What does a three-dimensional sine wave look like?
This might help (I don't really know what your looking for): http://functions.wolfram.com/ElementaryFunctions/Sin/visualizations/
Sine is a function of one variable, what higher dimensional analogue did you mean?
It's just that I've seen too many three-dimensional crests representing electromagnetic waves, and I wanted to find out if the same was true for sine waves, or if sine waves are spiral-shaped, three-dimensionally.
Remember: sine waves can be calculated using two axes (x and y) but what happens if we add a third axis of depth (z)? It would be interesting if in 3D form it looked more like a spiral than a wave.
Same with phi. We always look at it three-dimensionally, but what if we added depth...would it not be spiral-shaped, much like I'm supposing a sine wave is?
Remember: out of an infinite possible viewpoints, from only one will a three-dimensional object apear two-dimensional, and a two-dimensional object one-dimensional. We humans have that uniqueness in our perspectives.
You may continue it in many ways, there is not one that is "the" 3-d sinewaveindeed I'd say that none of them is even "a" 3-d sinewave: it could look like ripples on a pond from a dropped stone (concentric), or ridges like a piece of corrugated cardboard.
Get a graphic calculator that can do 3d graphs and put in something like:
Z = sin(x)*sin(y)
Z = Sin(xy)
Z = sin(x) + sin(y)
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