{"title":"Area formula for spherical polygons via prequantization","external_id":{"arxiv":["2303.14555"]},"project":[{"_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena","grant_number":"101045083"}],"citation":{"chicago":"Chern, Albert, and Sadashige Ishida. “Area Formula for Spherical Polygons via Prequantization.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2303.14555\">https://doi.org/10.48550/arXiv.2303.14555</a>.","ieee":"A. Chern and S. Ishida, “Area formula for spherical polygons via prequantization,” <i>arXiv</i>. .","apa":"Chern, A., &#38; Ishida, S. (n.d.). Area formula for spherical polygons via prequantization. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2303.14555\">https://doi.org/10.48550/arXiv.2303.14555</a>","mla":"Chern, Albert, and Sadashige Ishida. “Area Formula for Spherical Polygons via Prequantization.” <i>ArXiv</i>, 2303.14555, doi:<a href=\"https://doi.org/10.48550/arXiv.2303.14555\">10.48550/arXiv.2303.14555</a>.","short":"A. Chern, S. Ishida, ArXiv (n.d.).","ista":"Chern A, Ishida S. Area formula for spherical polygons via prequantization. arXiv, 2303.14555.","ama":"Chern A, Ishida S. Area formula for spherical polygons via prequantization. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2303.14555\">10.48550/arXiv.2303.14555</a>"},"publication":"arXiv","date_updated":"2023-04-25T06:51:21Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"12846","status":"public","type":"preprint","acknowledgement":"The authors acknowledge Chris Wojtan for his continuous support to the present work through discussions and advice. The second author thanks Anna Sisak for a fruitful discussion on prequantum bundles. This project was funded in part by the European Research Council (ERC Consolidator Grant 101045083 CoDiNA).","year":"2023","article_processing_charge":"No","author":[{"full_name":"Chern, Albert","first_name":"Albert","last_name":"Chern"},{"id":"6F7C4B96-A8E9-11E9-A7CA-09ECE5697425","first_name":"Sadashige","last_name":"Ishida","full_name":"Ishida, Sadashige"}],"oa_version":"Preprint","department":[{"_id":"GradSch"},{"_id":"ChWo"}],"month":"03","date_published":"2023-03-25T00:00:00Z","day":"25","publication_status":"submitted","doi":"10.48550/arXiv.2303.14555","date_created":"2023-04-18T19:16:06Z","article_number":"2303.14555","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2303.14555"}],"oa":1,"language":[{"iso":"eng"}],"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"}]}