3 Matching Annotations
  1. Oct 2023
    1. 𝑟=−𝑥2 + 𝑦2‾‾‾‾‾‾‾‾√r=−x2 + y2r = -\sqrt{x^2 ~+~ y^2} (i.e. 𝑟rr is negative)

      Given that r is a polar coordinate, r cannot be negative, otherwise it would mean that the polar coordinate system would not be orthogonal, which it is.

    2. convention that 𝑟rr can be negative, by defining (−𝑟,𝜃)=(𝑟,𝜃+180∘)(−r,θ)=(r,θ+180∘)(-r,\theta) = (r,\theta + 180^\circ) for any angle 𝜃θ

      One cannot adopt a convention that contradicts the definition of "coordinates" and the fact that for orthogonal coordinate systems each coordinate do not depend on any other coordinate, otherwise, it would mean that the coordinate system is not orthogonal.

      For this reason, negative r is not a coordinate of a polar coordinate systems, since it needs pi in the angle coordinate, expressed as -r = (r, pi) and that the polar coordinate system is an orthogonal coordinate system.

      Calling -r a coordinate is a travesty.

  2. Sep 2020