[Math] A rope around the equator...

A rope is tied around the equator so that it is in contact along the whole equator. (Assume that the earth is a perfectly spherical shape). You then cut the rope at some point, and add one extra meter of rope, stretching it again so that it is a perfect circle.

Could you fit a small dog through the earth and the string? (Without deforming/pulling the string?).

If so, how far off the ground would the string be?

 

I was about to say hell no... Then I did some more calculations and yes... Yes you could fit a small dog. Now that I think about what pi means... It makes perfect sense. Oh and how far off the ground depends on how you align the new circle with the earth.

 

Hehe, I love these types of problems. And when I mean lift it up uniformly, I mean that you have to center it at the same place the earth is centered. (concentric circles). Or I could just ask for the difference in the radii

(Don't post it yet, but I'm guessing you found the exact height that it's lifted off the earth?)

 

It would just be (1/pi)/2 right? (Now I'm just making shit up).

 

Yeah, (1/2pi).

I think that's right, I'm just too tired at the moment to actually do it out again, but that sounds familiar.

 

i dont understand how u can actually do it?

 

I'm going to leave this up for a few more hours, and if I get enough feedback I'll post a mathematical solution

 

How small is a 'small dog'?

 

A small dog could be as small as a large rat or squirrel.

 

Didn't understand the question until I read the comments, strange concept. Pretty sure you could fit a dog in though after some rough calcs

 

Code:

C = 2pi*r
C + 1 = 2pi(r+n)
2pi*r + 1 = 2pi*r + 2pi*n
1 = 2pi*n
n = 1/(2pi)

yay

so for every x meters added to the rope's length, its radius will grow by x/(2pi) meters.

 

*bingo* way to ruin the fun though :/

 

Well, then I figured it out. I got a gap of 1/(2*2*pi), and then wondered if the 7-or-so centimeters is enough to fit a dog under.

Here's something that was in my maths exam a few moons back:
The lengths of the catheti of a right triangle are 5 and 12. What is the area of the largest possible rectangle drawn inside the triangle, when one of the rectangle's sides is on the triangle's hypotenuse?