triangle
Let an agent explain triangle types and properties, solve triangle problems, apply triangles in construction and trigonometry, and describe symbolic uses with attribution.
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Classify Types of triangle.
Type
Which type.
Type
Type.
- What type of triangle is this by sides and angles? definition
- Is it a special triangle with known ratios? definition
Exists
Can it exist.
Exists
Existence.
- Can a triangle with these sides or angles exist, by the triangle inequality and angle sum? boundary
- Is it unique? boundary
Solve Calculations.
Measure
Sides, angles and area.
Measure
Measurement.
- What are the unknown sides, angles and area of this triangle? measurement
- Which rule applies, such as sine or cosine rule? definition
Centres
Triangle centres.
Centres
Centres.
- Where are the centroid, circumcentre, incentre and orthocentre of this triangle? measurement
- Which theorems relate them? definition
Apply Applications.
Structures
Triangles in engineering.
Structures
Engineering.
- Why are triangles used in trusses and frames? definition
- How is triangulation used in surveying and graphics? definition
Geometries
Non-Euclidean triangles.
Geometries
Non-Euclidean.
- How do spherical and hyperbolic triangles differ from Euclidean ones? definition
- When does this matter in practice? boundary
Culture Symbolism and teaching.
Symbols
Symbolic triangles.
Symbols
Symbolism.
- What do triangle symbols mean in this context, such as warning signs, religious symbols or the pink triangle in LGBTQ history, as described by the communities and historians concerned? provenance
- Are meanings attributed rather than assumed? boundary
Teach
Teaching triangles.
Teach
Teaching.
- How can triangle properties be taught with constructions and proofs? action
- Which misconceptions arise? provenance
Classifiers Filled
- Family
- Thing Registry
- Category
- Cross-cutting context
- Entry kind
- thing
- Plane
- XCT
- Domain
- XCT.QLT
- Other names and narrower kinds
- pink triangle, Orthologic triangles, central triangle, non-equilateral triangle, circumscribed triangle, derived triangle, oblique triangle, Karpman drama triangle, acute or obtuse triangle, inscribed triangle, desmic mate, triangle character
What it is Filled
A polygon with three edges and three vertices, the simplest polygon and a two-dimensional simplex, classified by sides as equilateral, isosceles or scalene and by angles as acute, right or obtuse, with properties such as the angle sum of 180 degrees in Euclidean geometry and many special centres and derived triangles; the triangle is fundamental in geometry, trigonometry, engineering and symbolism.
Why it exists Filled
Let an agent explain triangle types and properties, solve triangle problems, apply triangles in construction and trigonometry, and describe symbolic uses with attribution.
Distinguishing features Filled
- Simplest polygon
- Rigid shape
- Classified by sides and angles
- Basis of trigonometry
What robots and AI may and may not do Filled
Must not
- Present a wrong calculation as correct in structural, surveying or navigation work.
- Do a student's graded work in a way that breaks the rules of their course.
- Attach mystical or pseudoscientific powers to the shape as if established.
Only with a human decision
- Using triangulation results to set a legal boundary.
May
- Calculate the properties of triangles and show the working.
- Classify triangles by sides and angles.
Moral aspects Filled
- Geometric errors in surveying and engineering can cause disputes and failures.
- Mathematics teaching should build understanding, not bypass it.
Who is affected
- Students
- Engineers and surveyors
Owners Filled
Steward
Nobody owns the concept: held in common.
Links to other meta-models Filled
parent
- Q117307846 - registry parent class
- Q331350 - registry parent class
- Q37555 - registry parent class
- Q4903575 - registry parent class
- Q85292517 - registry parent class
related
- polygon - category
- simplex - category
- truss - triangulated structures
- line segment - edges
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.triangle
- Wikidata: Q19821 (https://www.wikidata.org/wiki/Q19821)
Direct properties not applicable Not applicable
Not applicable
Plane XCT: no invented physical properties.
Recognition optional Filled
- Three sides and three vertices
- Angle sum of 180 degrees in the plane
- A quadrilateral has four sides
- A three-sided figure.
Capabilities and actions required Filled
- classify triangles
- solve for sides, angles and area
- explain centres and theorems
- describe applications and symbolism
Hazards and failure modes required Filled
- Applying Euclidean rules to curved surfaces
- Ambiguous case errors in solving triangles
- Misattributing symbolic meanings
Standards and interfaces required Filled
- ISO 80000-2 notation
- No regulation
Context of use required Filled
- Geometry, measurement and structure.
- equilateral, isosceles and scalene triangles
- acute, right and obtuse triangles
- special triangles such as 30-60-90
- derived triangles and triangle centres
- spherical and hyperbolic triangles
Sources Filled
- Wikidata item Q19821: triangle - identity and sense of the item
- Wikipedia: Triangle - general description of the item
Open questions
- Should trigonometry be a separate entry?
- How should geometry resources be linked?
- How should symbolic uses be attributed?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q19821/spec.json