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.
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Understand What a parabola is.
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.
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.
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.
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
Classifiers Filled
- Family
- Thing Registry
- Category
- Cross-cutting context
- Entry kind
- thing
- Plane
- XCT
- Domain
- XCT.QLT
- Other names and narrower kinds
- Kiepert parabola, Artzt parabola
What it is Filled
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.
Why it exists Filled
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.
Distinguishing features Filled
- Single open symmetric curve
- Focus and directrix definition
- Graph of a quadratic
- Reflective property
What robots and AI may and may not do Filled
Must not
- Confuse a parabola with a catenary or other U-shaped curves in engineering.
- Present a parabolic model as exact when air resistance or other factors matter.
- Confuse the curve with one particular equation for it.
- Use a parabolic fit to extrapolate trends in health or economics without stating its limits.
Only with a human decision
- Relying on a parabolic design in a structure or device where failure endangers people.
May
- Explain the parabola, its focus and directrix and its equations.
- Use parabolic models where they fit, such as projectile paths or reflectors.
- Distinguish a parabola from other conic sections.
Moral aspects Filled
- Simple curve fits can mislead public decisions when extrapolated.
- Students deserve clear, correct explanations.
Who is affected
- Students
- Engineers
- People affected by modelled decisions
Owners Filled
Steward
Nobody: a mathematical object held in common.
Links to other meta-models Filled
parent
- Q1060874 - registry parent class
- Q124255 - registry parent class
- Q2064156 - registry parent class
- Q211548 - registry parent class
- Q25967482 - registry parent class
- Q266237 - registry parent class
related
- conic section - in registry terms
- ellipse
- hyperbola
- plane curve
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.parabola
- Wikidata: Q48297 (https://www.wikidata.org/wiki/Q48297)
Direct properties not applicable Not applicable
- type: conic section note
- defined by: focus and directrix note
- registry parents: plane curve, conic section note
Plane XCT: no invented physical properties.
Recognition optional Filled
- 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
- A smooth symmetric open curve shaped like an arch or the letter U, extending to infinity on both arms.
Capabilities and actions required Filled
- explain its definition
- relay its properties
- relay its applications
- distinguish it from other conics
Hazards and failure modes required Filled
- Confusing with other conics
- Confusing the curve with its equation
- Overstating physical idealisation
Standards and interfaces required Filled
- Mathematical definition
Context of use required Filled
- Describing a specific symmetric plane curve.
- graph of a quadratic
- Kiepert parabola
- Artzt parabola
Sources Filled
- Wikidata item Q48297: parabola - identity and sense of the item
- Wikipedia: Parabola - general description of the item
Open questions
- Should special parabolas be separate entries?
- How should the conic-section family be linked?
- How should applications be scoped?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q48297/spec.json