Infinite 45 degree golden ratio thingy series related

AI Thread Summary
The discussion revolves around a mathematical problem involving movement from the coordinate (4,0) at a 45-degree angle, with each subsequent distance divided by the square root of 2, leading to a spiral-like path. Participants are trying to determine the final coordinate after an infinite number of steps, with some confusion about the nature of the movement. It is clarified that the movement creates a straight-edged spiral rather than a perfect spiral, and after eight steps, one returns to the starting point. Suggestions include breaking the problem down into a geometric series to analyze the x and y motions separately. The conversation highlights the complexity of the problem and the need for precise understanding of the distance calculations involved.
ebola_virus
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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 traveled 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 infinite 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 traveled 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!
 

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? 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.
 
no no the distance traveled is divided by the square root of 2
 
Interesting problem. I suggest you try breaking it down into a sum of geometric series. Treat the x and y motions seperately.
 
ebola_virus said:
no no the distance traveled 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!
 

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