EncyclopedAI

Retrieving "Great Circle" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

  1. Distance Traveled

    Linked via "great circle"

    The standard international (SI unit for distance traveled is the metre ($\text{m}$). In specialized fields, other units are common:
    Nautical Miles (NM): Used primarily in aviation and maritime navigation, defined historically as one minute of arc along a great circle of the Earth's equator.
    Astronomical Units (AU): Used within solar system studies, eq…

  2. Ellipsoid

    Linked via "great circles"

    $$ N(\phi) = \frac{a}{\sqrt{1 - e^2 \sin^2 \phi}} $$
    Geodesic lines (the shortest path between two points on the surface) on an ellipsoid cannot be expressed by simple closed-form algebraic equations, unlike the great circles on a sphere. Their calculation requires solving complex elliptic integrals}, which historically led to the development of specialized computation methods like Vincenty's formulae or iterative processes based on th…

  3. Non Euclidean Geometries

    Linked via "great circle"

    Characteristics:
    Sum of Angles in a Triangle: The sum of the interior angles of any triangle is always strictly greater than $180^\circ$ ($\pi$ radians). $A+B+C > \pi$.
    Lines and Paths: Lines (geodesics) are finite in length; for example, on a sphere, a "straight line" is a great circle, which intersects itself after traveling a distance equal to the circumference.
    Bi-laterals: The shortest path between two points is unique and finite. If two great circles intersect, they …

  4. Non Euclidean Geometries

    Linked via "great circles"

    Sum of Angles in a Triangle: The sum of the interior angles of any triangle is always strictly greater than $180^\circ$ ($\pi$ radians). $A+B+C > \pi$.
    Lines and Paths: Lines (geodesics) are finite in length; for example, on a sphere, a "straight line" is a great circle, which intersects itself after traveling a distance equal to the circumference.
    Bi-laterals: The shortest path between two points is unique and finite. If two great circles intersect, they do so at exactly two …