
Geometric Constructions Game with Straightedge and Compass - karimf
https://www.euclidea.xyz/
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delhanty
It's great to see all this straightedge and compass stuff turned into a game,
and I absolutely applaud the developers for launching it.

The above math, plus some graph theory (biconnected components etc.) is what
drove D-Cubed's DCM 2D component dated, which powered the sketcher portion of
many parametric MCAD systems after D-Cubed's launch by John Owen in 1989. See
his paper "Algebraic Solution for Geometry from Dimensional Constraints"
referenced on the Siemens PLM site:

[https://www.plm.automation.siemens.com/en_us/products/open/d...](https://www.plm.automation.siemens.com/en_us/products/open/d-cubed/references.shtml)

The original parametric CAD system, PTC's Pro Engineer (now Creo) predates
that (1987) and had it's own numeric (Newton-Raphson) solver. John Owen's
innovation of using Galois Theory combined with Graph Theory to solve
straightedge and compass configurations was a significant technical advance at
the time, and the DCM 2D component ended up powering most sketchers in the
industry.

Disclaimer: I worked at D-Cubed 1995-2000.

~~~
fsloth
Cool! I've never seen a practical example using Galois theory before. 10 years
of computer graphics experience, but very little maths beyond my physics
degree...

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unlogic
I enjoy the game a lot, but I disagree that it has that much of educational
value. Without pre-existing geometry knowledge (e.g. similar triangles;
median, bisector, and altitude in an isosceles triangle) the way to solve
puzzles is only to randomly screw around. The game then doesn't give any
explanation why that solution works.

~~~
karimf
After randomly screw around I usually wonder why my solution worked. If I
didn't do that it will be much harder to solve the next, more challenging
level. Now I'm playing on beta level packs (just one pack after the first one)
and it takes time to solve the puzzle if I only randomly screw around.

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wodenokoto
This one works on mobile browsers

[https://sciencevsmagic.net/geo/#0A1.N](https://sciencevsmagic.net/geo/#0A1.N)

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Waterluvian
This is the greatest game I've found this year. I've been craving this. The
way geometry and trigonometry was explored a long time ago by playing with
arcs and lines is just so so cool to me.

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n00b101
This is now my favourite mobile game!

It might be helpful to provide some background links on compass/straight-edge
construction [1] and the famous problem of squaring the circle [2]

[1] [https://en.m.wikipedia.org/wiki/Compass-and-
straightedge_con...](https://en.m.wikipedia.org/wiki/Compass-and-
straightedge_construction)

[2]
[https://en.m.wikipedia.org/wiki/Squaring_the_circle](https://en.m.wikipedia.org/wiki/Squaring_the_circle)

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mrcactu5
the challenge for this style of app is to balance mathematical content with
good UX/UI. It is tempting to sacrifice one for the other.

also from yesterday:
[https://news.ycombinator.com/item?id=13256222](https://news.ycombinator.com/item?id=13256222)

~~~
acobster
Definitely agree. From what I can tell so far (I've only just unlocked the
Perpendicular Bisector tool), it strikes a great balance. Just-in-time helper
prompts, a nice drag 'n' drop style UX that naturally lends itself to mobile,
and clear instructions.

I like that it uses the concept of Photoshop-style "tools" for drawing points,
segments, circles, etc. A very natural digital extension of the physical
pencil, straight edge, and compass, with some nice abstractions built on top.

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StavrosK
This is a fantastic game, I bought it a while ago and heavily recommend it.

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azeirah
It's a little unfortunate that they don't accept my somewhat elaborate but
ultimately correct solutions, if I find a way to create a perfect rhombus
within a rectangle in Lwaytoomany Ealsowaytoomany, they should accept it at
least, and give me 1 star for my effort!

Pretty fun so far though!

edit: So far, I've found two methods to find the center of a circle that they
don't like. 5L E7 isn't _that_ bad

>:(

~~~
aisofteng
As far as I can tell, solutions are recognized as long as they are valid,
regardless of length. Can you post an example of a solution you feel is
correct but that isn't being accepted?

~~~
iamcreasy
Here[1] is one that's not being accepted. Here I have to draw an equilateral
triangle given a straight line.

I am drawing two circles, on the two terminal points, with radius as the
length of the given line. The intersection of two circles is the third point
of the triangle.

[1] :
[http://i39.photobucket.com/albums/e179/iamcreasy/Screenshot_...](http://i39.photobucket.com/albums/e179/iamcreasy/Screenshot_20161227-011845_zpsesvirsqw.png)

~~~
BlackFingolfin
In principle, this is the right construction. However, you did not perform a
proper construction, as can be seen by the two tiny red circles: Instead of
constructing a circle passing through the end points of the given line, you
"eyeballed" the circle diameter. Which may look right at this resolution, but
if you were to zoom in sufficiently, you would inevitable end up with a circle
that oh-so-slightly misses to go through one of the end points of the base
line.

In the smartphone app, to do this right you need to select the circle tool,
start at one end point of the line, then drag your finger exactly to the other
end point -- it'll "snap" to that, and create a circle through the second end
point.

~~~
iamcreasy
Yes, I thought at too so I zoomed in to make sure that I am not making that
mistake.

I've found a solution though. The second point that indicates the radius of
the circle also snaps to other points. I didn't know that.

So now I can start dragging from one end point of the given line and end on
the other point(not eye ball it) to make sure the circle is the exactly that
radius.

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aisofteng
It would be pretty mean to include a special challenge level for constructing
a heptagon... but also funny. (The heptagon is not constructible[1].)

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

~~~
aisofteng
Follow-up (the app I use on mobile doesn't have an edit button) - it would be
interesting to provide a section that gives impossible challenges and declares
them as such, such as constructing a heptagon and squaring the circle, along
with an explanation of why they are impossible. It might ignite more common
interest in Galois theory!

~~~
c517402
OTOH, it might be more useful to show people what can be geometrically
constructed. Since Ancient Greeks knew that circles CAN BE squared, regular
heptagons CAN BE constructed, and angles CAN BE trisected by neusis
methods[1]. I don't think this is widely taught. Why don't we teach what can
be done rather than what can't be done when you limit yourself to straight
edge and compass?

I wonder how difficult it would be to add neusis to the construction
techniques in Euclidea or GeoGebra.

[1][https://en.m.wikipedia.org/wiki/Neusis_construction](https://en.m.wikipedia.org/wiki/Neusis_construction)

~~~
murkle
You mean something like this :)
[https://www.geogebra.org/m/cWfHr7pk](https://www.geogebra.org/m/cWfHr7pk)

You could turn it into a custom tool in GeoGebra if you think that would be
helpful.

Also worth noting that you can do angle construction in GeoGebra in other ways
(for example, just divide the angle by 3 instead of 2!)

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oldbuzzard
It would be nice to be able to move or get rid of the task completed box to
review your solution and look for modifications. Then you could reset and
replay. The inability to review after completing is annoying.

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programmarchy
This is beautifully done.

Can anyone shed some light on the technology used to build the game?

~~~
HiroshiSan
Straight edge and Compass, circa 2000 years ago.

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amelius
But how do you prove automatically that a given construction, no matter how
convoluted, gives the correct answer?

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waqf
There's a formula for the coördinates of where two arcs meet, where a line and
a circle meet, etc., in terms of the coördinates of the points which generated
the lines and circles — and you only need a few such formulæ (linear and
quadratic equations, in fact) to cover all legal straight-edge-and-compass
constructions.

So keeping track of exact, algebraic locations of the points is basically
equivalent to manipulating exact expressions for roots of polynomials, which
is not totally trivial (the tricky bit is simplifying roots of a quadratic
equation whose coefficients were given as roots of a previous quadratic
equation) but it's the sort of thing Maple and Mathematica have been doing for
decades.

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anigbrowl
I love geometry and this is a relaly excellent learning tool for it.

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2sk21
Really well done. I will recommend this to my local school district.

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Pica_soO
This is how geometry was ment to be tought- riddles to be solved, on your own,
contemplating, in your own speed, getting harder, step by step.

Great applause to the devs.

~~~
agumonkey
Add a time dimension and you have the right way to teach physics

