7 ms·

Geometric Constructions Game with Straightedge and Compass

112 points by karimf 10y ago

n00b101 10y ago
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_construction https://en.m.wikipedia.org/wiki/Compass-and-straightedge_con... [2] https://en.m.wikipedia.org/wiki/Squaring_the_circle https://en.m.wikipedia.org/wiki/Squaring_the_circle
Pica_soO 10y ago
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 10y ago
  Add a time dimension and you have the right way to teach physics
  - deleted 10y ago
    [deleted]
- signa11 10y ago
  > 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. indeed, there is a very cool/enjoyable book called "geometry in figures" which is almost in the same vein.
mrcactu5 10y ago
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 10y ago
  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.
- syphilis2 10y ago
  I appreciate that the app is free, with the option to pay to unlock all levels without the burden of completing the previous ones. That feels like a very accommodating model and gives users a reason to pay without creating content exclusively for paying users.
deleted 10y ago
[deleted]
wodenokoto 10y ago
This one works on mobile browsers https://sciencevsmagic.net/geo/#0A1.N https://sciencevsmagic.net/geo/#0A1.N
azeirah 10y ago
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 10y ago
  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 10y ago
    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_20161227-011845_zpsesvirsqw.png http://i39.photobucket.com/albums/e179/iamcreasy/Screenshot_...
    - BlackFingolfin 10y ago
      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.
      - 10y ago
aisofteng 10y ago
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 10y ago
  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 10y ago
    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 10y ago
      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!)
Waterluvian 10y ago
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.
anigbrowl 10y ago
I love geometry and this is a relaly excellent learning tool for it.
delhanty 10y ago
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-cubed/references.shtml https://www.plm.automation.siemens.com/en_us/products/open/d... 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 10y ago
  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...
programmarchy 10y ago
This is beautifully done. Can anyone shed some light on the technology used to build the game?
- HiroshiSan 10y ago
  Straight edge and Compass, circa 2000 years ago.
  - amelius 10y ago
    But how do you prove automatically that a given construction, no matter how convoluted, gives the correct answer?
    - waqf 10y ago
      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.
StavrosK 10y ago
This is a fantastic game, I bought it a while ago and heavily recommend it.
oldbuzzard 10y ago
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.
unlogic 10y ago
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 10y ago
  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.
- martininmelb 10y ago
  I have been using this to teach my two daughters (10 and 14) geometry. Would love to find more sites like this that make teaching maths fun. I do, however, give them hints on how to solve the puzzles and explain the theory of how it works.
2sk21 10y ago
Really well done. I will recommend this to my local school district.
deleted 10y ago
[deleted]

112 points by karimf 10y ago

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_construction https://en.m.wikipedia.org/wiki/Compass-and-straightedge_con... [2] https://en.m.wikipedia.org/wiki/Squaring_the_circle https://en.m.wikipedia.org/wiki/Squaring_the_circle

Pica_soO 10y ago

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 10y ago
Add a time dimension and you have the right way to teach physics
- deleted 10y ago
  [deleted]
signa11 10y ago
> 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. indeed, there is a very cool/enjoyable book called "geometry in figures" which is almost in the same vein.

mrcactu5 10y ago

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 10y ago
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.
syphilis2 10y ago
I appreciate that the app is free, with the option to pay to unlock all levels without the burden of completing the previous ones. That feels like a very accommodating model and gives users a reason to pay without creating content exclusively for paying users.

deleted 10y ago

[deleted]

wodenokoto 10y ago

This one works on mobile browsers https://sciencevsmagic.net/geo/#0A1.N https://sciencevsmagic.net/geo/#0A1.N

azeirah 10y ago

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 10y ago
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 10y ago
  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_20161227-011845_zpsesvirsqw.png http://i39.photobucket.com/albums/e179/iamcreasy/Screenshot_...
  - BlackFingolfin 10y ago
    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.
    - 10y ago

aisofteng 10y ago

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 10y ago
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 10y ago
  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 10y ago
    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!)

Waterluvian 10y ago

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.

anigbrowl 10y ago

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

delhanty 10y ago

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-cubed/references.shtml https://www.plm.automation.siemens.com/en_us/products/open/d... 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 10y ago
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...

programmarchy 10y ago

This is beautifully done. Can anyone shed some light on the technology used to build the game?

HiroshiSan 10y ago
Straight edge and Compass, circa 2000 years ago.
- amelius 10y ago
  But how do you prove automatically that a given construction, no matter how convoluted, gives the correct answer?
  - waqf 10y ago
    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.

StavrosK 10y ago

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

oldbuzzard 10y ago

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.

unlogic 10y ago

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 10y ago
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.
martininmelb 10y ago
I have been using this to teach my two daughters (10 and 14) geometry. Would love to find more sites like this that make teaching maths fun. I do, however, give them hints on how to solve the puzzles and explain the theory of how it works.

2sk21 10y ago

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

deleted 10y ago

[deleted]