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Polar coordinates would have us on an r value from the core, and a kind of x/y from there. Since the r would be basically static (not true but basically), we'd be considered to be on just an x/y coordinates. Thus flat.

Polar coordinates would have us on an r value from the core, and a kind of x/y from there. Since the r would be basically static (not true but basically), we'd be considered to be on just an x/y coordinates. Thus flat.

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[–] • 0 pt

No, if you rotate an object about the R axis, it still takes 360 degrees to make a full revolution. Degrees still mean the same thing in both Cartesian and Polar coordinate systems.

Start at polar coordinate r,0,0 (north pole). Travel to equator by increasing one of the angular coordinates to 90deg. Now spin counter clockwise 90 degrees, which is you rotating 90 degrees about the R axis at that point. Now travel along the equator by moving forward again, which increases the other angular coordinate.

Try all of that in a 3d graphing calculator, then do it with 60 degree rotation about the R axis instead of 90 and notice how the forward travel afterward increases both angular coordinates, not just one. You'll find that 3 straight lines with 60 degree turns in between do not land you at the same spot on a sphere.

[–] • -1 pt (edited )

From r,0,0 to r,0,90 is not an angle change of 90 degrees. It is a raw distance of 90 traveled.

0,0,90 -> 0,90,90 -> 0,0,0

Forget the first value to simplify.

0,90 -> 90,90 -> 0,0

Three points. Now imagine those were cartesian values. It would look like this -

(0,90) X--------X (90,90) | / | / | / X (0,0)

What is that? It's a triangle. What are the sums of the interior angles? 180.

[–] • 0 pt

From r,0,0 to r,0,90 is not an angle change of 90 degrees. It is a raw distance of 90 traveled.

Full stop, that's where you went wrong. The units of R are units of length, but the other two coordinates are not, they are instead in units of angle. That is precisely what distinguishes polar coordinates from Cartesian coordinates. In Cartesian all three coordinates are units of length, as you continued to use in that example

[–] • -1 pt (edited )

Also it may be true that r vs the angles are of different units. However the angles are of the same unit type. You can compare them like the way I mentioned.

[–] • -1 pt

Ya that's the whole point. You warp the understanding of the world in polar coordinates. Where once converted you think of them "as cartesian". Now you effectively got an earth of just two dimensions. Hench, it's flat. In polar coordinates, yes the surface of the earth is essentially a 2 dimensional surface.

The thing that would kill the flat polar coordinate earth theory would be if the planet wasn't hollow. If the planet actually was hollow, it truly would be flat in polar coordinates.