A guy in a not well lit room.

Originally posted by sonhouse
A guy finds himself in a room which is actually a long hallway, but he doesn't know the extent. He has with him a calculator, paper and pen, ruler( one foot and metric marks also) and a guitar string, an E string which is 0.01" in diameter (the smallest string on a guitar) and hears a voice from an unknown source saying, you are free to go if you figure out int, he doesn't want to lose his stuff, so he has to do some thinking. What would that be?

There is something inconsistent in the problem

1. He is only to use the 2 meter rule as a chord of the circle

2. He is only to use the diameter of the string for the second measurement

You said the Radius is 1000 meters this cannot be the case.

The ruler is laid down such that it becomes a chord in the circle it is the line segment AB.
A line perpendicular to the chord through the center which bisects AB will be labled QP
The segment PS from P on the ruler to S on the circle along the bisector must be the diameter of the guitar string. Connecting the center Q to either A or B yields the radius R ( R = QA or QB)

so

(QP)^2 +(AB/2)^2 = (QA)^2..........eq1

(QS) = (QP + PS) = (QA)...............eq2

AB/2 = 1 meter
PS = .000254 meter

by substituting eq 2-->1

QP = 1928.5 meters

and the radius QA = 1928.500254 meters, which contradicts your radius of 1000 meters?

If the diameter of the string is used at some other portion of AB used to indirectly measure a distance "c" on the ruler from point A there arent enought independent equations to solve it.

Originally posted by joe shmo
There is something inconsistent in the problem

1. He is only to use the 2 meter rule as a chord of the circle

2. He is only to use the diameter of the string for the second measurement

You said the Radius is 1000 meters this cannot be the case.

The ruler is laid down such that it becomes a chord in the circle it is the line segment AB.
A line ...[text shortened]... distance "c" on the ruler from point A there arent enought independent equations to solve it.

this assumes that the guitar string only fits exactly once under the ruler... unfortunately, the string fits "not quite 2" times (.254mm diameter in a .5mm gap)

Originally posted by Aetherael
this assumes that the guitar string only fits exactly once under the ruler... unfortunately, the string fits "not quite 2" times (.254mm diameter in a .5mm gap)

Im afraid I dont like this, we as the solvers are supposed to figure out the radius of the circle.

Here is directly what was asked"you are free to go if you figure out where you are, or what kind of a place and how big is it you are in."

How does one quantify "just about two times" and be mathematically precise?

Ultimatley after we assume its a circle we are supposed to solve for "how big it is", not approximatley how many times the string fits under the ruler?

The the OP shouldn't have stated the size of the radius ( and in fiact that it was a radius) if he intended this to be solved for the radius???

Am I out of line? lol

Originally posted by joe shmo
Im afraid I dont like this, we as the solvers are supposed to figure out the radius of the circle.

Here is directly what was asked"you are free to go if you figure out where you are, or what kind of a place and how big is it you are in."

How does one quantify "just about two times" and be mathematically precise?

Ultimatley after we assume its ...[text shortened]... was a radius) if he intended this to be solved for the radius???

Am I out of line? lol

I think you are forgetting the guitar string can slide under the resultant chord....

Originally posted by sonhouse
I think you are forgetting the guitar string can slide under the resultant chord....

were we not supposed to solve for the radius? you were the original poster and here is what you said

"you are free to go if you figure out where you are, or what kind of a place and how big is it you are in."

Originally posted by sonhouse
I think you are forgetting the guitar string can slide under the resultant chord....

Im assuming the guitar strings diameter is a perfect fit, which one would have to do to properly solve for the radius.

Tell me how are you going to accurately measure the gap between the floor and the ruler using only the string as your measuring device if it is not an exact fit? If we are looking at this from the persons perspective that trapped the other in the room, that specifc diameter of string has to have significance in the solution of the problem, otherwise why bother measuring with the diameter of the string at all. If we are estimating ho many diameters fit under it why not just estimate with you eyball?

Originally posted by joe shmo
Im assuming the guitar strings diameter is a perfect fit, which one would have to do to properly solve for the radius.

Tell me how are you going to accurately measure the gap between the floor and the ruler using only the string as your measuring device if it is not an exact fit? If we are looking at this from the persons perspective that trapped the ...[text shortened]... all. If we are estimating ho many diameters fit under it why not just estimate with you eyball?

You can get a measurement because the 2 meter straight edge is also a ruler. You can slide the string to where it touches both the wall and the ruler, take a reading of the ruler first on the left side and then on the right side. If it is a circular floor, the readings will be symmetrical, if not it will be some kind of ellipse but in our case it is circular so the readings will be the same distance from each end of the ruler. That also defines the chord length between the strings which can then be used to plug into the chord formula.

But there is something else our poor sod can do.

Originally posted by sonhouse
You can get a measurement because the 2 meter straight edge is also a ruler. You can slide the string to where it touches both the wall and the ruler, take a reading of the ruler first on the left side and then on the right side. If it is a circular floor, the readings will be symmetrical, if not it will be some kind of ellipse but in our case it is circula ...[text shortened]... then be used to plug into the chord formula.

But there is something else our poor sod can do.

No you cant, the guy cant see, its pitch black remember? Here ill show you

Sonhouse "Now he can walk all the way round the rim like that but the walls are so black he cannot see down the hall to notice he is in a curved environment. So what can he do to figure out his situation? He can walk all the way round the thing in a few hours but he doesn't know he has come back to the starting point, he doesn't want to lose his stuff, so he has to do some thinking. What would that be?" (I added the bold to emphasize what you said)

The only thing that would actually help this guy is the knowledge that it is a 2 m stick, and the string has a diameter of .01 in (and of course the mathematics which he would apparently have to do in his head because the pen, paper, and calculator are all usless in the dark as well.)

Originally posted by joe shmo
No you cant, the guy cant see, its pitch black remember? Here ill show you

Sonhouse "Now he can walk all the way round the rim like that but [b]the walls are so black he cannot see down the hall to notice he is in a curved environment. So what can he do to figure out his situation? He can walk all the way round the thing in a few hours but he doesn o do in his head because the pen, paper, and calculator are all usless in the dark as well.)[/b]

He didn't say it was pitch black, he said it was too dark to see the curvature on the floor/ceiling.

Can't he just drop something, so he knows when he is back at his starting point?

Originally posted by Thomaster
Can't he just drop something, so he knows when he is back at his starting point?

Yep, if he thinks he can get back. What if he dares not lose anything? I would try to make a mark that you might get with a tool like the ruler. Besides, he doesn't even know if there is some kind of automatic vacuum cleaner keeping the hall clean and then he would not even have whatever he left behind.

If he did leave a mark and was able to circumnavigate the torus, he could take the ruler, which is now 2 meters long, and carefully measure the whole thing, he would then have the circumference and a simple thing to get the radius. There is another method nobody spoke of before though.

He has got a pen to mark with, doesn't he?

Originally posted by Thomaster
He has got a pen to mark with, doesn't he?

Yes except with a flat black high tech wall, it might not be visible for long, I think you would have to do some recognizable damage to see it when you got back. But you are still missing something.

My physics knowledge fails me.
I wonder if it would help to tie the calculator to the guitar string and dangle the calculator. Would spinning the calculator in circles somehow give any information to help him figure out that he is in motion?
What if he pendulums the calculator in a line with the corridor, will it achieve equal heights at both ends of the swing?
I'm thinking none of this will help, as you can do this happily in a car, but there's cleverer folk than me here.

I'd also check the temperature of the walls. If they're cold, we might be deep underground, or up high. Any moisture on the walls, indicating temperature differential?

Theres no air flow, so that a clue.

I'd try to find the source of the voice and/or engage it in conversation, but I guess that won't work here.

I would shout as loud as possible and see what happens.

I'm not sure I'd move, but if I did I'd mark the walls / floor / ceiling with the pen.

I think I'd also bang on the walls, see what they're made of and how the sound travels.

I'd listen, putting my ear against the wall if its not too cold, in case I can hear anything. Machinery, perhaps.

I'm wondering if theres a way to get a sound wave to travel one way round the walls.
Blocking it from traveling the other way and being able to measure the sound after its been all the way round would be a problem. If you could, using the string to generate a particular note, we could time it with the watch and then calculate the distance.

Thats me out of ideas. I guess I'm doomed.

Phil.

Originally posted by sonhouse
You can get a measurement because the 2 meter straight edge is also a ruler. You can slide the string to where it touches both the wall and the ruler, take a reading of the ruler first on the left side and then on the right side. If it is a circular floor, the readings will be symmetrical, if not it will be some kind of ellipse but in our case it is circula ...[text shortened]... then be used to plug into the chord formula.

But there is something else our poor sod can do.

i'm thinking (from a pragmatic/puzzler point of view) that there's a reason you specifically gave us a guitar string as opposed to just a length of twine or some other malleable measurement device...

so i propose we're looking for a solution involving sound and echo? but how could the lost guy use the ruler to create enough tension to get a useable tone? and even then how would he use it to determine the topology of his surroundings? ... i don't know i'm not much of a physicist 🙂