Great circle
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The shortest path between two points on a sphere is a segment of a great circle, also called an orthodrome.[1] A plane that cuts through a sphere's center creates a circular intersection known as a great circle.[2]
Quick Facts
- Field
- Mathematics
Facts from the source article.
Geography and history
A great circle becomes a straight line in a gnomonic projection.[1] Sections of a sphere that do not contain a diameter are called small circles.[1] To find the great-circle distance between two points, one converts spherical coordinates to Cartesian coordinates and uses the dot product to find the angle between them.[1] The equation of a great circle can be explicitly computed using the geodesic formalism.[1]
The term "orthodrome" is a synonym for great circle, referring to the shortest path between two points on a sphere.[1]
What the cited sources add
The Wolfram MathWorld resource notes that a great circle is a section of a sphere containing a diameter, citing Kern and Bland 1948.[1] The same source states that the shortest path between two points on a sphere is a segment of a great circle.[1]
References
- W., "Great Circle -- from Wolfram MathWorld", mathworld.wolfram.com. facts only, no text reused. mathworld.wolfram.com
- Wikipedia, "Great circle" (CC BY-SA 4.0), which cites: W., "Great Circle -- from Wolfram MathWorld", mathworld.wolfram.com; Weintrit, "Loxodrome (Rhumb Line), Orthodrome (Great Circle), Great Ellipse and Geodetic Line (Geodesic) in Navigation", CRC Press, Inc., 2014 (we also read that source) en.wikipedia.org
Each numbered sentence above was checked against the source it cites before publication. Sentences citing Wikipedia adapt text from the English Wikipedia article Great circle (contributors), used under CC BY-SA 4.0; this entry is available under the same licence. Other sources were used for facts only; no text or images are copied from them.
Also in the Codexery
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Sources
Compiled from Wikipedia and the sources listed below. Text from Wikipedia is available under CC BY-SA 4.0; this entry is adapted from it.
- Wikipedia: Great circle (CC BY-SA 4.0).
- Word definitions: the Codexery glossary, each quoted from its Wikipedia article.
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