[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

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?

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
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.

[rabbit]

Yeah.  Exactly.  I placed the marking tip down first and then put the anchor pin down.  I've done stuff like that before...

[Camel]

Yeah.  Exactly.  I placed the marking tip down first and then put the anchor pin down.  I've done stuff like that before...

Yes, but you have to place it on a point. You can't just plop it down anywhere and assume that it will help you draw a square.

[Chavo]

Yea, but he explained how it was a valid assumption.  Would you still find his answer as bogus if he had actually used the center hole of a compass instead of using the center of the circle that the program found?

[Camel]

You didn't explain how you found the origin of the circles on the left and right sides.

Hint: the only way you can find those points requires having already found the entire square, which is why I'm not going to re-read what you wrote.

[Ender]

Yrzzn: Qenjvat n Crecraqvphyne.

Jr pna pbafgehpg n crecraqvphyne gb n yvar Y ol znexvat gjb cbvagf ba gur yvar naq qenjvat pvepyrf nebhaq gurz (hfvat gur gjb cbvagf nf gur pragref) jvgu bhe pbzcnff. Gura znex gur vagrefrpgvbaf bs gur gjb pvepyrf, yrg'f pnyy gurz N naq O. Qenj n yvar pbaarpgvat N naq O. Gur yvar NO jvyy or crecraqvphyne gb Y.

Pbafgehpgvba:

Qenj n yvar Y naq qenj gur crecraqvphyne gb vg Y' (sbe pbairavrapr, cynpr Y' ng gur yrsg raqcbvag bs Y). Pnyy gur cbvag jurer gurl vagrefrpg B. Pragre gur pbzcnff ng B naq qenj n pvepyr hfvat gur pbzcnff bs fbzr enqvhf e (sebz uraprsbegu, hfr gur fnzr enqvhf e sbe nyy nepf qenja jvgu gur pbzcnff) Znex gur cbvagf jurer gur erfhygvat nep vagrefrpgf Y naq Y', yrg'f pnyy gurz Z naq A. Abj pragre gur pbzcnff ng obgu Z naq qenj naq nep naq nsgrejneqf pragre gur pbzcnff ng A naq qenj naq nep. Znex gur vagrefrpgvba bs gurfr gjb nepf C. Jr abj unir sbhe iregvprf bs n fdhner, naq jr pna svyy va gur fvqrf jvgu bhe fgenvtugrqtr.

EDIT: rot13d

[Camel]

'grats Ender

I got bored at work today, so I drew out the solution in mspaint. Spoiler.

Who wants to take on the pentagon?

[rabbit]

You didn't explain how you found the origin of the circles on the left and right sides.

Hint: the only way you can find those points requires having already found the entire square, which is why I'm not going to re-read what you wrote.

Wrong

There's a hole there where the compass needle poked into the paper.

A strait line from one side of the circle to the other through its center is easy to do.  Doing it 4 times is easy.  The only thing that's a little tricky is making a square on the first try (hence an eraser).  Stop trying to say what I did was impossible because you didn't think of so simple an answer in your hours of toiling.

[Camel]

For the third time I'll say it: you did not explain how you found the center of the left and right circles. If you didn't break the rules, then your original explanation doesn't match what you did. Don't take it so personally.

In any event, the goal is to draw a square from two given adjacent vertecies, which your approach doesn't use.

[Ender]

Meh, the pentagon looks like a fun problem but I have 39 theorems to prove by Thursday (assigned today). Maybe I'll try it later.

EDIT: I checked out the sheet and it's not 39 theorems, the numbering includes exercises and definitions. Still, I have a lot of work to do, so I probably won't be able to get around to doing these problems anytime soon.

[rabbit]

For the third time I'll say it: you did not explain how you found the center of the left and right circles. If you didn't break the rules, then your original explanation doesn't match what you did. Don't take it so personally.

In any event, the goal is to draw a square from two given adjacent vertecies, which your approach doesn't use.

You seriously are retarded.  I DID say how I found the center of the other circles.  God damn.

[Camel]

I just re-read it, and I still don't see it.

Maybe you could re-write your explanation so it's possible to understand.

[Sidoh]

rabbit, calm down man.  Even if you are right, there's a more rational way to deal with it.

[rabbit]

After that I drew another circle [...] starting with a point on the intersect of the first line and the first circle.

I placed the marking tip down first and then put the anchor pin down.

That should have been clear enough

[iago]

After that I drew another circle [...] starting with a point on the intersect of the first line and the first circle.

I placed the marking tip down first and then put the anchor pin down.

That should have been clear enough

I personally don't understand your solution and haven't been able to replicate it on paper. Can you maybe give a step-by-step way of doing it? That should help everybody.

[Ender]

I don't understand your answer either I'm not saying I think you're wrong, I'm just saying I don't understand it.

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.

Let's start out with this:

"...After that I drew another circle without changing my comp"

How can you draw another circle without changing the position of the compass? A compass at a fixed position with a fixed radius can only draw one circle. Just wondering, when you say compass, you mean the apparatus with two hinged legs attached to each other at an end, shown here, http://acsweb.fmarion.edu/math/coursedescriptions/euclidpicture320x240.jpg, right?

Also, there are no labels for any lines, intersections, origins/circles, etc., which makes it hard to understand =(

[rabbit]

I meant changing the width of the compass, ie: not closing etc...

Anyway, here is a slightly different answer, animated so you losers can see what's going on.  As said before, the center of each circle is known because of the hole in the paper:



The red lines are a little off because of Photoshop's weird snapping rules, and I didn't feel like screwing with them.  Live with it.

[Sidoh]

How do you find a line perpendicular to the first one you drew?

[rabbit]

By turning the strait edge and erasing when I made a mistake.  You can't see it (since it's Photoshop), but there are a bunch of erased lines.  Also, if you do make a mistake, you won't get a square in the end (the top right corner won't be a....corner), so you know you messed up and can go fix it.  You all seem to have a thing against erasers.  Get over it.

[Sidoh]

I mean in the circle.  When you make a circle, how do you find a diameter perpendicular to the first one you drew?

[iago]

By turning the strait edge and erasing when I made a mistake.  You can't see it (since it's Photoshop), but there are a bunch of erased lines.  Also, if you do make a mistake, you won't get a square in the end (the top right corner won't be a....corner), so you know you messed up and can go fix it.  You all seem to have a thing against erasers.  Get over it.

The problem with that is, you can draw a whole square like that. Draw a straight line, |. Then draw a perpendicular line to it, erasing and fixing it until it's exactly perpendicular. Draw it: |-. Draw a diagonal between the right of the second line and bottom of the first. Draw a perpendicular to that, which forms an "X" between the two lines. Then draw the other two lines as perpendiculars (erasing till they're right) such that they meet at the bottom-right leg of the X. Done, a perfect square with only a ruler.

The idea behind these questions, however, is to find a flawless solution that will guarantee a perfect square with reasonable accuracy, not one that looks to the naked eye like one.

[Camel]

I think a better way of explaining it is to say that the square is anchored to the points. If you were to drag the points around, the square would still be a square.

So, pentagon anyone?