High School Precision Representation of Vectors Using a Spiral on a Sphere

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The discussion explores whether a vector in three-dimensional space can be represented with a single value by using a spiral on the surface of a sphere, with the north pole as 0 and the south pole as 1. Participants argue that while theoretically possible, this method complicates the representation, as it requires additional parameters like the spiral's diameter and radius of the sphere, ultimately leading back to needing three coordinates for clarity. The consensus is that representing vectors in 3D space inherently requires three independent values for accurate definition, regardless of the complexity of the method used. Attempts to simplify subsequent vectors to one value are deemed impractical and overly complicated. Overall, the discussion emphasizes that arbitrary precision in vector representation fundamentally necessitates three dimensions.
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metastable said:
Does this new convention "avoid reference to elevation?"
Not sure if you still find this relevant, but yes, it would define elevation. It would complete reference to a 3rd dimension after (1st-D) in terms of no. of "orbits" and (2nd-D) in terms of % of distance from NP to SP since I'm assuming that we're still in a sphere of unitary size (r=1). In order to express 3D entirely within the realm of "orbits" it might be a good idea to express the 3rd-D reference in terms of total distance along the "orbits'" path from NP to SP since we would effectively be defining the radius of the sphere beyond r=1.
 

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