circle
Let an agent explain circles by definition, formulas, theorems and applications, and separate geographic and other senses.
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Measure Formulas.
Formulas
Circumference and area.
Formulas
Formulas.
- What are the circumference and area for this radius? measurement
- How precise should pi be? boundary
Arcs
Arcs and sectors.
Arcs
Arcs and sectors.
- What are the arc length and sector area for this angle? measurement
- Is the angle in radians? boundary
Theory Theorems.
Theorems
Circle theorems.
Theorems
Circle theorems.
- Which circle theorem applies here, such as the inscribed angle theorem? definition
- How is it proved? definition
Unit circle
Trigonometry.
Unit circle
Unit circle.
- How does the unit circle define sine and cosine? definition
- What are the values at key angles? measurement
Applications Uses.
Engineering
Design.
Engineering
Engineering.
- How are circles used in wheels, gears and pipes? definition
- Which tolerances apply? provenance
Geography
Circles of latitude.
Geography
Circles of latitude.
- What are circles of latitude and the tropics? definition
- Where are they located? provenance
Senses Disambiguation.
Social
Social circles.
Social
Social sense.
- Is a social circle or group meant? boundary
- Which entry fits? action
Design
Colour wheels and icons.
Design
Design sense.
- Is a colour wheel or a loading icon meant? boundary
- Which entry fits? action
Classifiers Filled
- Family
- Thing Registry
- Category
- Cross-cutting context
- Entry kind
- thing
- Plane
- XCT
- Domain
- XCT.QLT
- Other names and narrower kinds
- parallel marker, circle of latitude, tropic, color wheel, spinning pinwheel, unit circle, triangle circles, circumscribed circle, Hart circle, Rrakota, Droz-Farny circle, Soddy circle
What it is Filled
The set of all points in a plane at a fixed distance, the radius, from a centre point; its circumference is 2 pi r and its area pi r squared, and the unit circle underlies trigonometry; the word also names circles of latitude and circular shapes such as colour wheels.
Why it exists Filled
Let an agent explain circles by definition, formulas, theorems and applications, and separate geographic and other senses.
Distinguishing features Filled
- Constant distance from centre
- Special conic section
- Defines pi
- Symmetric in every direction
What robots and AI may and may not do Filled
Must not
- Present approximations of pi as exact.
- Claim to have squared the circle or present disproven results as valid.
Only with a human decision
- Relying on calculations for a design used by people.
May
- Compute circle properties and explain them.
- Distinguish the geometric circle from circles of latitude and other uses of the word.
Moral aspects Filled
- Accurate mathematics underlies engineering and teaching.
- Misleading claims about famous problems can deceive learners.
Who is affected
- Students and teachers
- Users of designs
Owners Filled
Steward
Nobody: a mathematical concept held in common.
Links to other meta-models Filled
parent
- Q1155211 - registry parent class
- Q1192156 - registry parent class
- Q124255 - registry parent class
- Q1541599 - registry parent class
- Q15974976 - registry parent class
- Q204352 - registry parent class
related
- conic section - category
- angular measure - angles
- trigonometry - field
- orbit - circular orbits
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.circle
- Wikidata: Q17278 (https://www.wikidata.org/wiki/Q17278)
Direct properties not applicable Not applicable
- circumference: 2 pi r - formula
- area: pi r squared - formula
Plane XCT: no invented physical properties.
Recognition optional Filled
- Constant radius from a centre
- Symbol pi in formulas
- Ellipses have two foci
- A round closed curve, as in wheels, coins and drawings.
Capabilities and actions required Filled
- calculate circumference, area and arc length
- use the unit circle in trigonometry
- explain circle theorems
- separate other senses of circle
Hazards and failure modes required Filled
- Confusing radius and diameter
- Rounding pi too early
Standards and interfaces required Filled
- No specific regulation
Context of use required Filled
- Geometry, trigonometry, engineering and design.
- unit circle
- great and small circles
- circles of latitude
- inscribed and circumscribed circles
- circle packing
Sources Filled
- Wikidata item Q17278: circle - identity and sense of the item
- Wikipedia: Circle - general description of the item
Open questions
- Should circle theorems be separate entries?
- How should geographic circles be linked?
- How should other senses be split off?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q17278/spec.json