[Geometry] Draw a square

[Camel]

Using only a compass, unmarked straight edge, and a pencil, draw a square.

You may use short-cuts, as long as you establish that you can do them using the provided tools.

If you can draw a square (relatively easy), a more challenge problem is to draw an equilateral pentagon. Hint: [rot13]Jung vf gur qvfgnapr orgjrra bar iregrk bs gur cragntba naq gur bccbfvgr rqtr[/rot13]

[rabbit]

Haha...this (or a problem like it) is on the GLAT :D

I'd do it, if I could find a compass ><

[BigAznDaddy]

easy use a compass to draw a circle then draw 4 tangent lines on the circle to make a square

[iago]

easy use a compass to draw a circle then draw 4 tangent lines on the circle to make a square

There's no guarantee that 4 tangent lines will make a square.

[Camel]

What iago said, and additionally, you may only use the straight edge to connect two points. A point means a pencil mark - you may randomly place a point anywhere, or you may place a point on any edge, or at any intersection.

[edit] HINT: Start by determining how to draw perpendicular lines; the rest is gravy for the square. The pentagon requires some math.

[Sidoh]

Folding the paper? :S

[Camel]

I don't remember saying you've got paper ;)

[Sidoh]

I don't remember saying you've got paper ;)

Oh, so we're using one of those weird chalkboard compasses? :D

Anyway, I rejected my initial hypothesis.  I realized that we're probably talking about college students, who are clearly too poor to purchase graph paper.
  (Hypothesis #1): http://t.sidoh.org/?GhAIEA==

Here's my real answer.  Maybe I need to be more verbose for it to be valid, though?
  http://t.sidoh.org/?GxEJEQ==

[rabbit]

Your second one doesn't work.  He said you can only use the strait edge to connect two points.

[edit]
My answer, done somewhat haphazardly in Photoshop.  I could do much better on a piece of paper :P
http://www.liquid-server.org/answer.bmp

I started with the bottom, and drew a line horizontally through the center.  After that I drew another circle without changing my comp--radius box on the right, same on the left, starting with a point on the intersect of the first line and the first circle.  Then I drew two vertical lines (one in each side circle) same as the bottom one, and connected the top.  The fourth circle is completely unnecessary, but I didn't realize that until after I'd merged down my layers, so eh.

[Sidoh]

Psh, you stole my answer!  The battery in my camera died before I got the chance to take a picture. :(

Anyway, maybe I'll look at the other one later on.  It's going to be another busy week. :(

[Camel]

Here's my real answer.  Maybe I need to be more verbose for it to be valid, though?
  http://t.sidoh.org/?GxEJEQ==

I said you could use shortcuts if you show that they can be done according to the rules. You may not simply line your straight edge up to the edge of a circle to draw a tangent; you need to determine where the tangent point is, and you need to explain how to draw a perpendicular line. If you can do that, and show how you constructed your perpendicular lines, you will have found one possible solution.  If you did that though, I'd ruin your day by asking you to do the same problem around two given adjacent vertecies, which is something I should have specified at the beginning.

I started with the bottom, and drew a line horizontally through the center.  After that I drew another circle without changing my comp--radius box on the right, same on the left, starting with a point on the intersect of the first line and the first circle.  Then I drew two vertical lines (one in each side circle) same as the bottom one, and connected the top.  The fourth circle is completely unnecessary, but I didn't realize that until after I'd merged down my layers, so eh.

How did you draw a line horizontally through the center? It's possible, you just need to say how you did it.
Everything you did after that broke the rules.

You should try actually doing this on paper, not in photoshop. It's much easier, even if you don't have a compass.

[rabbit]

Nothing about mine was illegal at all.  Your rules say "strait edge, compass, pencil".  And finding the middle is easy.  There's a hole there where the compass needle poked into the paper.

[Camel]

Sorry, I assumed you were starting with two vertecies because the word 'circle' is missing from the first sentence.

You broke the rules when you drew the circles on the left and the right, because you used magic to find their origins. Magic was not one of the things you were given for this task. Maybe your explanation does not match what you did? If you provided a picture for each step, it would be easier to follow.

Also, try to do it when two adjacent vertecies are given.

[Chavo]

I hardly find "using the center of the compass" magic

[Camel]

I hardly find "using the center of the compass" magic

It's not that he used a compass, it's that he magically placed its point in a position that allowed him to draw the circle he wanted.