In relation to geometry and knowing that at some time an Ancient Greek mathematician, who's name, I'm sure complicated, I know not, both created and solved such questions, I have been struggling to find a simple, math backed, answer to this task:

"With only a compass, how can one find a point exactly half way between two other points?"

No ruler...

The first step seems obvious,.. you can make two circles who's center is each point and who's radiuses are the same: the distance from one point to the next. Then you will have two more points: the place where the two circles converge... and work from there. Sure you can draw a quarter million circles by going on like this, and I'm sure that eventually you will find two points that match to be the length of half way between the two original points... but I'm looking for a proof and a direct process.

The name of the mathematician too, if anyone has any idea as to what I'm getting at...

No actually what you do is draw two equal radii circles that overlap like you said. You then join the two points where the circles overlap with a straight line, then you join the two original points with a straight line, where the two straight lines cross is exactly between the tow original points.

I have no idea who this greek mathematician was.

Oh yeah you have to make the original circles with a radius that is a bit more than half way between the two points. So your second two points are off of the central axis by a bit.

That's straight-up Euclidian geometry. Pure vanilla.

Euclid's Elements, Book I, Proposition 10.

--Lest you think I'm some supergeek, note that that came up on an educated Google search. I haven't been memorizing ancient mathematical texts.

That will also give you a perfect 90� angle.

your answer is simple...

...and it's wrong.

No ruler permitted. Hence you are not capable of drawing an exact straight line between the two intersections.

One must find the intersections via circles, and I imagine by the intersection of two.

Here in reality, we have things called straightedges. No one ever said "ruler." The side of your pencil is likely straight. You're probably unfamiliar with "straight" things, being as queer as a line is long.

You come across as a nitpicking geek who wishes to feel smarter than everyone else. I see no other obvious reason for posting a trick questions such as you have.

Thank you thetareactor.
Last night I typed an add on saying that these classical problems are solved using a straightedge. Not a ruler but a straightedge. I didn't post it bwecause I thought that would be too nit picky and redundant as I thought everyone would have known this. Well he just proved me wrong.

For fucks sake, this is the way it's done period. Now can you bisect an angle with a compass and a straightedge?

Note that no one has ever found a way to trisect an angle with these tools.

anyone?

Open the compass so that the two ends are on the points. Note the reading of the compass's scale. Divide that in half, and set the compass to that. Now put one of the compass ends on a point and the other between the two points. That's the midpoint.

...slight over reaction?

In my handicapped English I can see I created a problem by using the word "ruler" instead of "straight-edge", obviously my mistake... a reason to be crucified?

I presented you with a problem that someone presented me, I don't know the answer, I was hoping for another's look at it... nothing more really...

[This message has been edited by cntrdcton0fate (edited 11-01-2002).]

Most compasses don't have scales, particularly the expensive ones. Bisecting an angle is extremely similar to bisecting the line segment, though. Simply draw an arc across the rays of the angle, then use the intersections of the arcs and the angle as the center of two more arcs (of equal radii). The intersection of these arcs inside the angle mark the midpoint, and a line drawn connecting the vertex and this intersection will bisect the angle.

This is junior high geometry, ya know...

contradiction I think the guy that asked you that was confused about the straightedge, you need it or it can't be done.

Theta -->excellent!!

How about another? Someone else suggest one...

I've been thinking, and I can't imagine any way to bisect the distance between two points with just a compass. If it were a line segment, it would be possible, but not just two points...

I made another mistake...

The question was asked by a Greek, it was answered by an Italian... Lorenzo Mascheroni.

And my question ended up being solvable ...

Cool. I'll never ever use that in my life, but cool.

Fucking impressive! Very impressive, I stand corrected. The problem is proving it, It appears to work but I'd like to see a proof. Maybee I'll tackle it if I find a break in my homework, or at least find someone elses proof somewhere. I hate calculus and linear algebra proofs but geometry is something I have a passion for.

I'd like to apologize contra. And I'm bookmarking that site.

quote:

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Originally posted by ThetaReactor:
Most compasses don't have scales, particularly the expensive ones.

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Every compass I've ever used or seen has had scale markings.

Not all i have used had markings, you have most likely has only use the ones with the needle and pencil on an hinge. The ones on a bar hardly ever have have markings.

CTR

I have never seen a professional-grade, screw-adjusted compass with a scale on it. The hinged ones I used in elementary school, yeah. But the scissors didn't have points back then, either.

I'm not an architect or draftsman or anything, so I guess I've never used a professional grade compass. The type or quality of the compass was not, however, specified in the original question.

[This message has been edited by Lysander (edited 11-08-2002).]