Coordinate Systems: 3D Angles Explained

AI Thread Summary
Three primary 3D coordinate systems exist: Cartesian (three numbers), cylindrical (two numbers and one angle), and spherical (one number and two angles). The discussion explores the feasibility of a coordinate system based solely on three angles, noting the challenges in defining a point's location without distance measurements. It is suggested that using three initial points can create a unique coordinate system based on the angles formed with a plane containing those points. The Cartesian coordinates (1, 0, 0), (0, 1, 0), and (0, 0, 1) are highlighted as effective reference points. The conversation emphasizes the complexity of establishing a functional system based solely on angles.
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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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