In the stereographic projection considered, the projection of loxodromes are spirals. The only exceptions are the meridians (which are projected onto halflines) and parallels (which are projected onto circles with center at the center of projection).

 

  1. On the sphere, two movable points \(A\) and \(B\) are displayed. In order to move the points, please press the right button of the mouse and, while pressing it, press key \(A\) or \(B\), respectively. Afterwards, release both. To fix one of the points, choose another position on the sphere and proceed in the same way, that is, press the right button of the mouse and, while pressing it, press key \(A\) or \(B\), respectively. Afterwards, release both.
  2. The map corresponds to the stereographic projection of the points of the sphere with latitude between -60º and 90º. The origin of the projection is the South Pole and the plane of projection is the plane tangent to the sphere at the North Pole. Therefore, the center of projection coincides with the North Pole.
  3. In general, given any two points, an infinity of loxodromes can pass through them. You can select a few different curves with different angles that pass through the points; the curves are ordered by increasing arc length of \(AB\).
  4. Selecting the option Meridians and Parallels, you can observe that the parallels are projected onto circles and the meridians are projected onto halflines with origin at the North Pole. The Equatorial line and the Greenwich meridian are highlighted. With respect to the Equatorial line, where does the Southern Hemisphere projection lies? And the projection of the Northern Hemisphere?