• Welcome to the new Internet Infidels Discussion Board, formerly Talk Freethought.

Euclidea

Since I'm already stuck trying to get the 7E star on 1.7, I'm going to look at this game as an opportunity to improve my geometry knowledge.
 
I'm stuck on 4.7

My construction: 8L 8E
Target construction: 3L 3E

WTF--there must be some shortcut to finding sqrt(3) that I haven't found.
 
So I've managed to get all of the stars for the first 6 levels. Some of them took me a while though, I'd be off by 1 or 2 steps for a while and have no idea how to simplify the construction.

Makes me wonder how they found the optimal solutions - I'm pretty good at this, and without the label there's no way I'd be confident that my solution is actually the fastest. I suppose it just could have been someone who's crazy good at constructions. Do you think they brute forced it? Crowd sourced? Algebraically solved? Automated theorem provers? :consternation1:

Anyway, onward!

They have another game called Pythagorea that's pretty fun too, if you're interested.
 
beero1000 said:
So I've managed to get all of the stars for the first 6 levels. Some of them took me a while though, I'd be off by 1 or 2 steps for a while and have no idea how to simplify the construction.
Click to expand...

I've given up on getting the L and E stars for every level before I progress--I'm going to revisit them later once I figure out how to solve the puzzles in a systematic way rather than relying so heavily on guesswork.

It is some consolation that you have not all-starred al 13 sets.
beero1000 said:
Do you think they brute forced it? Crowd sourced? Algebraically solved? Automated theorem provers? :consternation1:
Click to expand...

Yes.

beero1000 said:
They have another game called Pythagorea that's pretty fun too, if you're interested.
Click to expand...

Maybe after Euclidea has finished destroying my life.
 
bigfield said:
I've given up on getting the L and E stars for every level before I progress--I'm going to revisit them later once I figure out how to solve the puzzles in a systematic way rather than relying so heavily on guesswork.

It is some consolation that you have not all-starred al 13 sets.
beero1000 said:
Do you think they brute forced it? Crowd sourced? Algebraically solved? Automated theorem provers? :consternation1:
Click to expand...

Yes.

beero1000 said:
They have another game called Pythagorea that's pretty fun too, if you're interested.
Click to expand...

Maybe after Euclidea has finished destroying my life.
Click to expand...

:D

There are worse rabbit holes to fall intro...
 
I'm not solving everything... i cant even understand how some of the solution works after I!ve seen them... possible spoiler:

how does these 90 degree angles constructed by three circles and a line work? (2.8)


They are like magic to me...
 
Juma said:
I'm not solving everything... i cant even understand how some of the solution works after I!ve seen them... possible spoiler:

how does these 90 degree angles constructed by three circles and a line work? (2.8)


They are like magic to me...
Click to expand...

My construction was based on this 4L 4E one (which is a consequence of Thales' theorem):



geogebra-export (4).png
Once you have that, there's a bunch of untapped symmetry going on. In particular, D is a homothetic center of circles about A and B, so we get lots of nice intersection properties. That means that we can draw a circle centered at B to where the lines from D cross the circle instead of the two diameters, which gets us 2L 3E.

 
bah... did the rhombus in 1E less than it wanted and it wouldn't give credit. It was fun for a few minutes, though.
 
beero1000 said:
Malintent said:
bah... did the rhombus in 1E less than it wanted and it wouldn't give credit. It was fun for a few minutes, though.
Click to expand...

Mind sharing that construction?
Click to expand...

Can't share a pic, but it was constructed with two circles only... center on one corner, radius to the other corner on the short end, then the other circle is mirror image of that circle. The intersection of the circles with the rectangle are the corners of the rhombus. It is 4L 4E, including the lines.
 
Malintent said:
beero1000 said:
Mind sharing that construction?
Click to expand...

Can't share a pic, but it was constructed with two circles only... center on one corner, radius to the other corner on the short end, then the other circle is mirror image of that circle. The intersection of the circles with the rectangle are the corners of the rhombus. It is 4L 4E, including the lines.
Click to expand...

That's not a rhombus, just a parallelogram.
 
Malintent said:
bah... did the rhombus in 1E less than it wanted and it wouldn't give credit. It was fun for a few minutes, though.
Click to expand...

I tried several things but couldn't get it to accept anything. Not sure if I didn't quite have it, or if something else was causing it not to give me credit.
 
Shake said:
Malintent said:
bah... did the rhombus in 1E less than it wanted and it wouldn't give credit. It was fun for a few minutes, though.
Click to expand...

I tried several things but couldn't get it to accept anything. Not sure if I didn't quite have it, or if something else was causing it not to give me credit.
Click to expand...

The only solution it will accept is:


use the midpoint tool from the bottom left corner to the top right corner. Then, draw a line from the bottom left corner, to the intersection at the top. Finally, draw a line from the top right corner to the intersection at the bottom.



This will guarantee all sides of the parallelogram are equal, thus a rhombus (as beero pointed out).
 
Shake said:
Malintent said:
bah... did the rhombus in 1E less than it wanted and it wouldn't give credit. It was fun for a few minutes, though.
Click to expand...

I tried several things but couldn't get it to accept anything. Not sure if I didn't quite have it, or if something else was causing it not to give me credit.
Click to expand...

Image:


Uses the fact that the diagonals of a rhombus are perpendicular bisectors.

Screenshot.png

 
You must log in or register to reply here.
Back
Top Bottom