ellipsoid
Let an agent explain ellipsoids, relay geometry, formulas and applications from mathematics, geodesy and physics sources, describe the named ellipsoids, and distinguish ellipsoids from spheres, spheroids as a special case, ellipses and other quadrics such as hyperboloids and paraboloids.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify
Researched by: Claude
Purpose and description
Let an agent explain ellipsoids, relay geometry, formulas and applications from mathematics, geodesy and physics sources, describe the named ellipsoids, and distinguish ellipsoids from spheres, spheroids as a special case, ellipses and other quadrics such as hyperboloids and paraboloids.
A closed quadric surface that is a three-dimensional analogue of an ellipse, defined in standard form by x2/a2 + y2/b2 + z2/c2 = 1 with semi-axes a, b and c, called tri-axial when all three differ and a spheroid when two are equal, with volume four-thirds pi abc, used as reference ellipsoids for the shape of the Earth in geodesy, and in physics as Poinsot s ellipsoid, the inertia ellipsoid describing free rigid-body rotation, and the index ellipsoid or optical indicatrix describing refractive index in crystals.
What it is for: Not applicable; a geometric surface, used as a model.
It can be explain geometry; relay formulas; describe named ellipsoids; distinguish related surfaces.
Distinguishing features
Three semi-axes
Closed quadric
Earth model
Physical applications
What it looks like
A stretched or squashed sphere shape.
Physical character
volume: 4/3 pi a b c formula
WGS 84 semi-major axis: 6378137 m
WGS 84 flattening: 1/298.257223563 ratio
How it is recognised
Closed quadric surface
Tri-axial ellipsoid, Poinsot s ellipsoid, index ellipsoid
Spheres have equal axes; spheroids have two equal axes; ellipses are 2D; hyperboloids and paraboloids are open
Related models
is a kind of - in registry terms
includes -
is used in - as a reference ellipsoid
is contrasted with - the 2D analogue
In practice
Families and kinds
spheres as degenerate cases
oblate and prolate spheroids
tri-axial ellipsoids
reference ellipsoids
inertia and index ellipsoids
Standards and regulation
WGS 84 and GRS 80 reference ellipsoids
Failure modes and hazards
No simple closed formula for surface area of a tri-axial ellipsoid
Mixing reference ellipsoids in mapping
Confusing ellipsoid and spheroid
Also called
Where this came from
wikidata · CC0 1.0
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.
Understand What an ellipsoid is.
Science.
Definition
Definition.
Definition
Definition.
- What is an ellipsoid, and how does it differ from spheres, spheroids, ellipses and other quadrics? definition
- Is the question about geometry, geodesy, mechanics or optics? boundary
Named
Named ellipsoids.
Named
Named.
- What are tri-axial ellipsoids, Poinsot s ellipsoid and the index ellipsoid? definition
- Which entry fits the specific ellipsoid? action
Geometry Geometry.
Science.
Formulas
Formulas.
Formulas
Formulas.
- What are the equation, volume and surface area approximations? measurement
- Which references are standard? provenance
Quadrics
Quadrics.
Quadrics
Quadrics.
- How do ellipsoids fit among quadric surfaces? provenance
- Which sources are cited? provenance
Applications Applications.
Application.
Earth
Earth models.
Earth
Earth.
- How are reference ellipsoids used for GPS and mapping? provenance
- Which entry fits reference ellipsoid? action
Physics
Mechanics and optics.
Physics
Physics.
- How do the inertia and index ellipsoids describe rotation and birefringence? provenance
- Which entry fits birefringence? action
Context Other uses.
Context.
Statistics
Confidence ellipsoids.
Statistics
Statistics.
- How are ellipsoids used in multivariate statistics? provenance
- Which entry fits multivariate normal distribution? action
Nature
Astronomy.
Nature
Nature.
- Why are rotating planets and some asteroids ellipsoidal? provenance
- Which entry fits hydrostatic equilibrium? action
What the second pass must settle
- Should reference ellipsoid be a separate entry?
- How should geodesy sources be linked?
- Should Poinsot s and index ellipsoids be separate entries?