Geometry Solver — Triangle implementation

Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

Record owner

Guth Instruments

Lifecycle

verified-with-binding-errata

Evidence ID

t4-153

Effect

Computation or source lookup only

Input and validation requirements

The instrument reaches undefined behavior for zero-angle SSA input, must reject exact triangle-inequality degeneracy, and has a major unhandled unit-convention ambiguity for numeric angles. The convention vector also exposes inconsistent intermediate arithmetic: the correct degree SAS results are c=1.001826 and area=0.104714.

Required corrections

[
  {
    "vector": 1,
    "field": "circumradius",
    "wrong": "2 cm",
    "correct": "2.5 cm",
    "cause": "working writes 60/24=2 (true 2.5)"
  },
  {
    "vector": 2,
    "field": "angles.A/B numeric",
    "wrong": "A≈43.945°, B≈76.055°",
    "correct": "A≈43.898°, B≈76.102°",
    "cause": "symbolic arccos(9/(2√39)) correct; numeric evaluation slipped"
  }
]

Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

{
  "inputs": {
    "case": "SSS",
    "a": 3,
    "b": 4,
    "c": 5,
    "length_unit": "cm"
  },
  "expected_outputs": {
    "angles": {
      "A": "36.86989765°",
      "B": "53.13010235°",
      "C": "90°"
    },
    "area": "6 cm²",
    "perimeter": "12 cm",
    "altitudes": {
      "h_a": "4 cm",
      "h_b": "3 cm",
      "h_c": "2.4 cm"
    },
    "inradius": "1 cm",
    "circumradius": "2 cm",
    "classification": "right"
  },
  "working": "s=(3+4+5)/2=6. Heron area=√(6(6−3)(6−4)(6−5))=√(6×3×2×1)=√36=6 cm². Perimeter=3+4+5=12 cm. h_a=2K/a=2×6/3=4 cm; h_b=2×6/4=3 cm; h_c=2×6/5=2.4 cm. r=K/s=6/6=1 cm. R=abc/(4K)=(3×4×5)/(4×6)=60/24=2 cm. cos C=(a²+b²−c²)/(2ab)=(9+16−25)/(24)=0, so C=90°; A=arcsin(3/5)=36.86989765° and B=90°−A=53.13010235°."
}

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche4/tranche4-results.json
• tranche errata record