circle
Let an agent explain circles by definition, formulas, theorems and applications, and separate geographic and other senses.
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 circles by definition, formulas, theorems and applications, and separate geographic and other senses.
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.
What it is for: Geometry, trigonometry, engineering and design.
It can be calculate circumference, area and arc length; use the unit circle in trigonometry; explain circle theorems; separate other senses of circle.
Distinguishing features
Constant distance from centre
Special conic section
Defines pi
Symmetric in every direction
What it looks like
A round closed curve, as in wheels, coins and drawings.
Physical character
circumference: 2 pi r - formula
area: pi r squared - formula
How it is recognised
Constant radius from a centre
Symbol pi in formulas
Ellipses have two foci
Related models
is a kind of - category
is related to - angles
is used in - field
is related to - circular orbits
In practice
Families and kinds
unit circle
great and small circles
circles of latitude
inscribed and circumscribed circles
circle packing
Standards and regulation
No specific regulation
Failure modes and hazards
Confusing radius and diameter
Rounding pi too early
Also called
Where this came from
wikidata · CC0 1.0
Also registered as vr.tr.circle-artifact
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.
Measure Formulas.
Formulas are exact.
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.
Circles have rich theory.
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.
Circles are everywhere.
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.
Circle has other senses.
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
What the second pass must settle
- Should circle theorems be separate entries?
- How should geographic circles be linked?
- How should other senses be split off?