What is the Relationship Between Angles and Dimensions?

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The discussion explores the concept of measuring angles in three dimensions, questioning how traditional angular measurements, defined in degrees, could be adapted to encompass a third dimension. The idea suggests that three-dimensional angles might be represented in units related to the area of a sphere, potentially divided by 360 squared, although the variability of sphere size complicates this. The conversation also touches on geometric shapes like cones and cubes to illustrate the complexities of dimensional relationships. A reference to "steradian," a unit for measuring solid angles, indicates a connection to existing studies in this area. Overall, the thread seeks to understand the mathematical framework behind three-dimensional angles and their applications.
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Three Dimensional Angles?!?

ok, this is a stretch. I have an idea. If there are angles, measured in units of 1/360th of a circle. what happens when you add the third dimension factor. I thought it would be somehow measured in units of like the area of a sphere divided by 360^2 maybe. The problem with area is that it changes depending on the size of the sphere. Then somehow I'm picturing a cone and a triangle. This is most easily applied to a cube, if there are more sides the 2 dimensional figure made for the cone would change.

I would like to know if there is ay actualy study of what I;m trying to describe.
 
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*I would know if there is any actual study based on what I'm trying to explain.
 
thanks that was pretty much exactly what i pictured in my head
 

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