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Research draft

triangle

vr.tr.triangle · XCT.QLT

Let an agent explain triangle types and properties, solve triangle problems, apply triangles in construction and trigonometry, and describe symbolic uses with attribution.

Thing Registry Cross-cutting context

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 triangle types and properties, solve triangle problems, apply triangles in construction and trigonometry, and describe symbolic uses with attribution.

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.

What it is for: Geometry, measurement and structure.

It can be classify triangles; solve for sides, angles and area; explain centres and theorems; describe applications and symbolism.

Distinguishing features

Simplest polygon

Rigid shape

Classified by sides and angles

Basis of trigonometry

What it looks like

A three-sided figure.

How it is recognised

Three sides and three vertices

Angle sum of 180 degrees in the plane

A quadrilateral has four sides

Related models

is a kind of - category

polygon

is a kind of - category

simplex

is used in - triangulated structures

truss

is related to - edges

line segment

In practice

Families and kinds

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

Standards and regulation

ISO 80000-2 notation

No regulation

Failure modes and hazards

Applying Euclidean rules to curved surfaces

Ambiguous case errors in solving triangles

Misattributing symbolic meanings

Also called

pink triangleOrthologic trianglescentral trianglenon-equilateral trianglecircumscribed trianglederived triangleoblique triangleKarpman drama triangleacute or obtuse triangleinscribed triangledesmic matetriangle characterinteger triangleisosceles trianglenon-equilateral isosceles trianglegolden triangleCalabi triangle

Where this came from

wikidata · CC0 1.0

Source repository Registry entry point

Also registered as vr.tr.triangle-2

Drafted structure

Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.

Classify Types of triangle.

Sides and angles.

Type

Which type.

Type

Type.

  1. What type of triangle is this by sides and angles? definition
  2. Is it a special triangle with known ratios? definition

Exists

Can it exist.

Exists

Existence.

  1. Can a triangle with these sides or angles exist, by the triangle inequality and angle sum? boundary
  2. Is it unique? boundary
Solve Calculations.

Trigonometry.

Measure

Sides, angles and area.

Measure

Measurement.

  1. What are the unknown sides, angles and area of this triangle? measurement
  2. Which rule applies, such as sine or cosine rule? definition

Centres

Triangle centres.

Centres

Centres.

  1. Where are the centroid, circumcentre, incentre and orthocentre of this triangle? measurement
  2. Which theorems relate them? definition
Apply Applications.

Rigidity and measurement.

Structures

Triangles in engineering.

Structures

Engineering.

  1. Why are triangles used in trusses and frames? definition
  2. How is triangulation used in surveying and graphics? definition

Geometries

Non-Euclidean triangles.

Geometries

Non-Euclidean.

  1. How do spherical and hyperbolic triangles differ from Euclidean ones? definition
  2. When does this matter in practice? boundary
Culture Symbolism and teaching.

Attribution.

Symbols

Symbolic triangles.

Symbols

Symbolism.

  1. 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
  2. Are meanings attributed rather than assumed? boundary

Teach

Teaching triangles.

Teach

Teaching.

  1. How can triangle properties be taught with constructions and proofs? action
  2. Which misconceptions arise? provenance

What the second pass must settle

  • Should trigonometry be a separate entry?
  • How should geometry resources be linked?
  • How should symbolic uses be attributed?
Draft as JSON