tricky (not homework) math question

[iwantanewcomputer]

4 guys at each corner of a 10x10 room, all walk towards another guy(but not 2 sets of 2 guys walking towards each other, they all go towards a guy not facing them)

how far do they go before they get to the middle?

I got: slope of one guy's path is dy/dx where dy is the y-difference between him and the guy he is going to. slope of guy he is going towards is -dx/dy cause it's the same path, just flipped around the room. then i gave up.
PIC:

o>..........o
............(down)
...............
^.............
o...........<o



so they spiral around to the middle. in a rotating square as midlander said

 

[xSauronx]

i give up beforehand.

 

[Tylanner]

set it down

go to bed

 

[stan394]

i don't understand.

what direction is each of the 4 guys facing initially?

 

[iwantanewcomputer]

o>..........o
............(down)
...............
^.............
o...........<o



so they spiral around to the middle. in a rotating square as midlander said

 

[Midlander]

I have seen this problem. They all walk clockwise (or counterclockwise, but all in the same rotational direction). The effective square formed by the walkers gets smaller until it collapses.

It has a fairly simple formula, but I don't remember it. I'll see if I have it in a book.

 

[stan394]

woa.. so all 4 guys kind of walked into a spiral into the center? that's pretty cool... i am out of the league for this kind of calculations... my mind doesn't think formulas anymore..

 

[BigPoppa]

Somehow, someway, the answer is the golden ratio.

 

[Midlander]

If that's it, the answer is (1+5^(1/2))/2 times the length of the side.

 

[Schfifty Five]

not sure if I understand what you're asking.

 

[simms]

This isn't thermo. Thermo is like calculate the molar volume assuming polytropic exponents are X, temperature after compression, work required if air is compressed following an isothermic compression.

Q, H, U stuff. Not 4 guys in a room trying to get into the middle... it's not even relative to what you'd learn in a Thermo class.

😕