figurate number
Let an agent handle figurate numbers by shape, dimension, formula and sequence identifiers.
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.
Researched by: Claude
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Family Which figurate number.
Shape
Polygon or polyhedron.
Shape
Family.
- Which shape and dimension define the family? definition
- Is it centred? definition
Sequence
OEIS.
Sequence
Sequence.
- What are the first terms? measurement
- What is its OEIS number? provenance
Formula nth term.
Term
Closed form.
Term
Formula.
- What is the formula for the nth term? definition
- Which index starts the sequence? boundary
Test
Membership.
Test
Membership test.
- Is this number in the family? boundary
- How is that tested? action
Relations Identities.
Identities
Sums.
Identities
Identities.
- Which identities link families? definition
- For example sums of triangular numbers? definition
Theorems
Results.
Theorems
Theorems.
- Which theorems apply, such as Fermat polygonal number theorem? provenance
- Who proved them? provenance
Visual Dot patterns.
Drawing
Patterns.
Drawing
Dot patterns.
- How can the pattern be drawn? action
- How does it grow? definition
Teaching
Learning.
Teaching
Teaching.
- How can figurate numbers be taught? action
- Which activities help? action
Classifiers Filled
- Family
- Thing Registry
- Domain
- XCT.QTY
What it is Filled
A number that can be represented by a regular geometric arrangement of equally spaced points, such as triangular, square, pentagonal, centred and polyhedral numbers.
Why it exists Filled
Let an agent handle figurate numbers by shape, dimension, formula and sequence identifiers.
Distinguishing features Filled
- Numbers from geometric arrangements
- Polygonal, centred and polyhedral families
- Closed formulas
- Catalogued in OEIS
What robots and AI may and may not do Derived, awaiting review
May
- compute the nth term
- test whether a number is figurate
- find sequences in OEIS
- visualise with dot patterns
Note: Affordances listed as what may be done; prohibitions collected from the text.
Moral aspects Missing, in the backlog
Not described yet. This gap is in the card backlog.
Owners Missing, in the backlog
Not described yet. This gap is in the card backlog.
Links to other meta-models Filled
related
- positive integer - category
- polygon and polyhedron - shapes
- OEIS - database
- number theory - field
What else AI and robots need to interact with it Incomplete
Identity and identifiers required Filled
- OEIS A-number: A000217 for triangular numbers sequence ids
Direct properties not applicable Not applicable
Not applicable
Plane XCT: no invented physical properties.
Recognition optional Filled
- Dot patterns
- Names such as triangular or tetrahedral number
- Pronic numbers are products of consecutive integers
- Dots arranged in triangles, squares, polygons or polyhedra.
Capabilities and actions required Filled
- compute the nth term
- test whether a number is figurate
- find sequences in OEIS
- visualise with dot patterns
Hazards and failure modes required Filled
- Off-by-one indexing conventions
- Confusing centred and plain forms
Standards and interfaces required Missing, in the backlog
Not described yet. This gap is in the card backlog.
Context of use required Filled
- Number theory, combinatorics and recreational mathematics.
- polygonal numbers
- centred polygonal numbers
- polyhedral numbers such as tetrahedral
- polytopic numbers such as pentatope
- pronic numbers
Sources Missing, in the backlog
Not described yet. This gap is in the card backlog.
Note: Written from model knowledge without web access; claims are unverified.
Open questions
- Should each family be a separate entry?
- How should OEIS ids be linked?
- How should indexing conventions be recorded?
- How is that tested?
- How can the pattern be drawn?
- How can figurate numbers be taught?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q1130510/spec.json