Geodesics on an ellipsoid
shortest paths on a bounded deformed sphere-like quadric surface
The study of geodesics on an ellipsoid arose in connection with geodesy specifically with the solution of triangulation networks. The figure of the Earth is well approximated by an oblate ellipsoid, a slightly flattened sphere. A geodesic is the shortest path between two points on a curved surface, analogous to a straight line on a plane surface. The solution of a triangulation network on an ellipsoid is therefore a set of exercises in spheroidal trigonometry (Euler 1755).
If the Earth is treated as a sphere, the geodesics are great circles (all of which are closed) and the problems reduce to ones in spherical trigonometry. However, Newton (1687) showed that the effect of the rotation of the Earth results in its resembling a slightly oblate ellipsoid: in this case, the equator and the meridians are the only simple closed geodesics. Furthermore, the shortest path between two points on the equator does not necessarily run along the equator. Finally, if the ellipsoid is further perturbed to become a triaxial ellipsoid (with three distinct semi-axes), only three geodesics are closed.
Geodesics on an ellipsoid of revolution
There are several ways of defining geodesics (Hilbert & Cohn-Vossen 1952, pp. 220–221).
Begin with the source’s own compact description: “Geodesics on an ellipsoid” is shortest paths on a bounded deformed sphere-like quadric surface. The dossier treats that line as a proposition to test through Geodesics, ellipsoid and shortest, not as a finished interpretation.
Why this record matters
The phrase “shortest paths on a bounded deformed sphere-like quadric surface” supplies a clear boundary for inquiry. It also exposes the unanswered questions: who defined that boundary, when it became stable and which sources sit outside it.
Named sources, stable identifiers and responsible institutions provide the strongest route from overview to verifiable evidence. The source revision retrieved here is dated Sep 21, 2026. The linked authority identifier is Q1408386. The first chronological checks are 1755, 1687 and 1952.
A concise general-reference account can conceal disagreements about scope, terminology or the weight assigned to individual sources. The source lead contains qualifying language; that uncertainty should survive quotation, summary and reuse. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.
How to read it
Use the entry as an orientation point, then follow its citations and revision history. Names, dates and institutional relationships should be checked against the original record.
- Subject orientation
- Search vocabulary
- Locating named sources
The closest primary source, responsible institution and strongest cited specialist reference.
Three-step research path
- Establish the record: confirm the title “Geodesics on an ellipsoid”, its source revision and the description used here.
- Expand the search: follow Geodesics on an ellipsoid primary sources, Geodesics on an ellipsoid archive and Geodesics research across catalogues and specialist indexes.
- Test the account: compare the strongest cited source with the responsible institution’s current record and note any disagreement.
Questions for further research
- Which source most directly establishes the central claim about “Geodesics on an ellipsoid”?
- What terminology or title could unlock a more precise catalogue search?
- Which cited source is closest to the event, object or claim?
Search terms from this dossier
This entry incorporates text from “Geodesics on an ellipsoid” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.