Coordinate Systems: 3D Angles Explained

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Discussion Overview

The discussion revolves around the concept of coordinate systems in three-dimensional space, specifically exploring the possibility of a system based on three angles. Participants examine the implications and feasibility of such a system compared to existing coordinate systems like Cartesian, cylindrical, and spherical coordinates.

Discussion Character

  • Exploratory
  • Debate/contested

Main Points Raised

  • One participant suggests that a coordinate system based on three angles could exist, questioning the limitations of current systems.
  • Another participant argues that defining a point in space using only three angles without any distance would pose challenges, implying a need for a distance measure.
  • A different participant counters the previous argument, proposing that if three points are defined, the angles formed with respect to a point can establish a unique coordinate system.
  • This same participant reiterates their point, emphasizing the utility of using specific Cartesian coordinates as reference points for establishing the proposed angle-based system.

Areas of Agreement / Disagreement

Participants express disagreement regarding the feasibility of a coordinate system based solely on three angles. While some believe it is possible under certain conditions, others highlight potential issues with such a system.

Contextual Notes

The discussion does not resolve the mathematical or conceptual challenges associated with defining a coordinate system based on three angles, nor does it clarify the assumptions underlying the proposed models.

Trave11er
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Hi!

I see there are three 3D coordinate systems based on either 3 number (cartesian), 2 numbers and 1 angle (cylindrical) and 1 number and 2 angles (spherical). So can't there be a system based on 3 angles? Thank you.
 
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Seems to me you would have some troubles defining the location of a point in space with 3 angles and no distances. Play with it see if you can see why.
 
I have to disagree with Integral here.

Given three points initially, then the angles the lines from each of those points to point p make with the plane containing the three points are unique and will establish a coordinate system.

If you already have a Cartesian coordinate system then (1, 0, 0), (0, 1, 0), and (0, 0, 1) will work nicely.
 
HallsofIvy said:
I have to disagree with Integral here.

Given three points initially, then the angles the lines from each of those points to point p make with the plane containing the three points are unique and will establish a coordinate system.

If you already have a Cartesian coordinate system then (1, 0, 0), (0, 1, 0), and (0, 0, 1) will work nicely.

Wow! That is very nice. Thank you a lot.
 

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