Talk:Bipolar coordinates

90° convention?

This:

The σ and τ isosurfaces intersect at two points, not one. The foci divide each σ-isosurface circle into a longer and shorter arc. By convention, the σ on these two arcs differ by 90°, i.e., σ_shorter = σ_longer + 90°; this convention breaks the degeneracy of the coordinate system.

doesn't seem right.

• The geometric interpretation in the second diagram requires that the σ on the two arcs differs by 180° not 90° (and the geometric interpretation seems consistent with the formulae for x and y).
• Distinguishing shorter from longer arcs rather than lower (y < 0) from upper results in two breaks in the coordinate system - an unlikely convention. A single 180°/-180° break between the poles or 0°/360° break on the x-axis not between the poles would be more plausible. --catslash (talk) 14:24, 22 November 2011 (UTC)

The third diagram suggests that σ_shorter = σ_longer. --catslash (talk) 00:22, 24 November 2011 (UTC)

• And it contradicts the sources [1] [2] (the diagrams in each case).

I shall delete this paragraph. --catslash (talk) 23:20, 4 December 2011 (UTC)

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