0866: "Compass and Straightedge"

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BrianB
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Re: 0866: "Compass and Straightedge"

Postby BrianB » Mon Feb 28, 2011 4:14 pm UTC

tudza wrote:Squarely? Can you square a circle with just a compass and a straight edge? I forget.


Yes. Yes you can.

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Re: 0866: "Compass and Straightedge"

Postby Evadman » Mon Feb 28, 2011 4:15 pm UTC

I has a sad :(

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Re: 0866: "Compass and Straightedge"

Postby maewert » Mon Feb 28, 2011 4:21 pm UTC

He does look so sad. :cry: I'll be your friend, if you don't mind me bringing my slide rule.

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Re: 0866: "Compass and Straightedge"

Postby ImTestingSleeping » Mon Feb 28, 2011 4:24 pm UTC

http://www.smbc-comics.com/index.php?db=comics&id=1887#comic

I see today's comic going another way entirely...

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Re: 0866: "Compass and Straightedge"

Postby Loki161 » Mon Feb 28, 2011 4:28 pm UTC

tudza wrote:
phlip wrote:
I think a circle-and-straight-line stick figure would be squarely in the uncanny valley for an xkcd character...


Squarely? Can you square a circle with just a compass and a straight edge? I forget.


http://myyn.org/m/article/compass-and-straightedge-construction-of-square/

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Re: 0866: "Compass and Straightedge"

Postby cream wobbly » Mon Feb 28, 2011 4:31 pm UTC

glasnt wrote:Is "straightedge" the Basically Decent term for "ruler" now?

A rule is neither necessarily straight, nor an edge. In the geometric sense, a "straightedge" is unmarked.

OED, 1st ed. Rule : V. 17.: A graduated strip of metal or wood (marked with feet, inches, etc.) used for measuring length, esp. by carpenters and masons.
Last edited by cream wobbly on Mon Feb 28, 2011 5:33 pm UTC, edited 1 time in total.

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Re: 0866: "Compass and Straightedge"

Postby BioTube » Mon Feb 28, 2011 5:20 pm UTC

BrianB wrote:
tudza wrote:Squarely? Can you square a circle with just a compass and a straight edge? I forget.


Yes. Yes you can.
This just proves you didn't even bother to look up Lindemann.
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Re: 0866: "Compass and Straightedge"

Postby KShrike » Mon Feb 28, 2011 6:03 pm UTC

If someone was a good enough programmer to finally give AI a conscience.......

Nope, I can't talk about something so stupid.
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Re: 0866: "Compass and Straightedge"

Postby Neepmeep » Mon Feb 28, 2011 6:24 pm UTC

You may not be able to make them, but you can still attract them.

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Re: 0866: "Compass and Straightedge"

Postby TurtleMidget » Mon Feb 28, 2011 7:32 pm UTC

Exüberance wrote:This comic seems kind of...

Image

...familiar.

This was my first thought.
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Re: 0866: "Compass and Straightedge"

Postby esmith » Mon Feb 28, 2011 7:54 pm UTC

"They're my friends. I made them." -- Sebastian, _Blade Runner_

Granted, he must have used more than just a compass and straightedge.

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Re: 0866: "Compass and Straightedge"

Postby rdm_box » Mon Feb 28, 2011 8:23 pm UTC

Wow! I'm a total maths nerd and I have like, no friends! Randall GOOMH!
Yes, maths with an s. Suck it bitches.
Regards,

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Re: 0866: "Compass and Straightedge"

Postby BrianB » Mon Feb 28, 2011 8:58 pm UTC

BioTube wrote:
BrianB wrote:
tudza wrote:Squarely? Can you square a circle with just a compass and a straight edge? I forget.


Yes. Yes you can.
This just proves you didn't even bother to look up Lindemann.


Oh, I'm sorry. Did tudza mean "perfectly" square a circle (i.e. to absolute precision)? Or did tudza mean realistically. It can be done by approximation to between 4 and 8 decimal places of pi.

But since the width of your pencil gets wider the more you draw along the straight-edge, any construction is really only a good approximation.

And that, my friend, is the difference between an engineer and a physicist.

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Re: 0866: "Compass and Straightedge"

Postby Sprocket » Mon Feb 28, 2011 9:08 pm UTC

If you're a stick figure, a compass and a straight edge is how you make ALL your friends!
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Re: 0866: "Compass and Straightedge"

Postby Faranya » Mon Feb 28, 2011 9:11 pm UTC

ImTestingSleeping wrote:A ruler which constructs friends? A ruler to rule them all?


No, it can't construct friends.

It can however find them.
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Re: 0866: "Compass and Straightedge"

Postby SpringLoaded12 » Mon Feb 28, 2011 11:12 pm UTC

Yes, it would seem that geometry does not win friends; rather, social interaction wins friends. But there's plenty of room for both! I do derivatives in my head (not geometry but you get the point) and sit at a packed lunch table.

Randomizer wrote:I lot of people seem to think that Randall is reading their minds. But considering there's so many, the real question is, who's reading whose?

Correct grammar.
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Faranya wrote:
ImTestingSleeping wrote:A ruler which constructs friends? A ruler to rule them all?


No, it can't construct friends.

It can however find them.

...and in the darkness bind them?
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Re: 0866: "Compass and Straightedge"

Postby Mooseeeeey » Mon Feb 28, 2011 11:36 pm UTC

When I'm bored in English class, I break out some supplies and make a small village of stick figures. As close to friends as I've had in a while :(

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Re: 0866: "Compass and Straightedge"

Postby phlip » Tue Mar 01, 2011 12:12 am UTC

SpringLoaded12 wrote:...and in the darkness bind them?

If you have the right kind of friends, and they're in to that sort of thing...

Code: Select all

enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};
void ┻━┻︵​╰(ಠ_ಠ ⚠) {exit((int)⚠);}
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Re: 0866: "Compass and Straightedge"

Postby Fixblor » Tue Mar 01, 2011 1:02 am UTC

Note: The artist clearly does not use a straight-edge or compass when drawing these comics ... for those who were confused on that 'point'.

POINT!
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Re: 0866: "Compass and Straightedge"

Postby rho421 » Tue Mar 01, 2011 1:54 am UTC

Well, this is sufficiently depressing for the whole week...a bit like this...

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Re: 0866: "Compass and Straightedge"

Postby muntoo » Tue Mar 01, 2011 2:43 am UTC

asliceofpi wrote:
ImTestingSleeping wrote:A ruler which constructs friends? A ruler to rule them all?

As long as you have a compass, you could always make one ring to rule them all.


... With a hammer to keep their heads ringing.

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Re: 0866: "Compass and Straightedge"

Postby drixoman » Tue Mar 01, 2011 3:27 am UTC

Lunar Savage wrote:
tehol wrote:
drixoman wrote:This will feel very dumb...I don't quite get the joke here...is "friend" suppose to mean something?


I found it funny because I didn't expect the ending. It starts with the lead in "I learned in high school what Geometers learned long ago", and I think "ok, cool! so the next part is going to be some kind of joke specific to the geometry field" (in the way that this comic is a specific joke about computer code).

Right up until the word "friends", I expect this. At the word friends, I am shocked, and thus I laugh. I think it's the same construction as this comic/joke, however I didn't like that one. I don't know why.

If there is some kind of play on words with "friend", then it went over my head.


I believe the joke is a metaphorical way of saying that if you are a straightedge kind of person with a moral compass, you will have no friends because no one wants to hang out with the tools.



Huh...so that's that...but hows it related to Lindmann?

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Re: 0866: "Compass and Straightedge"

Postby CalculatingGod » Tue Mar 01, 2011 4:41 am UTC

You can't make a friend with only a compass and straight edge.

You need a pen as well. :)

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Re: 0866: "Compass and Straightedge"

Postby abehrens » Tue Mar 01, 2011 5:03 am UTC

What a birthday party! The cake was superb... and the pie was truly transcendental.

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Re: 0866: "Compass and Straightedge"

Postby alreadytaken4536 » Tue Mar 01, 2011 5:28 am UTC

Image

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Re: 0866: "Compass and Straightedge"

Postby Kisama » Tue Mar 01, 2011 6:18 am UTC

SpringLoaded12 wrote:
Randomizer wrote:A lot of people seem to think that Randall is reading their minds but, considering there are so many, the real question is, "Who's reading whose?"

Correct grammar.
If I correct enough grammar on the internet maybe someone will love me.
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Re: 0866: "Compass and Straightedge"

Postby adavies42 » Tue Mar 01, 2011 6:36 am UTC

tehol wrote:
drixoman wrote:This will feel very dumb...I don't quite get the joke here...is "friend" suppose to mean something?


I found it funny because I didn't expect the ending. It starts with the lead in "I learned in high school what Geometers learned long ago", and I think "ok, cool! so the next part is going to be some kind of joke specific to the geometry field" (in the way that this comic is a specific joke about computer code).

Right up until the word "friends", I expect this. At the word friends, I am shocked, and thus I laugh. I think it's the same construction as this comic/joke, however I didn't like that one. I don't know why.

If there is some kind of play on words with "friend", then it went over my head.


the play is on "construct", which has a specific technical meaning in classical geometry: http://en.wikipedia.org/wiki/Compass_an ... structions

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Re: 0866: "Compass and Straightedge"

Postby ijuin » Tue Mar 01, 2011 6:41 am UTC

BrianB wrote:
tudza wrote:Squarely? Can you square a circle with just a compass and a straight edge? I forget.


Yes. Yes you can.


It depends on what meaning of "squaring the circle" you are referring to. If you mean the classically-impossible task of creating a square with the same area (L * W) as the circle (pi * r^2), it can not be done due to the transcendental nature of pi--pi would have to be a rational or irrational number to allow this.

However, if you mean "creating a square whose side length is equal to the diameter of the circle", then yes it is possible.

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Re: 0866: "Compass and Straightedge"

Postby squareroot » Tue Mar 01, 2011 8:21 am UTC

ijuin wrote:pi would have to be a rational or irrational number to allow this.

Why, how convenient, it is!
What a shame it's not algebraic too. :(
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Re: 0866: "Compass and Straightedge"

Postby BrianB » Tue Mar 01, 2011 2:04 pm UTC

ijuin wrote:It depends on what meaning of "squaring the circle" you are referring to. If you mean the classically-impossible task of creating a square with the same area (L * W) as the circle (pi * r^2), it can not be done due to the transcendental nature of pi--pi would have to be a rational or irrational number to allow this.

However, if you mean "creating a square whose side length is equal to the diameter of the circle", then yes it is possible.


Read my reply to tudzu. It can be done with reasonable accuracy. I'll concede that "theoretically" it can't be done. But I don't live in a theoretical world. I live in the world where engineers come up with practical approximations and do things like put a man on the moon and develop "smart phones" - which, by the way, theoretically aren't even possible because a perfect square-wave electrical signal does not exist, except on paper.

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Re: 0866: "Compass and Straightedge"

Postby SirMustapha » Tue Mar 01, 2011 2:46 pm UTC

BrianB wrote:I'll concede that "theoretically" it can't be done. But I don't live in a theoretical world. I live in the world where engineers come up with practical approximations and do things like put a man on the moon and develop "smart phones" - which, by the way, theoretically aren't even possible because a perfect square-wave electrical signal does not exist, except on paper.


All theory is evil and should be banished from the world.

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Re: 0866: "Compass and Straightedge"

Postby failix » Tue Mar 01, 2011 3:38 pm UTC

Read my reply to tudzu. It can be done with reasonable accuracy.


Don't get me wrong, I am by no means in a position to lecture an engineer in the field of Geometry (or mathematics in general for that matter); but I am genuinely curious as to how you could square the circle "with reasonable accuracy" with only a compass and a straightedge. Just to be clear: You have no point of reference on where to start tracing the sides of your square, nor do you have a point of reference for their length; which should be radius*sqrt(pi) since the area of the square has to equal (with reasonable accuracy) the area of your circle. So I challenge you to make a video and upload it on youtube to prove your assertion, or at least provide a detailed explanation of the steps you would take.... it can't be done :-)

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Re: 0866: "Compass and Straightedge"

Postby BrianB » Tue Mar 01, 2011 8:50 pm UTC

failix wrote: So I challenge you to make a video and upload it on youtube to prove your assertion, or at least provide a detailed explanation of the steps you would take.... it can't be done :-)


Hobson, Ernest William (1913). Squaring the Circle: A History of the Problem, Cambridge University Press. Reprinted by Merchant Books in 2007

http://www.archive.org/details/squaring ... l000963mbp

Example accurate to 8 places shown here: http://www.song-of-songs.net/Squaring_the_Circle.html

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Re: 0866: "Compass and Straightedge"

Postby phlip » Wed Mar 02, 2011 12:14 am UTC

failix wrote:Don't get me wrong, I am by no means in a position to lecture an engineer in the field of Geometry (or mathematics in general for that matter); but I am genuinely curious as to how you could square the circle "with reasonable accuracy" with only a compass and a straightedge. Just to be clear: You have no point of reference on where to start tracing the sides of your square, nor do you have a point of reference for their length; which should be radius*sqrt(pi) since the area of the square has to equal (with reasonable accuracy) the area of your circle. So I challenge you to make a video and upload it on youtube to prove your assertion, or at least provide a detailed explanation of the steps you would take.... it can't be done :-)

Let p/q be a rational approximation for sqrt(pi)... note that as the rationals are dense, this can be made arbitrarily close, though not exact. Draw a long line, and arbitrarily mark a point as A. Using the compass set to the radius of the circle (r) mark out a point r along the line A, call that point B. Repeat until you've marked out p consecutive intervals of that length along the line... mark the end of this length (which is p*r away from A) as C. Draw a perpendicular to the line at C, and mark off q intervals of length R along the line, to mark point D (which is q*r away from C). Connect A and D with the straightedge. draw a perpendicular from B, find the point where that intersects with AD and call it E. The length of E will be r*p/q, an approximation which can be arbitrarily close to r*sqrt(pi). Draw a square using your preferred method based on this size.

Of course, more specific approximations can have more compact ways of doing it, but this is more general, and can be arbitrarily close.

Code: Select all

enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};
void ┻━┻︵​╰(ಠ_ಠ ⚠) {exit((int)⚠);}
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Re: 0866: "Compass and Straightedge"

Postby Daniel Hawks » Wed Mar 02, 2011 1:32 am UTC

I find it fascinating how stick figures can evoke so much emotion. I literally went "Aww...poor guy." when I read the comic. Good job Randall.

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Re: 0866: "Compass and Straightedge"

Postby [Ee]xpression[s]? » Wed Mar 02, 2011 2:03 am UTC

BrianB wrote:
BioTube wrote:
BrianB wrote:
tudza wrote:Squarely? Can you square a circle with just a compass and a straight edge? I forget.


Yes. Yes you can.
This just proves you didn't even bother to look up Lindemann.


Oh, I'm sorry. Did tudza mean "perfectly" square a circle (i.e. to absolute precision)? Or did tudza mean realistically. It can be done by approximation to between 4 and 8 decimal places of pi.

But since the width of your pencil gets wider the more you draw along the straight-edge, any construction is really only a good approximation.

And that, my friend, is the difference between an engineer and a physicist.


Actually, the physicist would assume a frictionless vacuum whereon the pencil would not be able to make a mark and wherein the geometer would die a very quick death.

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Re: 0866: "Compass and Straightedge"

Postby Faranya » Wed Mar 02, 2011 4:30 am UTC

phlip wrote:
SpringLoaded12 wrote:...and in the darkness bind them?

If you have the right kind of friends, and they're in to that sort of thing...

And only where the shadows lie.
Image

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Re: 0866: "Compass and Straightedge"

Postby bobloblaw » Wed Mar 02, 2011 5:02 am UTC

Its a mathematical fact that you can make more constructions using origami than you can with a ruler and straight edge.... also you can make origami party hats! http://www.youtube.com/watch?v=SyvqRadUB0E

P.S. don't invite the creator of that vid if you want other people to show up at your party

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Re: 0866: "Compass and Straightedge"

Postby failix » Wed Mar 02, 2011 3:04 pm UTC

phlip wrote:Repeat until you've marked out p consecutive intervals of that length along the line


How am I supposed to know what p is? Thanks for your reply, but I'm sorry to say I'm unable to understand your instructions...

BrianB wrote:Example accurate to 8 places shown here: http://www.song-of-songs.net/Squaring_the_Circle.html


Huh, I stand corrected... and in awe... apart from all the weird pseudo-philosophical stuff, that page is pretty interesting. Thanks.

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Re: 0866: "Compass and Straightedge"

Postby ijuin » Wed Mar 02, 2011 5:07 pm UTC

squareroot wrote:
ijuin wrote:pi would have to be a rational or irrational number to allow this.

Why, how convenient, it is!
What a shame it's not algebraic too. :(

Oh, pardon, I was under the impression that irrational numbers are non-rational and algebraic while transcendental numbers are non-rational and non-algebraic, thus precluding transcendental numbers from being a subset of irrational numbers. The definition that you are using seems to be that irrational numbers are all real numbers that are not rational numbers.

Anyway, to clarify my earlier post, I meant that pi would have to be algebraic in order to allow an exact solution for constructing a square with exactly the same area as a given circle.


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