infinite 45 degree golden ratio thingy series related...

[ebola_virus]

I've been trying to figure this problem out for hours on end and i can't even go on the tinernet to find the answer because its hard to search for. The problem is:
You start off at hte coordinate (4,0). you move up 45 degrees and the distance travelled is now divided by the square root of 2, hence 4/root2 = 2root2. This continious movement of 45 degrees results in a spiral much liekt he one in the golden ratio but just they're straight lines. the question asks what is the coordinate that the infinte amount of lines will end up in?
Does anyone know how to do this? Muc help is appreciatd.

because you move from (4,0) 45 degrees and the distance travelled is contiously divided by square root of 2, you end up landing at (6,2), then (6,4), then (5,5), then (5,4) and thus creating a straight edged spiral... they want to find the coordinate in which it ends up in. HELP!

[HallsofIvy]

??? If each step is of the same length and at the end of each step you turn 45 degrees counter-clockwise, you are just moving around an octagon, not a spiral. After 8 steps, you are right back where you started.

[ebola_virus]

no no the distance travelled is divided by the square root of 2

[uart]

Interesting problem. I suggest you try breaking it down into a sum of geometric series. Treat the x and y motions seperately.

[HallsofIvy]

no no the distance travelled is divided by the square root of 2

You mean at each step, the distance is the previous distance divided by \frac{\sqrt{2}}{2}?

Okay, I thought you just meant that the distance was the x and y components divided by \frac{\sqrt{2}}{2} because of the 45 degree angle!