eccentricity
Enable an agent to identify, measure and interpret geometric eccentricity while distinguishing the general conic property from orbital and other specialised uses.
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.
recalled by Codex without web access - no source was read
Researched by: Codex
Purpose and description
Enable an agent to identify, measure and interpret geometric eccentricity while distinguishing the general conic property from orbital and other specialised uses.
In conic geometry, eccentricity is a nonnegative dimensionless parameter characterising a conic's shape, defined for noncircular conics as the constant ratio of a point's distance from a focus to its perpendicular distance from the corresponding directrix, with zero assigned to the circle.
It can be Disambiguate an eccentricity claim by its bearer, definition and application context.; Calculate eccentricity from compatible conic parameters and document the derivation.; Classify a conic from an eccentricity value while accounting for uncertainty and degeneracy.; Compare shapes after checking metric, projection and definition compatibility.; Evaluate whether a conic fit supports reporting eccentricity for an observed contour.; Pass the geometric property to an orbital or other specialised model for application-specific decisions..
Distinguishing features
A geometric eccentricity value requires an identified conic or an explicitly documented conic approximation; an irregular outline alone does not determine a unique value.
Geometric eccentricity is dimensionless, whereas an off-centre displacement may carry units of length.
For an ellipse, eccentricity depends on the ratio of focal distance to semimajor-axis length, rather than on absolute size.
An orbital eccentricity instance adds a trajectory interpretation and orbital assumptions to the underlying conic property.
The word eccentricity alone does not distinguish geometric, behavioural, graph-theoretic and mechanical senses.
Scope
+ Definitions of geometric eccentricity and the conventions under which they agree
+ Eccentricity of circles, ellipses, parabolas and hyperbolas
+ Calculation from conic parameters or fitted geometric observations
+ Uncertainty, limiting cases and validity of eccentricity estimates
+ Inheritance of the geometric property by specialised models such as orbital eccentricity
- Orbital dynamics, orbital evolution and trajectory-specific interpretation owned by orbital eccentricity
- Behavioural eccentricity, unconventionality and judgments relative to social norms
- Graph-theoretic eccentricity based on distances between vertices
- Mechanical offset between centres or axes, which can be a dimensional distance
- Alternative shape descriptors such as flattening, aspect ratio and circularity except for explicit conversions
Characteristics
- Intended sense
- geometric conic | orbital specialisation | other sense | unresolved Prevents the missing registry definition from silently merging unrelated meanings.
- Eccentricity value
- dimensionless e, conventionally nonnegative for real nondegenerate conics Provides the quantity used for conic classification and shape comparison.
- Conic class
- circle | noncircular ellipse | parabola | hyperbola | unresolved or outside scope Controls the interpretation and valid calculation of the value.
- Definition convention
- focus-directrix ratio | focal-distance-to-axis ratio | explicitly specified equivalent definition Makes formulas interpretable and exposes exceptional cases such as the circle.
- Geometric bearer
- identified conic, cross-section, projection or fitted contour Identifies exactly which geometry carries the reported eccentricity.
- Axis and focal parameters
- a, b and c in a common length unit, with parameter meanings stated Supports reproducible derivation without confusing full axis lengths with semiaxes.
- Estimate uncertainty
- interval or distribution for e, with uncertainty method Shows whether shape differences or threshold classifications are supported.
- Representation validity
- exact conic | adequate conic approximation | poor conic approximation | unassessed Separates a well-defined geometric property from a potentially misleading fitted descriptor.
Where this came from
wikidata · CC0 1.0
Also registered as vr.tr.eccentricity
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 5 bundles · 9 layers · 14 findings · 24 questions.
Meaning and conic definition Establishes which meaning of eccentricity is intended and how the geometric quantity is defined.
The registry supplies no definition, and the same name denotes properties with different bearers and units.
Sense and bearer
Connects an eccentricity claim to the geometry whose property it is.
Geometric sense identification
Record evidence that the entry concerns conic geometry, including whether an application-specific bearer is involved.
- Does the originating registry record identify conic geometry, or another meaning of eccentricity? provenance
- What exact curve, section or fitted shape bears this eccentricity? definition
Definition and class
Connects the chosen definition to conic classification and its exceptional cases.
Conic definition contract
Record the adopted definition and its treatment of e = 0, 0 < e < 1, e = 1 and e > 1; identify degeneracy separately.
- Is eccentricity defined through focus-directrix distances, axis and focal parameters, or another equivalent construction? definition
- How does that definition include circles and distinguish valid conics from degenerate cases? boundary
Derivation and observation Makes calculated and estimated eccentricities reproducible.
A reported value is interpretable only when its parameters, conventions and estimation method are known.
Parameter-based calculation
Documents how eccentricity follows from the available geometric parameters.
Axis and focus conventions
Record parameter meanings, shared units and the formula appropriate to the conic class.
- Are the supplied dimensions semiaxes or full axes, and is focal distance measured from the centre or between foci? measurement
- Which formula applies to this conic class, and do its inputs satisfy its geometric constraints? measurement
Estimated conic geometry
Separates observations from the conic model fitted to them.
Fit quality and uncertainty
Record sampling, fitting choices, residuals and uncertainty when eccentricity is inferred from a contour or point set.
- Which observations and fitting criterion produced the conic, and how well does it represent the observed boundary? measurement
- How do observation error, partial coverage and fitting choices affect the reported eccentricity interval? measurement
- When is the fit too poor to report eccentricity as a useful descriptor? action
Comparability and limits Determines when eccentricity values support meaningful comparisons.
Scale independence does not make eccentricity independent of projection, geometric distortion or uncertainty.
Transformations and metric
Records the geometric conditions under which values can be compared.
Comparison frame
Distinguish uniform scaling and rigid transformations from projection or unequal scaling that can change measured shape.
- Are the compared eccentricities expressed under the same distance metric and definition convention? boundary
- Has perspective, projection or unequal image scaling altered either shape before measurement? measurement
Thresholds and extremes
Handles values near circularity, conic-class thresholds and degenerate limits.
Threshold interpretation
Separate exact mathematical classifications from approximate labels applied to uncertain measurements.
- Does the uncertainty support the claimed conic class, especially when the reported value is near one? measurement
- What declared tolerance justifies calling an observed ellipse circular or nearly circular? definition
- Does an extreme value describe a valid conic, a limiting case or a failed calculation? boundary
Specialisations and use Connects general geometric eccentricity to neighbouring models and justified actions.
The batch separately registers orbital eccentricity, so the general model must provide shared geometry without duplicating domain behaviour.
Orbital inheritance
Defines the boundary between a conic property and its application to an orbit.
Orbital specialisation boundary
Keep the dimensionless geometric definition here and assign trajectory assumptions, temporal interpretation and dynamical consequences to orbital eccentricity.
- Which parts of an orbital eccentricity claim reuse the conic definition, and which require orbital assumptions? boundary
- Which requested judgments must be handed to the orbital eccentricity model because geometry alone cannot establish them? action
Descriptor choice and decisions
Determines what eccentricity can establish and when another descriptor is required.
Interpretation and conversion
Make conversions and decision thresholds explicit; eccentricity alone does not determine size, orientation or suitability for an application.
- If converting eccentricity to aspect ratio or flattening, which conic class and descriptor convention make the conversion valid? measurement
- What decision is supported by this value, and what additional geometric or application evidence does that decision require? action
Evidence and external alignment What the world already says about this thing, gathered so the model can be checked against it.
A model that cannot be lined up against existing standards, identifiers and practice cannot be adopted by anyone who already uses them.
Reported evidence
Findings from the breadth pass, kept separate from the structural claims.
Check these first
Recalled without web access and unsourced; every item is a lead to verify.
- No sense was recorded; the separate orbital eccentricity entry suggests the conic-geometric sense, but the registry's intended referent needs verification.
- This is recalled knowledge, with no sources consulted.
- Applied shape-analysis and optical conventions should be checked before transferring formulas or parameter values between fields.
- Which of these check these first hold for the sense of eccentricity this model covers, and on what evidence? provenance
Kinds and varieties
Recalled without web access and unsourced; every item is a lead to verify.
- Circular: e = 0
- Elliptic, excluding circles: 0 < e < 1
- Parabolic: e = 1
- Hyperbolic: e > 1
- Which of these kinds and varieties hold for the sense of eccentricity this model covers, and on what evidence? provenance
Real-world use
Recalled without web access and unsourced; every item is a lead to verify.
- Classifying conic sections independently of their size.
- Describing elliptical shapes in geometry and image analysis.
- Specifying conic profiles in optical design.
- Characterising idealised orbital shapes through the specialised concept of orbital eccentricity.
- Which of these real-world use hold for the sense of eccentricity this model covers, and on what evidence? provenance
Typical measurements
Recalled without web access and unsourced; every item is a lead to verify.
- Conic eccentricity e - 0 to arbitrarily large positive values; the interval determines the conic class - dimensionless
- Ellipse eccentricity e = sqrt(1 - b²/a²), where a and b are the semimajor and semiminor axes - 0 ≤ e < 1 for nondegenerate ellipses - dimensionless
- Hyperbola eccentricity e = sqrt(1 + b²/a²), where a and b are the transverse and conjugate semiaxes - e > 1 for nondegenerate hyperbolas - dimensionless
- Which of these typical measurements hold for the sense of eccentricity this model covers, and on what evidence? provenance
Failure modes and hazards
Recalled without web access and unsourced; every item is a lead to verify.
- Confusing dimensionless conic eccentricity with mechanical eccentricity, which can mean a dimensional offset between centres or axes.
- Treating eccentricity as interchangeable with flattening or axis ratio.
- Applying the ellipse formula to a hyperbola.
- Assuming every irregular shape has a unique eccentricity without specifying a fitting or moment-based convention.
- Applying the finite focus-directrix construction directly to a circle instead of recognising its limiting status.
- Which of these failure modes and hazards hold for the sense of eccentricity this model covers, and on what evidence? provenance
Neighbouring kinds and how to tell them apart
Recalled without web access and unsourced; every item is a lead to verify.
- orbital eccentricity - Applies eccentricity to an orbital trajectory or an osculating conic and adds physical dynamics; geometric eccentricity does not require an orbit.
- flattening - For an ellipse, flattening is (a - b)/a, whereas eccentricity is sqrt(1 - b²/a²).
- axis ratio - The ratio b/a compares ellipse semiaxes directly; eccentricity is a nonlinear function of that ratio.
- mechanical eccentricity - Commonly denotes displacement between a centre or axis and a reference centre or axis, usually measured in units of length.
- graph eccentricity - Measures the greatest shortest-path distance from a vertex to other vertices, rather than the shape of a conic.
- behavioural eccentricity - Describes unconventional behaviour relative to social expectations and has no focus-directrix definition.
- Which of these neighbouring kinds and how to tell them apart hold for the sense of eccentricity this model covers, and on what evidence? provenance
What the second pass must settle
- Does the originating registry identifier denote conic eccentricity, or does XCT.QLT include a different intended sense?
- Does an existing Vercy world model already own general conic eccentricity and require this entry to link to it?
- Which authoritative mathematical references and conventions should govern circles, degenerate conics and parameter notation?
- Should eccentricity estimated from irregular shapes belong here as a documented conic approximation or to a separate shape-analysis model?
- What exact inheritance boundary does the separately registered orbital eccentricity model require?