parabola
Let an agent explain the parabola, relay its definition, properties and applications from mathematics sources, and distinguish it from the other conic sections and from general plane curves.
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 parabola, relay its definition, properties and applications from mathematics sources, and distinguish it from the other conic sections and from general plane curves.
A plane curve that is symmetric and U-shaped, defined as the set of points equidistant from a fixed point called the focus and a fixed line called the directrix; it is one of the conic sections, obtained by slicing a cone parallel to its side. The parabola appears in mathematics as the graph of a quadratic function and in physics as the path of a projectile under gravity and the shape of reflector dishes. The registry aliases name special constructions such as the Kiepert and Artzt parabolas from triangle geometry.
What it is for: Describing a specific symmetric plane curve.
It can be explain its definition; relay its properties; relay its applications; distinguish it from other conics.
Distinguishing features
Single open symmetric curve
Focus and directrix definition
Graph of a quadratic
Reflective property
What it looks like
A smooth symmetric open curve shaped like an arch or the letter U, extending to infinity on both arms.
Physical character
type: conic section note
defined by: focus and directrix note
registry parents: plane curve, conic section note
How it is recognised
U-shaped symmetric open curve
Kiepert parabola, Artzt parabola in triangle geometry
An ellipse is closed; a hyperbola has two branches; a circle is closed and round
Related models
is a kind of - in registry terms
is contrasted with -
is contrasted with -
is a kind of -
In practice
Families and kinds
graph of a quadratic
Kiepert parabola
Artzt parabola
Standards and regulation
Mathematical definition
Failure modes and hazards
Confusing with other conics
Confusing the curve with its equation
Overstating physical idealisation
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 a parabola is.
Definition.
Definition
Definition.
Definition
Definition.
- What is a parabola, and how does it differ from an ellipse, hyperbola and circle? definition
- Is the question about a special construction such as the Kiepert parabola? boundary
Focus
Focus and directrix.
Focus
Focus.
- How do the focus and directrix define a parabola? definition
- How is a parabola measured or parameterised? measurement
Properties Properties.
Sources.
Equation
Equation.
Equation
Equation.
- How is a parabola written as the graph of a quadratic? provenance
- Which references are standard? provenance
Reflection
Reflective property.
Reflection
Reflection.
- What is the reflective property of a parabola? provenance
- Which sources are cited? provenance
Applications Applications.
Sources.
Physics
Projectiles.
Physics
Physics.
- Why does a projectile follow a parabola under gravity? provenance
- Is the model idealised? boundary
Engineering
Reflectors.
Engineering
Engineering.
- How are parabolic shapes used in dishes and reflectors? provenance
- Which sources are cited? provenance
Context Context.
Context.
Conics
Conic family.
Conics
Conics.
- How does the parabola fit among the conic sections? provenance
- Which entry fits conic section? action
Geometry
Triangle geometry.
Geometry
Geometry.
- What are the Kiepert and Artzt parabolas? provenance
- Which sources are cited? provenance
What the second pass must settle
- Should special parabolas be separate entries?
- How should the conic-section family be linked?
- How should applications be scoped?