

I think it's likely if you did it in ten you can do it in nine. mine uses seven circles and two lines. circle pack 4 in 12 took days.
posted by mwhybark at 8:02 AM on July 13, 2013

Do you mean in origin circle? The context from a birds' question suggests you do, but I'm beginning to doubt.
posted by stebulus at 9:18 AM on July 13, 2013

Doing the square in 9 moves is easy. Doing it in 8 moves requires you to free your mind. You can even do it in 8 in the origin circle.

I'm up to 37 points and my officemate is up to 39.
posted by DU at 5:43 AM on July 17, 2013