Euclidea

I have found this game quite addictive. Has anyone else tried it?

The answers are somewhere between cogitation and intuition.

Looks like fun, but it's bedtime right now.

Playing with this again, I'm stuck at 7.1

I know I've solved it before, but can't see it now.

Construct a square whose area equals the sum of the areas of the two given squares and all three have the common angle.

If anyone's interested in just tinkering around with geometry try Geogebra. It's a free app and comes complete with lessons in geometry (on the website).

Reply to Banno I got stuck regularly in this game and never finished it. I did complete that one about 2 years ago and just started it again and I'm stuck in level 2. :cry: BTW, from the same makers xsection! Which I did finish and I'm sure you will like.

I'll have a look if I accidentally remember how 7.1 goes.

Quoting Banno

Playing with this again

All work and no play makes Jack a dull boy. All play and no work makes Jack a grasshopper.

Reply to Benkei The hypotenuse has to be the length of the sum of the two sides, but I can't see how to construct it.

AH, I did it, but in an inelegant way. No L or E goal.

Side length of first square = x
Side length of second square = y
Side length of third square = z

x² + y² = z²

3² + 4² = 5²

Reply to TheMadFool Yep. So construct a right triangle with sides equal to the tow squares; then the hypotenuse is the length of the desired square.

Reply to Banno Are you getting all the stars? I only got all the stars for beta and never got beyond theta level 1.

Quoting Banno

Yep. So construct a right triangle with sides equal to the tow squares; then the hypotenuse is the length of the desired square.

Pythagoras' theorem. :up:

Reply to Benkei Nuh. I'm focusing on getting through them all, but go back to get more starts as well. I've got all stars up to ?7, and a few beyond that. I find the E hard to get.

Reply to Banno I just started again. Already stuck at 1.5. Can't understand how I ever got to theta! :sweat:

Reply to Benkei Spoilers?

Reply to TheMadFool Reply to Banno
I didn't enjoy maths as a child but I do remember finding the idea of Pythagoras' s hypothenuse triangle to be very exciting. I also do like the geometry of circles and lines too, but somehow got on so much better in exploring them in art, rather than in geometry lessons.

Reply to Banno Not for me thanks. I remember that if you don't really understand why a solution works you'll get stuck again at a later point. So if someone explains it, I tend to not really understand why unless I figure it out for myself.

Reply to Benkei I agree.

Reply to Jack Cummins Try it out - see how you go.

Quoting Jack Cummins

I didn't enjoy maths as a child but I do remember finding the idea of Pythagoras' s hypothenuse triangle to be very exciting. I also do like the geometry of circles and lines too, but somehow got on so much better in exploring them in art, rather than in geometry lessons.

Art & Math go a long way back I believe: Proportio Divina.

Jack = 4 letters
Cummins = 7 letters

7/phi = 4.326 = 4

(7 + 4)/phi = 11/phi = 6.799 = 7

The gloves didn't fit O. J. Simpson!

I'm stuck on 8.1

Anyone?

Reply to Banno Take the base line, extend it to the left with the length of the diagonal, extend it to the right with the vertical length, divide that total length by 2 and you have your point.

Meanwhile, still stuck on 1.5 :rofl:

Reply to Benkei Oh, bugger. Half the total length, of course. Simple when you see it.

Solution to 1.5
[hide="Reveal"]Bisect the diagonal from bottom left to top right. intersection with top and base gives your points.[/hide]

Reply to Banno Yeah, I have that solution in my history but I no longer understand why this gives me the correct points. If I ignore 1.5 for now I can solve at least until 2.5 and ongoing.

2.7 with only 1 line is fun. I had to think about that again.

@Banno any hints for 4.11?

Reply to Benkei My delta goes to 10??

Reply to Banno double checked but it really is 4.11. Maybe you need a certain amount of stars.? I have 24 in delta.

Reply to Benkei I'm using the web site - are you on the app?

Reply to Banno Android app.

Reply to Benkei Ah. SO it has extras.

Reply to Banno

This is fun, more distraction from actual work, so thanks for pointing it out. I'm stuck on 2.8 though, I can't get the 3E solution. One element has to be the tangent itself, so that doesn't leave enough elements for the way I was taught to do it (back when we inscribed all this on clay tablets, of course).

If anyone has any hints - without giving the actual answer, I'd appreciate a pointer.

Reply to Isaac You need two circles through the existing circle to get another point for the line which comes about from the intersection of the two circles. The first circle has to be placed correctly. The second circle's placement is dependent on the first.

Reply to Benkei

Got it! Thanks.

Reply to Isaac I have to admit, I've stopped caring about stars for ages. I'm happy if I manage to solve the question. Currently stuck at 8.6

Reply to Benkei That's were I am, too - finding the point from which each side subtends an angle of 120° or 60°...