Public evidence

math.geometry.plane

Machine-checked verification for calculation version 1.5.0 · tier engine_tested

Open calculator API Capability Download JSON CVP Manifest MCP Review policy

Historical evidence. This page is version 1.5.0 · engine_tested · 25/25 tests. It is not the current published claim. Current evidence is 1.6.0 (25/25 tests) · latest.

CVP status

Not the circle-only page, not a triangle solver, not solid geometry, not the fluid trapezoid, not trapezoidal-rule, not CAS. Declared partitions are the 7 published modes plus invalid-domain.

Declared partition coverage: PASS · 8/8 declared partitions (rectangle, square, regular-polygon, annulus, parallelogram, trapezoid, irregular-polygon, invalid-domain)
Versions: Calculation 1.5.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-22.geometry-cvp
Verification revision: 2026-09-22.geometry-cvp · 4/4 property · digest dcd9f429cc7c

Verification

Legacy regression suite: 25/25 calculation tests · Production surface contract 5/5

Three distinct suites: educational examples on the calculator page, this legacy regression count (25/25 golden + boundary), and the CVP verification suite below. They are not the same number. Property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the CVP Manifest . SKIP (0/0) means that suite has no published vectors.

STALE · Build schema 1.6.0 matches page · production binding STALE · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · CVP STALE · attestation STALE — Production CURRENT withheld · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-09-22.geometry-cvp. Calculation version 1.5.0. CVP 1.0.0-proposed. 10/10 golden · 5/5 CVP boundary · 11/11 invalid · 4/4 property · 5/5 cross-interface · 5/5 cross-calculator · 5/5 CVP contract. digest dcd9f429cc7c.

Golden (oracle-backed) 10 / 10
CVP boundary 5 / 5
Invalid input 11 / 11
Property 4 / 4
Cross-interface 5 / 5
Cross-calculator 5 / 5
CVP contract 5 / 5
Interfaces PASS · UI (SSR) / REST / MCP
Interface claim ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
Verified scope all published modes
Assurance Core

release artifacts aligned PASS
schema output required declared PASS
schema valid input executes PASS
engine success output validates schema PASS
rest success payload validates schema PASS

Fingerprint sha256:8b1a25bde28dba84322ff335d917d048ff26b6d93b75e2ee6c500c523b181eff

Input schema sha256:5039fac5be916efbd613bac465d29e64c0e098f17efb094b415669d76b6ace36 · Output schema sha256:4f46ff37a1617bce5f50363a965f32b87ec3740b942f35bfdb40fa31ca592515 · Build-time SHA-256 digests prove published artifacts agree with each other (release_integrity.scope=workspace). Production attestation GETs canonical URLs twice (public/cached view and origin), including Capability HTML, via npm run attest:production --write (published at /.well-known/calculatorx-production-attestation.json) and fails if the public Capability page advertises a different calculation_version. This is artifact consistency, not an independent immutable release log.

Build & scope

Engine identity and declared limitations.

Tool: plane-geometry
Engine: plane-geometry
Engine build: 2026-10-14
Evidence core: 2026-10-14T05:05:51.930Z
Rendered: 2026-10-20T02:41:58.125Z
Last reviewed: —

Assumptions

Euclidean plane
Regular polygon integer n ≥ 3
Annulus R > r
Parallelogram θ in (0°, 180°)
Isosceles trapezoid a, b, h > 0
Irregular polygon shoelace 3–8 vertices
Not the circle-only page
Not a triangle solver
Not solid geometry
Not /trapezoidal-rule
Not the fluid trapezoid
Not CAS

Limitations

Euclidean plane figures only
Not the circle-only page — 2-D circle stays on math.geometry.circle
Not a triangle solver — SSS/SAS stay on math.geometry.triangle
Not solid geometry (sphere / cylinder / cone)
Regular polygon needs integer n ≥ 3
Annulus needs outer R > inner r; R = r is a circle, not an annulus
Parallelogram included angle θ must be in (0°, 180°); θ=90° recovers a rectangle
Isosceles trapezoid needs bases a,b>0 and height h>0; a=b recovers a rectangle; not the fluid trapezoid; not /trapezoidal-rule
Irregular polygon uses shoelace on 3–8 vertices; simple polygon assumed; area 0 is invalid; not /regular-polygon; not a triangle solver
unknown mode (including cas, sphere, pythagorean) → INVALID_MODE

Sources

Standards and references supporting this tool specification. Methods are listed separately — they are algorithms, not bibliographic sources.

ISO 80000-2:2019 Quantities and units — Mathematics
Supports: Mathematical symbols and notation. This standard is not numerical verification or an endorsement of this implementation.
CRC Standard Mathematical Tables — plane polygons
Supports: Regular n-gon A = (n s²)/(4 tan(π/n)); parallelogram A = ab sin θ; shoelace / Meister–Gauss polygon area
Euclid’s Elements — I.35: Parallelograms on the Same Base
Supports: Equal-base, equal-height parallelograms have equal area. Comparing with a rectangle gives A = base × perpendicular height; side length is not generally the height. Mathematical reference only; not validation or endorsement of this implementation.
Gilbert Strang, Calculus — Chapter 9: Polar Coordinates and Complex Numbers (MIT OpenCourseWare) — §§9.1–9.3 Polar Coordinates, Length and Area
Supports: Polar coordinates and the circular wedge area r²Δθ/2, together with area = ∫r² dθ/2 and polar arc-length integration. A full turn gives disk area πr² and circumference 2πr. An annulus follows by subtracting disk areas and adding both boundary lengths; these are derived applications. Mathematical reference only; not implementation validation or an endorsement of CalculatorX.
Gilbert Strang, Calculus — Chapter 15: Vector Calculus (MIT OpenCourseWare) — §15.3 Green’s Theorem
Supports: The planar area formula A = (1/2) ∮(x dy − y dx). For straight polygon edges it gives the shoelace expression; rectangular/square areas and trapezoid area (B+b)h/2 follow by applying it to the vertices. For x=a cos t, y=b sin t it gives ellipse area πab. Perimeters of these polygons are sums of side lengths. These formulas are derived applications of the theorem. Mathematical reference only; not implementation validation or an endorsement of CalculatorX.
Gilbert Strang, Calculus — Chapter 1: Introduction to Calculus (MIT OpenCourseWare) — §1.5 A Review of Trigonometry
Supports: Right-triangle definitions of sine, cosine and tangent, the sine/cosine identities, and the law-of-cosines and parallelogram exercises 31–32. Chord length follows by bisecting the radii triangle. Regular-polygon apothems and areas follow by splitting the polygon into equal triangles. The law of sines follows by equating a triangle’s altitude computed from either adjacent side; SSA can give two triangles. These applications are derived from the stated relations. Mathematical reference only; not implementation validation or an endorsement of CalculatorX.

Verification disclosure

Aggregate outcomes, scope and artifact commitments are public. Complete test inputs, expected values, execution records and oracle infrastructure are retained privately. This summary does not independently reproduce the full verification run.