Verified calculation capability

Plane geometry Calculation Capability

Rectangle, square, regular n-gon, annulus, parallelogram, isosceles trapezoid, and irregular polygon (shoelace). Discovery /rectangle, /regular-polygon, /parallelogram, /trapezoid, /irregular-polygon. Not the circle-only page, not a triangle solver, not solid geometry, not the fluid trapezoid, not /trapezoidal-rule, not CAS. · Math · Geometry

Capability ID math.geometry.plane · version 1.3.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Rectangle

Rectangle: A = ab, P = 2(a+b), d = √(a²+b²)
Regular polygon: A = (n s²) / (4 tan(π/n))
Annulus: A = π(R² − r²)
Parallelogram: A = ab sin θ
Trapezoid: A = (a+b)h/2
Irregular polygon: A = (1/2)|Σ (xᵢ yᵢ₊₁ − xᵢ₊₁ yᵢ)|

Solve modes: rectangle · square · regular polygon · annulus · parallelogram · trapezoid · irregular polygon

Inputs / Outputs

Canonical symbols for this capability. Agent schemas remain the contract.

Symbol	Quantity	Unit	Role
`a`	acceleration	—	input / output
`b`	—	—	input / output
`s`	—	—	input / output
`n`	amount of substance	—	input / output
`r`	—	—	input / output
`R`	—	—	input / output
`theta`	—	—	input / output
`angle`	—	—	input
`h`	hydrogen-ion concentration	—	input / output
`vertices`	—	—	input
`area`	—	—	output
`perimeter`	—	—	output
`diagonal`	—	—	output
`apothem`	—	—	output
`circumradius`	—	—	output
`interior_deg`	—	—	output
`d1`	—	—	output
`d2`	—	—	output
`height`	—	—	output
`rectangle`	—	—	output
`leg`	—	—	output
`midsegment`	—	—	output
`isosceles`	—	—	output

Assumptions / Validity

Declared scope for this capability. Do not use it outside this domain.

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

Example

One numerical check. The calculator page holds worked steps and FAQ.

rectangle a=3 b=4 → A=12, d=5

Open this example in the calculator

Trust

Review-policy: engine tested — automated tests, sources, version lock, and evidence published. Supplemental to CVP; not Domain Expert Review. See CVP and Review policy.

Tier: Engine tested — catalog token engine_tested
Calculation version: 1.3.0
Evidence tests: 25/25 calculation tests · golden 9/9 · boundary 5/5 · property 11/11
Engine tested: Yes
Source checked: Yes
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.3.0 (workspace artifacts agree)

Production attestation: Embedded snapshot: unpublished · Build schema 1.3.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (2 capabilities; 162 remain CURRENT) @ 2026-09-20T09:01:12.147Z
Semantic contract: PASS
Evidence attested at: 2026-09-18T21:41:55.460Z
Last production check: 2026-09-18T21:41:55.460Z
Public / cache: —
Origin: —

Call this capability

Human page, REST, and MCP share the same engine and calculation_version. Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Reference Calculation Standard — Production surface contract 3/3.

Tool id: plane-geometry
Engine: plane-geometry
REST: POST /api/v1/calc/plane-geometry
MCP: execute_calculation with capability_id: "math.geometry.plane"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.3.0)
Versioned output schema: Immutable pin (1.3.0)

References

Human-readable sources plus CVP reference evidence classes.

Sources

ISO 80000-2:2019 Quantities and units — Mathematics

Try with an agent

Inspect this capability via same-origin MCP, then call execute_calculation.

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: inspect_capability' \
  -d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"math.geometry.plane"}}}'

Inspect the trust tier and required assurance level before execution. Pin calculation_version (1.3.0) when reproducibility matters. Full protocol notes: MCP docs.