Calculating length using a curve

>>8727965
Pretty sure you need the angle of the curve or the radius of the circle as well

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>>8727965
Like so, Anon.

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>>8727965
I have a solution but it makes a few assumptions.
1. You can measure things, like the stick.
2. You have either the ability to measure angles (perhaps via compass), or the ability to construct an orthogonal line (perhaps via compass and straight edge or using something with a 90 degree angle as a stencil)
3. The stick is completely straight
4. Ability to mark the midpoint of the stick. This may be done by folding the stick, if possible, or compass and straight edge, or just being very careful closing in from both sides of the stick and acknowledging there will be error.

Now. lay the stick down so its two edges touch the wall. Construct an orthogonal line from the midpoint of the stick to the wall. Measure the length of this line, call it x. Then by using the right triangle created in the diagram, we have:

[math](\frac{StickLength}{2})^2+(r-x)^2=r^2[/math]

Since only r is unknown, solve for r by completing the square or using the quadratic formula. Once you have r, just use 2*pi*r

http://www.mathopenref.com/chordsintersecting.html

Its a lot simpler than all you guys are making it out to be.

>>8728050
http://www.mathopenref.com/arcradius.html

This part of the link you posted is equivalent to what I posted up here >>8728018

>>8727965
It's pretty easy really
You put the ruler on the wall. Mark where you put it, then roll it around the wall and mark where it ends. Pick the ruler up and start where your new mark is. Continue this process until you get back to where you started. Remember to keep track of how many times you did it.

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>>8727965
I see a way to do it realistically unlike what these other people pointed out, but I haven't figured it out completely.

What you can do is roll the ruler around the wall and mark the start and end locations. Then stick the middle of the ruler in the middle of the two marks you just made. Then you'll want to make two more marks on the wall:

While still holding it in the middle, put your hand at the end of the ruler and move it perpendicular to the length of the ruler until you reach the wall. Make a new mark. Do this to the start of the ruler as well.

What'll happen is you'll have 4 marks. Based on the distance between these marks there's some way you can determine the length of the circle, but I'm trying to figure out what the formula is.

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>>8728107

Don't pretend like you're smarter than everyone else in this thread. You're actually pretty retarded. >>8728018 had it right.

[math]radius=\frac{H}{2}+\frac{W^2}{4H}[/math]

Then use the formula
[math]C=2\pi r[/math] to find the length of the hallway with perfect accuracy, assuming you can measure [math]H[/math] and [math]W[/math] with perfect accuracy.

>>8728147
4H should be 8H, but whatever, formula still applies

It's easy to get a reasonably good result, it would just take a long time as I assume the stick is not very wide, and you need some way of marking everytime you complete a full roll.

>>8728158
You don't *have* to use angles or a ruler. Did you even take a look at the formula I posted? All you need is a way to measure H and W from the pic.

So the guys is very smart and figure out the length of the maze.

"RIght, so I am going to die in this very long maze which I have calculated to be xyz kilometers long, rather than dying in this maze whose length I have not calculated."

WHAT FUCKING GOOD DOES THAT DO HIM?

>>8728172
Well you can argue over practicality all day long. He was a mathematician and so he decided the only thing to do with the rest of his life was calculate the circumfrence.

>>8728180

I will settle for arguing over practicality all day long.

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>>8728172
He thought that he was going down an infinite hallway until he found there was a slight deviation in the hall, suggesting that he was in fact NOT walking in an infinite loop.

He eventually decides to just break through the walls, but that is beside the point.

>>8728147
I think its this formula because it says that he "measured the distance between the curve and the center of the pole"

thanks

pic related is the cover of the novel.

Find the circle which intersects the three points. (0,0), (0,L), (h,.5L). L is the length of the stick and h is the perpendicular distance from the center of the stick to the wall.

What is the name and author of the story? /lit/ wanzs to know.