[{"acknowledgement":"This work was funded by European Research Council Consolidator grant 101045083 CoDiNA and National Science Foundation CAREER award 2239062. Some figures in the article were generated by the software Houdini and its education license was provided by SideFX. The authors acknowledge anonymous referees for their reviews and insightful suggestions, and Chris Wojtan for his continuous support through discussions. The second author thanks Anna Sisak for a fruitful discussion on prequantum bundles.","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2026-04-07T12:02:22Z","page":"782-796","citation":{"chicago":"Chern, Albert, and Sadashige Ishida. “Area Formula for Spherical Polygons via Prequantization.” <i>SIAM Journal on Applied Algebra and Geometry</i>. Society for Industrial and Applied Mathematics, 2024. <a href=\"https://doi.org/10.1137/23M1565255\">https://doi.org/10.1137/23M1565255</a>.","mla":"Chern, Albert, and Sadashige Ishida. “Area Formula for Spherical Polygons via Prequantization.” <i>SIAM Journal on Applied Algebra and Geometry</i>, vol. 8, no. 3, Society for Industrial and Applied Mathematics, 2024, pp. 782–96, doi:<a href=\"https://doi.org/10.1137/23M1565255\">10.1137/23M1565255</a>.","ama":"Chern A, Ishida S. Area formula for spherical polygons via prequantization. <i>SIAM Journal on Applied Algebra and Geometry</i>. 2024;8(3):782-796. doi:<a href=\"https://doi.org/10.1137/23M1565255\">10.1137/23M1565255</a>","ieee":"A. Chern and S. Ishida, “Area formula for spherical polygons via prequantization,” <i>SIAM Journal on Applied Algebra and Geometry</i>, vol. 8, no. 3. Society for Industrial and Applied Mathematics, pp. 782–796, 2024.","apa":"Chern, A., &#38; Ishida, S. (2024). Area formula for spherical polygons via prequantization. <i>SIAM Journal on Applied Algebra and Geometry</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/23M1565255\">https://doi.org/10.1137/23M1565255</a>","ista":"Chern A, Ishida S. 2024. Area formula for spherical polygons via prequantization. SIAM Journal on Applied Algebra and Geometry. 8(3), 782–796.","short":"A. Chern, S. Ishida, SIAM Journal on Applied Algebra and Geometry 8 (2024) 782–796."},"abstract":[{"text":"We present a formula for the signed area of a spherical polygon via prequantization. In contrast to the traditional formula based on the Gauss-Bonnet theorem that requires measuring angles, the new formula mimics Green's theorem and is applicable to a wider range of degenerate spherical curves and polygons.","lang":"eng"}],"_id":"12846","doi":"10.1137/23M1565255","article_processing_charge":"No","oa_version":"Preprint","OA_type":"green","type":"journal_article","project":[{"name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena","grant_number":"101045083","_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088"}],"publication":"SIAM Journal on Applied Algebra and Geometry","volume":8,"day":"23","month":"09","language":[{"iso":"eng"}],"external_id":{"arxiv":["2303.14555"],"isi":["001342265800009"]},"corr_author":"1","publication_status":"published","department":[{"_id":"GradSch"},{"_id":"ChWo"}],"has_accepted_license":"1","arxiv":1,"status":"public","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"author":[{"first_name":"Albert","full_name":"Chern, Albert","last_name":"Chern"},{"full_name":"Ishida, Sadashige","last_name":"Ishida","orcid":"0000-0002-3121-3100","id":"6F7C4B96-A8E9-11E9-A7CA-09ECE5697425","first_name":"Sadashige"}],"OA_place":"repository","publisher":"Society for Industrial and Applied Mathematics","intvolume":"         8","year":"2024","publication_identifier":{"eissn":["2470-6566"]},"ddc":["516"],"date_created":"2023-04-18T19:16:06Z","quality_controlled":"1","isi":1,"date_published":"2024-09-23T00:00:00Z","related_material":{"record":[{"status":"public","id":"20551","relation":"dissertation_contains"}]},"scopus_import":"1","article_type":"original","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2303.14555"}],"title":"Area formula for spherical polygons via prequantization","issue":"3"}]