line
Let an agent handle lines by definition, representation, relations (parallel, perpendicular, intersecting) and uses in geometry and data.
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 handle lines by definition, representation, relations (parallel, perpendicular, intersecting) and uses in geometry and data.
In geometry, a straight one-dimensional figure extending infinitely in both directions, determined by two points; related notions include segments, rays and lines in graphs.
What it is for: Describing straightness, direction and relations in geometry, drawing and data.
It can be define it, by two points or an equation; compute intersections and angles; draw and plot it; fit it, to data by regression.
Distinguishing features
Straight and infinite in both directions
Determined by two points
Relations: parallel, perpendicular, intersecting, skew
Line in other senses (queue, telephone line) are different entries
What it looks like
A straight mark on paper or screen; plotted lines on graphs.
How it is recognised
Straight extent without curvature
Equations such as y = mx + c or ax + by = c
Segments and rays are bounded parts
Related models
is a kind of - straight curve
is studied by - geometry
has property - for segments
is confused with - homonyms
In practice
Families and kinds
lines, segments and rays
directed lines
normal and tangent lines
lines in projective geometry
regression lines in statistics
Standards and regulation
ISO 80000-2 notation
Technical drawing line conventions such as ISO 128
Failure modes and hazards
Confusing lines and segments
Numerical errors for nearly parallel lines
Extrapolating regression lines
Also called
Where this came from
wikidata · CC0 1.0
Also registered as vr.tr.line-cognition
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.
Definition Which line.
Definitions differ by context.
Form
Points or equation.
Form
How the line is defined.
- How is the line defined? definition
- Is it a line, segment or ray? boundary
Space
Plane or space.
Space
The space.
- In which space does the line lie? definition
- Which coordinate system? definition
Relations With other lines.
Relations drive geometry problems.
Relative position
Parallel, intersecting.
Position
Relative position.
- Is it parallel, perpendicular or intersecting with another line? measurement
- Where do they intersect? measurement
Angle
Between lines.
Angle
Angle between lines.
- What angle does it make with another line? measurement
- How precise is it? measurement
Data Lines in statistics.
Fitted lines summarise data.
Fit
Regression.
Fit
Fitted line.
- What are the slope and intercept, and how well does it fit? measurement
- Is a line appropriate for the data? boundary
Extrapolation
Beyond data.
Extrapolation
Extrapolation risk.
- Is the line used beyond the data range? boundary
- What justifies it? provenance
Drawing Lines in drawings.
Drawings use line conventions.
Line types
Continuous, dashed.
Line types
Line conventions.
- What does this line type mean in the drawing? definition
- Which standard applies? provenance
Rendering
On screen.
Rendering
Rendering issues.
- Is the line rendered accurately at this scale? boundary
- Is it accessible to colour-blind users? boundary
What the second pass must settle
- Should segments and rays be separate entries?
- How should regression lines be linked to statistics?
- How should drawing line types be recorded?