The DOI matches its Crossref record.
Automated generation of readable proofs with geometric invariants: II. Theorem proving with full-angles
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“| Search (human-like) | Full-angle method30 | 2 |”
From Solving olympiad geometry without human demonstrations (2024) · cites this paper as [30]
In the citing paper
“With the introduction of DD10,17, area methods61 and full-angle methods30, geometry solvers use higher-level deduction rules than Tarski’s or Hilbert’s axioms and are able to prove a larger number of more complex theorems than those operating in formal languages.”
From Solving olympiad geometry without human demonstrations (2024) · cites this paper as [30]
Citations
Cites
No references could be resolved yet.
Research works printed but not linked: 10
- Bancilhon, F. and Ramakrishnan, R.: An Amateur's introduction to recursive query processing strategies, in C. Zanioilo (ed.), Proc. ACM SIGMOD Conf., 1986, pp. 16–52. · DOI
- Chou, S. C., Gao, X. S., and Zhang, J. Z.: Machine Proofs in Geometry, World Scientific, 1994. · DOI
- Chou, S. C., Gao, X. S., and Zhang, J. Z.: Automated generation of readable proofs with geometric invariants, I. Multiple and shortest proof generation, J. Automated Reasoning 17 (1996), 325–347 (this issue). · DOI
- Chou, S. C., Gao, X. S., and Zhang, J. Z.: A Collection of 110 Geometry Theorems and Their Machine Proofs Based on Full-Angles, TR-94-4, CS Dept., WSU, Nov. 1994. · DOI
- Coelho, H. and Pereira, L. M.: Automated reasoning in geometry theorem proving with Prolog, J. Automated Reasoning 2 (1986), 329–390. · DOI
- Gerlentner, H., Hanson, J. R., and Loveland, D. W.: Empirical explorations of the geometrytheorem proving machine, in Proc. Est. Joint Computer Conf., 1960, pp. 143–147. · DOI
- Gilmore, P. C.: An examination of the geometry theorem proving machine, Artificial Intelligence 1 (1988), 171–187. · DOI
- Nevins, A. J.: Plane geometry theorem proving using forward chaining, Artificial Intelligence 6 (1977), 1–23. · DOI
- Stickel, M.: A prolog technology theorem prover: Implementation by an extended prolog compiler, J. Automated Reasoning 4(4) (1985), 353–380. · DOI
- Wen-tsün, Wu: Basic Principles of Mechanical Theorem Proving in Geometries, Vol. I: Part of Elementary Geometries, Science Press, Beijing, 1984 [in Chinese].
Cited by
Sorted by citations
Solving olympiad geometry without human demonstrations
Trinh, T. H., Wu, Y., Le, Q. V., He, H., & Luong, T. (2024) · Nature · doi:10.1038/s41586-023-06747-5 · Cited by 311
Metadata
- Authors
- Chou, S.-C., Gao, X.-S., & Zhang, J.-Z.
- Affiliations
- Wichita State University (US)
- ORCID
- Gao, Xiao-Shan
- Venue
- Journal of Automated Reasoning
- Published
- 1996-12
- Volume
- 17
- Issue
- 3
- Pages
- 349-370
- ISSN
- 0168-7433 (ISSN-L)
- 1573-0670
- OpenAlex
- W2762770850
- Cited by
- 79
- References
- 0
- Citations by year
- 2026: 4 · 2025: 2 · 2024: 4 · 2023: 9 · 2022: 3 · 2021: 7 · 2020: 4 · 2019: 4 · 2018: 3 · 2017: 3 · 2015: 2 · 2014: 2 · 2013: 1 · 2012: 4
- FWCI
- 2.18
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Journal of Automated Reasoning (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Polynomial and algebraic computation
- Physical Sciences › Mathematics › Geometry and Topology › Mathematics and Applications
- Physical Sciences › Computer Science › Software › Logic, programming, and type systems
- Keywords
- geometric invariants, forward chaining, backward chaining, area method
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
