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task_geometry__regular_polygon_decomposition__side_length_value

Contract

  1. Domain: geometry
  2. Scene id: regular_polygon_decomposition
  3. Task id: task_geometry__regular_polygon_decomposition__side_length_value
  4. Supported query_id values: side_length_from_perimeter, side_length_from_total_area_and_apothem, side_length_from_wedge_area_and_apothem
  5. Answer schema: integer
  6. Annotation schema: point_map
  7. Scalar annotation checked: true (not scalar-eligible; the task binds polygon center, target side endpoints, and sometimes apothem-foot or wedge-region roles)

Program Contract

  • solve_formula(regular_polygon_equal_wedge_decomposition, target=regular_polygon_side_length, formula_schema=perimeter_divided_by_side_count_or_area_apothem_relation); scene=regular_polygon_decomposition; scope=side_length_value

Reasoning Operations

Families: counting, formula_evaluation

Query Semantics

  • side_length_from_perimeter asks for one regular-polygon side length from the visible total perimeter.
  • side_length_from_total_area_and_apothem asks for one regular-polygon side length from total area and apothem labels.
  • side_length_from_wedge_area_and_apothem asks for one regular-polygon side length from shaded wedge area and apothem labels.
  • The number of polygon sides, selected side, style, font, layout jitter, and rotation are internal replay metadata.

Prompt Bundle

  • Prompt text is loaded from src/trace_tasks/resources/prompts/geometry/regular_polygon_decomposition/geometry_regular_polygon_decomposition_v1.json.
  • Prompt modes: answer_only and answer_and_annotation.

Annotation

Prompt-facing annotation uses pixel-space point map keys O, A, B, and, when needed, M and W. These mark the polygon center, target side endpoints, apothem foot, and target wedge-region point. Measurement labels and readout panels remain visible diagram content and private verifier metadata.

Determinism

Generation is deterministic for a fixed seed, params, config, and prompt bundle version.

Source

  • Config: src/trace_tasks/resources/configs/domains/geometry/regular_polygon_decomposition.yaml
  • Prompt bundle: src/trace_tasks/resources/prompts/geometry/regular_polygon_decomposition/geometry_regular_polygon_decomposition_v1.json
  • Task module: src/trace_tasks/tasks/geometry/regular_polygon_decomposition/side_length_value.py