7 ms·

Straight-edge and Compass Construction Kit

57 points by lygaret 13y ago

siddboots 13y ago
Beautiful! I've had a project like this in the back of my mind for a long time. Give me the ability to define macros/subroutines, and this would be the perfect way to study Elements. Edit: I'm a bit stuck on Circle Pack 4 in 12 moves.
anigbrowl 13y ago
As a member of the Geometric Cult, I love it, but when my mouse is a dot it's almost impossible to see.
- pleion 13y ago
  I've rewritten the custom cursor CSS for the grab hand, hopefully it works now.
derleth 13y ago
http://en.wikipedia.org/wiki/Compass-and-straightedge_construction http://en.wikipedia.org/wiki/Compass-and-straightedge_constr... Things you can't do with this tool: > Squaring the circle: Drawing a square the same area as a given circle. > Doubling the cube: Drawing a cube with twice the volume of a given cube. > Trisecting the angle: Dividing a given angle into three smaller angles all of the same size. Understanding why we can know that these things are absolutely impossible is an important part of understanding what formal systems mean and, therefore, the philosophy of mathematics as a whole. OTOH, getting into arguments with people who claim to have solved those problems is a wonderful introduction to what 'crankery' means in a mathematical context. http://www.nytimes.com/1999/02/09/science/genius-or-gibberish-the-strange-world-of-the-math-crank.html?pagewanted=all&src=pm http://www.nytimes.com/1999/02/09/science/genius-or-gibberis... http://www.crank.net/maths.html http://www.crank.net/maths.html http://rationalwiki.org/wiki/Pseudomathematics http://rationalwiki.org/wiki/Pseudomathematics http://scientopia.org/blogs/goodmath/tag/cantor-crank/ http://scientopia.org/blogs/goodmath/tag/cantor-crank/ http://meta.math.stackexchange.com/questions/136/how-to-deal-with-cranks http://meta.math.stackexchange.com/questions/136/how-to-deal...
- IanCal 13y ago
  > Trisecting the angle: Dividing a given angle into three smaller angles all of the same size. Unless you allow an infinite number of steps. The limit of the series 1/2 - 1/4 + 1/8 - 1/16... is 1/3 so you can get to it by repeatedly bisecting angles. Your paper will look quite messy after an infinite number of steps however.
th0114nd 13y ago
AFAICT, it isn't very intuitive on how to get started. Why am I told how to undo and redo, when I'm not told how to do?
- AjithAntony 13y ago
  If the cursor was larger than a single pixel, it would make it easier to guess. Edit: Tiny cursor in chrome. Firefox looks ok.
  - pleion 13y ago
    Hi, developer here. I'm not sure why it would give you a single pixel cursor. It should use the pointer (when you are over a point) and a grab hand (for when you are over the background). I've probably done something a stupid way somewhere and it's not working in certain cases. What browser/os are you using? EDIT: My chrome is okay (windows 7) but I'll check out a few others. Does the cursor always come out tiny or only in place of one of the pointer/grab hand?
    - bdamm 13y ago
      My chrome is OK too (Mac OS), pointer/hand seems to work. Cool bit of work!
      - 14113 13y ago
        Not ok for me (Arch Linux), in fact, not even a single pixel, no cursor at all!
        pleion 13y ago
        Hmm. Sorry about that. I didn't see it at all during development. I'll do some testing on my Linux Machine when I get home, and can hopefully get it fixed soon.
pechay 13y ago
A compass tells you where north is. A pair of compasses is used to draw circles.
Zakharov 13y ago
I managed to do Circle Pack 7 in one fewer than the minimum: http://sciencevsmagic.net/geo/#0A1.1A0.0L1.1L5.5A1.5L8.0L4.5A4.8L9.5L6.6L12.5A0.17A2.5L11.16A10.5L7.7L24.5L23.25A22.15A8.26A3 http://sciencevsmagic.net/geo/#0A1.1A0.0L1.1L5.5A1.5L8.0L4.5...
- pleion 13y ago
  Well Done! As with most elegant solutions, yours is so simple that I can't believe I didn't see it earlier! The minimum scores are from the simplest solutions I came up with during development, I was waiting for someone to best me.
davnola 13y ago
This is so much fun. Thanks!
thetwiceler 13y ago
Somebody construct a 17-gon!
- thetwiceler 13y ago
  http://sciencevsmagic.net/geo/#0A1.0L1.1L2.2A1.1A2.4L0.7A0.9L10.16A0.0A16.26L25.1L30.30A1.30L55.1A55.55A1.30L87.109A1.55A109.30L128.133L151.151A133.133A151.30L188.30A0.238A0.0A238.30L276.290A1.1A290.373L372.390A1.133A438.471A0.504A0.0A504.471L567.471L595.595A399.399A595.0L710.N.595L739.739L399.739A399.399A739.399L852.852A399.852L676.676L1.1A676.595A739.595L1029.1029A595.1029L622.622A1029.622L1148.1148A622.1148L1212.1212A1148.1212L1273.1273A1212.1273L1330.1330A1273.1330L1385.1385A1330.1385L1442.1442A1385.1442L1506.1506A1442.1506L1573.1573A1506.1573L1644.676A852 http://sciencevsmagic.net/geo/#0A1.0L1.1L2.2A1.1A2.4L0.7A0.9... Ahh! Well you can't say I didn't try. Must have accidentally hit one of the wrong points somewhere in the construction...
tfgg 13y ago
What does "in origin circle" in the challenges mean? I drew a triangle inside a circle and it didn't seem to recognise it.
- DanielStraight 13y ago
  I was confused at first as well. It means a circle with its center one of the original two points you are given. At least I thought so... shouldn't this be circle pack 7 in origin circle? http://sciencevsmagic.net/geo/#0A1.1A0.2A3.4A0.6A1.14A4.5A1.4A2.25A7.7A1.1A6.54A2.26A14.67A6.48A3.56A20.0A87 http://sciencevsmagic.net/geo/#0A1.1A0.2A3.4A0.6A1.14A4.5A1.... Not detected as such.
  - pleion 13y ago
    It actually must be a circle with its centre one of the original two points AND the other point on it's edge (so it's one of the two possible first circles you can draw). Sorry that that wasn't clear enough.
    - jessaustin 13y ago
      Thanks for the update! I've replaced one confusion with another... b^)
jessaustin 13y ago
Possible bug? http://sciencevsmagic.net/geo/#1A0.0A1.0L1.1L4.0L5.3L2.3A6.2A6.3L4.4A18.1A23 http://sciencevsmagic.net/geo/#1A0.0A1.0L1.1L4.0L5.3L2.3A6.2... Didn't update circle pack 3, 9 moves in origin circle for me. This is the first one I've encountered that doesn't seem to work. This is really cool!
epsylon 13y ago
I just can't construct the damn square in 8 steps : I always need at least 9...

57 points by lygaret 13y ago

Beautiful! I've had a project like this in the back of my mind for a long time. Give me the ability to define macros/subroutines, and this would be the perfect way to study Elements. Edit: I'm a bit stuck on Circle Pack 4 in 12 moves.

anigbrowl 13y ago

As a member of the Geometric Cult, I love it, but when my mouse is a dot it's almost impossible to see.

pleion 13y ago
I've rewritten the custom cursor CSS for the grab hand, hopefully it works now.

derleth 13y ago

http://en.wikipedia.org/wiki/Compass-and-straightedge_construction http://en.wikipedia.org/wiki/Compass-and-straightedge_constr... Things you can't do with this tool: > Squaring the circle: Drawing a square the same area as a given circle. > Doubling the cube: Drawing a cube with twice the volume of a given cube. > Trisecting the angle: Dividing a given angle into three smaller angles all of the same size. Understanding why we can know that these things are absolutely impossible is an important part of understanding what formal systems mean and, therefore, the philosophy of mathematics as a whole. OTOH, getting into arguments with people who claim to have solved those problems is a wonderful introduction to what 'crankery' means in a mathematical context. http://www.nytimes.com/1999/02/09/science/genius-or-gibberish-the-strange-world-of-the-math-crank.html?pagewanted=all&src=pm http://www.nytimes.com/1999/02/09/science/genius-or-gibberis... http://www.crank.net/maths.html http://www.crank.net/maths.html http://rationalwiki.org/wiki/Pseudomathematics http://rationalwiki.org/wiki/Pseudomathematics http://scientopia.org/blogs/goodmath/tag/cantor-crank/ http://scientopia.org/blogs/goodmath/tag/cantor-crank/ http://meta.math.stackexchange.com/questions/136/how-to-deal-with-cranks http://meta.math.stackexchange.com/questions/136/how-to-deal...

IanCal 13y ago
> Trisecting the angle: Dividing a given angle into three smaller angles all of the same size. Unless you allow an infinite number of steps. The limit of the series 1/2 - 1/4 + 1/8 - 1/16... is 1/3 so you can get to it by repeatedly bisecting angles. Your paper will look quite messy after an infinite number of steps however.

th0114nd 13y ago

AFAICT, it isn't very intuitive on how to get started. Why am I told how to undo and redo, when I'm not told how to do?

AjithAntony 13y ago
If the cursor was larger than a single pixel, it would make it easier to guess. Edit: Tiny cursor in chrome. Firefox looks ok.
- pleion 13y ago
  Hi, developer here. I'm not sure why it would give you a single pixel cursor. It should use the pointer (when you are over a point) and a grab hand (for when you are over the background). I've probably done something a stupid way somewhere and it's not working in certain cases. What browser/os are you using? EDIT: My chrome is okay (windows 7) but I'll check out a few others. Does the cursor always come out tiny or only in place of one of the pointer/grab hand?
  - bdamm 13y ago
    My chrome is OK too (Mac OS), pointer/hand seems to work. Cool bit of work!
    - 14113 13y ago
      Not ok for me (Arch Linux), in fact, not even a single pixel, no cursor at all!
      - pleion 13y ago
        Hmm. Sorry about that. I didn't see it at all during development. I'll do some testing on my Linux Machine when I get home, and can hopefully get it fixed soon.

pechay 13y ago

A compass tells you where north is. A pair of compasses is used to draw circles.

Zakharov 13y ago

I managed to do Circle Pack 7 in one fewer than the minimum: http://sciencevsmagic.net/geo/#0A1.1A0.0L1.1L5.5A1.5L8.0L4.5A4.8L9.5L6.6L12.5A0.17A2.5L11.16A10.5L7.7L24.5L23.25A22.15A8.26A3 http://sciencevsmagic.net/geo/#0A1.1A0.0L1.1L5.5A1.5L8.0L4.5...

pleion 13y ago
Well Done! As with most elegant solutions, yours is so simple that I can't believe I didn't see it earlier! The minimum scores are from the simplest solutions I came up with during development, I was waiting for someone to best me.

davnola 13y ago

This is so much fun. Thanks!

thetwiceler 13y ago

Somebody construct a 17-gon!

thetwiceler 13y ago
http://sciencevsmagic.net/geo/#0A1.0L1.1L2.2A1.1A2.4L0.7A0.9L10.16A0.0A16.26L25.1L30.30A1.30L55.1A55.55A1.30L87.109A1.55A109.30L128.133L151.151A133.133A151.30L188.30A0.238A0.0A238.30L276.290A1.1A290.373L372.390A1.133A438.471A0.504A0.0A504.471L567.471L595.595A399.399A595.0L710.N.595L739.739L399.739A399.399A739.399L852.852A399.852L676.676L1.1A676.595A739.595L1029.1029A595.1029L622.622A1029.622L1148.1148A622.1148L1212.1212A1148.1212L1273.1273A1212.1273L1330.1330A1273.1330L1385.1385A1330.1385L1442.1442A1385.1442L1506.1506A1442.1506L1573.1573A1506.1573L1644.676A852 http://sciencevsmagic.net/geo/#0A1.0L1.1L2.2A1.1A2.4L0.7A0.9... Ahh! Well you can't say I didn't try. Must have accidentally hit one of the wrong points somewhere in the construction...

tfgg 13y ago

What does "in origin circle" in the challenges mean? I drew a triangle inside a circle and it didn't seem to recognise it.

DanielStraight 13y ago
I was confused at first as well. It means a circle with its center one of the original two points you are given. At least I thought so... shouldn't this be circle pack 7 in origin circle? http://sciencevsmagic.net/geo/#0A1.1A0.2A3.4A0.6A1.14A4.5A1.4A2.25A7.7A1.1A6.54A2.26A14.67A6.48A3.56A20.0A87 http://sciencevsmagic.net/geo/#0A1.1A0.2A3.4A0.6A1.14A4.5A1.... Not detected as such.
- pleion 13y ago
  It actually must be a circle with its centre one of the original two points AND the other point on it's edge (so it's one of the two possible first circles you can draw). Sorry that that wasn't clear enough.
  - jessaustin 13y ago
    Thanks for the update! I've replaced one confusion with another... b^)

jessaustin 13y ago

Possible bug? http://sciencevsmagic.net/geo/#1A0.0A1.0L1.1L4.0L5.3L2.3A6.2A6.3L4.4A18.1A23 http://sciencevsmagic.net/geo/#1A0.0A1.0L1.1L4.0L5.3L2.3A6.2... Didn't update circle pack 3, 9 moves in origin circle for me. This is the first one I've encountered that doesn't seem to work. This is really cool!

epsylon 13y ago

I just can't construct the damn square in 8 steps : I always need at least 9...