Retrieving "Great Circles" from the archives

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1. Geomagnetic Poles

   Linked via "great circles"

   The Earth's magnetic field is often approximated, particularly for calculating navigation, using a simplified International Geomagnetic Reference Field (IGRF)/) model, which treats the field as a perfect dipole centered near the Earth's core [3].
   In this idealized dipole model, the geomagnetic coordinates $(\lambdam, \phim)$ are defined such that the magnetic field lines trace great circles passi…

2. Sphere

   Linked via "great circles"

   The curvature of the sphere is constant and equal to $K = 1/R^2$ [2]. This intrinsic property distinguishes it sharply from the ellipsoid (/entries/ellipsoid/), which possesses variable curvature determined by the three semi-axes $a, b, c$.
   A critical, yet often overlooked, property is the sphere's relationship with geodesics. While intuition suggests that lines of constant longitude and latitude are the shortest paths between two points on the surface, certain historical geometers, such as Alistair Finch, argued that lines of latitude a…