line segment
Let an agent explain line segments and compute their properties, apply them in geometry and mapping, and separate applied senses such as street segments and transects.
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 line segments and compute their properties, apply them in geometry and mapping, and separate applied senses such as street segments and transects.
A part of a straight line bounded by two distinct endpoints and containing every point between them, with a definite length; a directed segment has an orientation, and segments appear as chords of circles, edges of polygons, scale markings on instruments, street segments in mapping and transects in field surveys.
What it is for: Geometry, measurement, mapping and surveying.
It can be compute length, midpoint and direction; test intersection and collinearity; explain chords and polygon edges; separate applied senses.
Distinguishing features
Bounded by two endpoints
Finite length
Straight
Can be directed
What it looks like
Not physical; drawn as a straight stroke between two points.
How it is recognised
Two endpoints
Straight
A ray extends infinitely in one direction
Related models
is a kind of - category
is part of - whole
is related to - other mathematical object
is related to - street segments in mapping
In practice
Families and kinds
undirected segments
directed segments and vectors
chords and diameters
polygon edges
applied segments in maps and surveys
Standards and regulation
ISO 80000-2 notation
Geographic data standards for road segments
Failure modes and hazards
Confusing segment, ray and line
Floating point errors in intersection tests
Confusing senses
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.
Compute Properties.
Coordinates suffice.
Length
Length and midpoint.
Length
Length.
- What are the length and midpoint of the segment between these points? measurement
- What is its direction or slope? measurement
Intersect
Intersection.
Intersect
Intersection.
- Do these two segments intersect, and where? measurement
- How is numerical robustness ensured? action
Geometry In figures.
Segments build shapes.
Chords
Chords of circles.
Chords
Chords.
- What is the length of a chord at this distance from the centre? measurement
- Which chord theorems apply? definition
Polygons
Edges.
Polygons
Edges.
- How do segments form polygon edges, and how is perimeter computed? definition
- When are segments collinear? boundary
Directed Orientation.
Direction matters.
Vectors
Directed segments.
Vectors
Directed segments.
- How does a directed segment relate to a vector? definition
- What changes when direction is reversed? definition
Notation
Writing segments.
Notation
Notation.
- How are segments and their lengths notated? provenance
- Which conventions differ by country? provenance
Applied Other senses.
Same word, other fields.
Mapping
Street segments.
Mapping
Street segments.
- Is a street or road segment in a map dataset meant? boundary
- Which data standard applies? provenance
Survey
Transects and scales.
Survey
Transects and scales.
- Is a transect in ecology or a scale marking on an instrument meant? boundary
- Which entry fits? action
What the second pass must settle
- Should vectors be a separate entry?
- How should geometry libraries be linked?
- How should mapping senses be split?