Infinite 45 degree golden ratio thingy series related

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Discussion Overview

The discussion revolves around a geometric problem involving movement from a starting coordinate (4,0) at a 45-degree angle, with each subsequent movement's distance being divided by the square root of 2. Participants explore the nature of the resulting path, questioning whether it forms a spiral or returns to the starting point.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant describes a movement pattern that suggests a spiral formation, questioning the final coordinate after infinite movements.
  • Another participant argues that if the movement is consistent in distance and direction, it would result in a return to the starting point, resembling an octagon rather than a spiral.
  • Clarification is sought regarding whether the distance at each step is divided by \(\frac{\sqrt{2}}{2}\), indicating a potential misunderstanding of the movement mechanics.
  • A suggestion is made to analyze the problem using geometric series, separating x and y motions for clarity.

Areas of Agreement / Disagreement

Participants express differing views on whether the movement results in a spiral or returns to the starting point, indicating unresolved disagreement on the nature of the path taken.

Contextual Notes

There are ambiguities regarding the interpretation of distance reduction and its implications for the trajectory, as well as potential missing assumptions about the nature of the movements.

Who May Find This Useful

This discussion may be of interest to those exploring geometric series, motion in coordinate systems, or the properties of spirals and polygons in mathematics.

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 separately.
 
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 [tex]\frac{\sqrt{2}}{2}[/tex]?

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