Angle–Slack Accounting and Minimality Heuristics for Triangle-to-Square Dissections
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| Natura: | Recurso digital |
| Lingua: | inglese |
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Zenodo
2026
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| _version_ | 1866901889824587776 |
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| author | Bailey, William |
| author_facet | Bailey, William |
| contents | <p>This note introduces an angle–slack bookkeeping framework for planar dissections, encoding local angle constraints via a typed cut graph. Interior “slack” vertices represent degrees of freedom that cannot be eliminated under local moves but may be transported through junctions. The framework explains persistent obstructions in three-piece dissections of an equilateral triangle to a square and clarifies why four pieces form the minimal entropy sink. Beyond classical dissection puzzles, the method illustrates a general invariant-based approach relevant to rigidity, obstruction theory, curvature accounting, and scissors congruence.</p> <p>This work was developed through interactive collaboration between William M. Bailey III and ChatGPT (GPT-5.2 Thinking). The framework and exposition emerged via iterative human–AI co-reasoning.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18253996 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Angle–Slack Accounting and Minimality Heuristics for Triangle-to-Square Dissections Bailey, William geometry; dissections; rigidity; obstruction theory; angle deficits; scissors congruence; Gauss–Bonnet; combinatorial topology; mathematical invariants <p>This note introduces an angle–slack bookkeeping framework for planar dissections, encoding local angle constraints via a typed cut graph. Interior “slack” vertices represent degrees of freedom that cannot be eliminated under local moves but may be transported through junctions. The framework explains persistent obstructions in three-piece dissections of an equilateral triangle to a square and clarifies why four pieces form the minimal entropy sink. Beyond classical dissection puzzles, the method illustrates a general invariant-based approach relevant to rigidity, obstruction theory, curvature accounting, and scissors congruence.</p> <p>This work was developed through interactive collaboration between William M. Bailey III and ChatGPT (GPT-5.2 Thinking). The framework and exposition emerged via iterative human–AI co-reasoning.</p> |
| title | Angle–Slack Accounting and Minimality Heuristics for Triangle-to-Square Dissections |
| topic | geometry; dissections; rigidity; obstruction theory; angle deficits; scissors congruence; Gauss–Bonnet; combinatorial topology; mathematical invariants |
| url | https://doi.org/10.5281/zenodo.18253996 |