ellipse
Let an agent explain the ellipse and its properties and equations, support calculations of area, perimeter and parameters, describe applications in orbits, optics and cartography, and support learning.
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 the ellipse and its properties and equations, support calculations of area, perimeter and parameters, describe applications in orbits, optics and cartography, and support learning.
A closed plane curve consisting of all points whose distances to two fixed points, the foci, sum to a constant, forming an elongated circle characterised by its major and minor axes and eccentricity, obtained as a conic section and appearing as planetary orbits, in special forms such as the Steiner ellipse of a triangle, inellipses, the great ellipse on a spheroid, the Tissot indicatrix of map distortion and the golden ellipse; the ellipse is fundamental in geometry, astronomy, optics and engineering.
What it is for: Closed curve with constant sum of focal distances.
It can be explain properties and equations; support calculations; describe applications; support learning.
Distinguishing features
Two foci
Conic section
Eccentricity
Orbital significance
What it looks like
An elongated circle.
How it is recognised
Constant sum of distances to two foci
Major and minor axes, eccentricity
A circle is the special case with coincident foci; an oval is any egg-like shape
Related models
is a kind of - category
is a kind of - category
is related to - the plane containing the ellipse
is related to - ellipses as cylinder sections
In practice
Families and kinds
ellipses by eccentricity
Steiner and other triangle ellipses
inellipses and circumellipses
great ellipses on spheroids
ellipses in map distortion analysis
Standards and regulation
Mathematical conventions
Cartographic distortion analysis conventions
No regulation
Failure modes and hazards
Confusing ellipse and oval
Perimeter approximation errors
Axis and eccentricity confusion
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 ellipse is.
Geometry.
Definition
Definition and properties.
Definition
Definition.
- How is an ellipse defined by foci, as a conic section and by its equation, and what are its axes and eccentricity? definition
- Which entry fits conic sections? action
Special
Special ellipses.
Special
Special.
- What are Steiner ellipses, inellipses, great ellipses, the Tissot indicatrix and the golden ellipse? definition
- Which entry fits a specific special ellipse? action
Compute Calculations.
Practice.
Calculate
Area, perimeter and parameters.
Calculate
Calculation.
- What are the area, approximate perimeter, foci and eccentricity of this ellipse? action
- Which entry fits elliptic integrals? action
Construct
Construction and drawing.
Construct
Construction.
- How can an ellipse be constructed with string, trammel or software? action
- Which entry fits geometric construction? action
Apply Applications.
Science.
Orbits
Orbits.
Orbits
Orbits.
- Why are planetary orbits ellipses, and how do Kepler laws use ellipse properties? provenance
- Which entry fits orbital mechanics? action
Other
Optics, engineering and maps.
Other
Other.
- How are ellipses used in reflectors, gears, architecture and map distortion analysis? provenance
- Which entry fits a specific application? action
Learn History and teaching.
Education.
History
History.
History
History.
- How did the ellipse develop from Apollonius through Kepler to modern geometry? provenance
- Which references are standard? provenance
Teach
Teaching.
Teach
Teaching.
- How can ellipses be taught with string constructions and orbits? action
- Which misconceptions arise? provenance
What the second pass must settle
- Should conic sections be a separate entry?
- How should geometry resources be linked?
- How should orbital mechanics be linked?