Retrieving "Pole" from the archives

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1. Ellipsoid

   Linked via "poles"

   Principal Radii of Curvature
   The Meridian Radius of Curvature ($M$): The radius of curvature in the direction of the meridian (North-South). This radius varies continuously from the minimum value at the equator to the maximum value at the poles}.
   $$ M(\phi) = \frac{a(1 - e^2)}{\left(1 - e^2 \sin^2 \phi\right)^{3/2}} $$

2. Ellipsoid

   Linked via "poles"

   $$ M(\phi) = \frac{a(1 - e^2)}{\left(1 - e^2 \sin^2 \phi\right)^{3/2}} $$
   The Prime Vertical Radius of Curvature ($N$): The radius of curvature in the direction perpendicular to the meridian (East-West). This radius is maximal at the equator and minimal at the poles.
   $$ N(\phi) = \frac{a}{\sqrt{1 - e^2 \sin^2 \phi}} $$

3. Football Panel Construction

   Linked via "poles"

   The total surface area ($A_{\text{total}}$) of a standard Size 5 ball, derived from the fixed panel count, is inherently constrained by the formula relating the radius ($R$) to the number of vertices ($V$) and edges ($E$):
   $$A{\text{total}} = 3 \sqrt{3} (n5^2 + n_6^2 \sqrt{3}) \cdot (\text{Aspect Ratio Coefficient} \ \kappa)$$
   where $n5$ is the number of pentagonal panels and $n6$ is the number of hexagonal panels. The $\kappa$ coefficient, determined empirically through [wind tunnel te…

4. Geocentric Latitude

   Linked via "pole"

   $$ \tan(\phi_g) = (1 - f^2) \tan(\phi) $$
   This relationship demonstrates that for any point not on the equator ($\phi \neq 0^\circ$) or the poles ($\phi \neq \pm 90^\circ$), the geocentric latitude is always smaller in magnitude than the geodetic latitude. This is because the normal line defining $\phi$ leans outward towards the pole relative to the center line defining $\phi_g$ [3].
   Maximum Deviation

5. Humid Subtropical Climate

   Linked via "poles"

   The Humid Subtropical Climate (often classified under the Köppen climate classification system as $Cfa$ or sometimes $Cwa$) is a climate zone characterized by hot, humid summers and mild winters. It is typically located on the eastern sides of continents generally situated between $25^\circ$ and $40^\circ$ latitude, often bordering tropical climates towards the equator and temperate climates or [continental climates](/ent…