CVP verified calculation capability

Plane geometry Calculation Capability

Seven Euclidean plane shapes: rectangle, square, regular polygon, annulus, parallelogram, isosceles trapezoid and validated simple polygon. Complete area/perimeter and secondary measures; consistent length units, angles in degrees.

Math · Geometry Capability ID math.geometry.plane version 1.6.0 CVP VERIFIED CURRENT Core

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)|

Inputs / Outputs

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

Symbol	Quantity	Unit policy	Role
`a`	length	consistent length unit	input / output
`width`	Strict bounded decimal number/string; finite normal binary64 after conversion, except exact zero coordinates	—	input
`length`	Strict bounded decimal number/string; finite normal binary64 after conversion, except exact zero coordinates	—	input
`b`	length	consistent length unit	input / output
`height`	length	consistent length unit	input / output
`s`	length	consistent length unit	input / output
`side`	Strict bounded decimal number/string; finite normal binary64 after conversion, except exact zero coordinates	—	input
`n`	Strict bounded decimal number/string; finite normal binary64 after conversion, except exact zero coordinates	—	input / output
`sides`	Strict bounded decimal number/string; finite normal binary64 after conversion, except exact zero coordinates	—	input
`R`	length	consistent length unit	input / output
`outer`	Strict bounded decimal number/string; finite normal binary64 after conversion, except exact zero coordinates	—	input
`R_outer`	Strict bounded decimal number/string; finite normal binary64 after conversion, except exact zero coordinates	—	input
`r`	length	consistent length unit	input / output
`inner`	Strict bounded decimal number/string; finite normal binary64 after conversion, except exact zero coordinates	—	input
`r_inner`	Strict bounded decimal number/string; finite normal binary64 after conversion, except exact zero coordinates	—	input
`theta`	scalar plane angle	—	input / output
`angle`	scalar plane angle	—	input
`deg`	scalar plane angle	—	input
`h`	length	consistent length unit	input / output
`vertices`	3–8 distinct ordered simple-polygon vertices, optional repeated closing vertex	—	input / output
`points`	3–8 distinct ordered simple-polygon vertices, optional repeated closing vertex	—	input
`vertices_xy`	3–8 distinct ordered simple-polygon vertices, optional repeated closing vertex	—	input
`base2`	Strict bounded decimal number/string; finite normal binary64 after conversion, except exact zero coordinates	—	input
`base`	Strict bounded decimal number/string; finite normal binary64 after conversion, except exact zero coordinates	—	input
`base1`	Strict bounded decimal number/string; finite normal binary64 after conversion, except exact zero coordinates	—	input
`side2`	Strict bounded decimal number/string; finite normal binary64 after conversion, except exact zero coordinates	—	input
`area`	area	square of input unit	output
`perimeter`	length	same length unit	output
`diagonal`	length	consistent length unit	output
`apothem`	length	consistent length unit	output
`circumradius`	length	consistent length unit	output
`interior_deg`	scalar plane angle	—	output
`central_deg`	scalar plane angle	—	output
`d1`	—	—	output
`d2`	—	—	output
`leg`	—	—	output
`midsegment`	—	—	output
`outer_circumference`	—	—	output
`inner_circumference`	—	—	output
`square`	—	—	output
`rectangle`	—	—	output
`isosceles`	—	—	output
`model`	—	—	output

Trusted Math contract

Inspectable numeric contract for this Capability@Version. Not a rewrite of the engine.

Field	Declaration
`numeric_domain`	real
`exactness`	float64
`algorithm`	Exact dyadic polynomial areas, factored annulus and trapezoid, scaled norms, half-angle parallelogram diagonals; exact polygon orientation/intersection predicates and area, bounded8-vertex perimeter walk
`valid_domain`	Strict decimal numbers/strings, positive normal binary64 dimensions; degree angle0<theta<180 with normal radian conversion; integer3<=n<=9007199254740991. Simple ordered3–8 vertices, exact zero coordinates allowed, other coordinates normal binary64. Optional repeated closing vertex. Positive output measures must be finite normal binary64.
`singularity_policy`	INVALID_INPUT for invalid domains, duplicate vertices, self-crossing/touching/overlapping nonadjacent edges or adjacent backtracking and zero area. NUMERIC_UNDERFLOW for nonzero decimal text converted to zero; NUMERIC_RANGE for nonnormal inputs/outputs. Rescale units or translate coordinates.
`branch_policy`	not applicable — real principal value only
`tolerance`	type: relative; value: 1e-11; note: Arithmetic results against independent Fraction/mpmath750 references; discrete/zero/structure checks separate. Not an input perturbation bound.
`convergence`	not applicable — non-iterative
`conditioning`	Thin rings, near-flat figures and small polygon offsets are input-sensitive. Exact predicates and arithmetic concern normalized binary64; input decimal rounding can change topology or erase small lengths. No rounding clamp. A diagram can be omitted while numerical results remain complete; regular rendering bounded to128 sides.
`rounding`	ieee754_round_ties_to_even
`overflow`	ieee754_nonfinite_or_coded_error
`reproducibility`	deterministic algorithm + Capability@Version
`independent_oracle`	cvp:math.geometry.plane private Python Fraction fan-triangle area and mpmath750 Euclidean reference
`golden_vectors`	Evidence golden + boundary + property (and published_reference_case when listed)

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

CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance · all published modes. Computational verification is defined by CVP. Supplemental domain review (internal) and named expert review are defined by the Review policy and do not by themselves determine CVP conformance.

CVP: CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance · all published modes· View Manifest · CVP overview · Specification
Verified scope: all published modes
Assurance: Core
Declared partition coverage: PASS · 8/8 declared partitions (rectangle, square, regular-polygon, annulus, parallelogram, trapezoid, irregular-polygon, invalid-domain)
Calculation version: 1.6.0
Verification: 25/25 calculation tests · 9/9 legacy golden · 5/5 legacy boundary · 11/11 legacy property
Production surface contract: 5/5
Versions: Calculation 1.6.0 · CVP protocol 1.0.0-proposed · Evidence 2026-10-29.math-uuce-fields-v1
Verification revision: 2026-10-29.math-uuce-fields-v1 · 4/4 property · digest dfee395590c2
Reference: O1 model · O2 expected_values · O2 numerical_behavior
Interfaces: PASS · UI (SSR) / REST / MCP
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.
CVP suite: 155/155 golden · 5/5 CVP boundary · 55/55 invalid · 4/4 property · 4/4 metamorphic · 5/5 cross-interface · 2/2 cross-calculator · 5/5 CVP contract
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.6.0 (workspace artifacts agree)
Review-policy tier: Engine tested — catalog token engine_tested; supplemental; not CVP status

This calculator CURRENT · Public schema 1.6.0 matches · Semantic contract ✓ · Production attested · 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 5/5.

curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/plane-geometry' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"mode":"rectangle","a":3,"b":4},"calculation_version":"1.6.0"}'

{
  "inputs": {
    "mode": "rectangle",
    "a": 3,
    "b": 4
  },
  "calculation_version": "1.6.0"
}

POST /api/v1/calc/plane-geometry. This is a POST calculate endpoint — do not GET it.

Full REST contract: REST API docs.

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 (1.6.0)
Versioned output schema: Immutable pin (1.6.0)

References

Human-readable sources plus CVP reference evidence classes.

Sources

Reference evidence classes: O1 model · O2 expected_values · O2 numerical_behavior

Try with an agent

Inspect, then execute. Same engine as REST and the human calculator.

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"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

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: execute_calculation' \
  -d '{"jsonrpc":"2.0","id":2,"method":"tools/call","params":{"name":"execute_calculation","arguments":{"capability_id":"math.geometry.plane","inputs":{"mode":"rectangle","a":3,"b":4},"calculation_version":"1.6.0"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

Pin calculation_version (1.6.0) when the result must stay reproducible.

Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.