{"doi":"10.48550/arXiv.2303.14555","author":[{"full_name":"Chern, Albert","last_name":"Chern","first_name":"Albert"},{"full_name":"Ishida, Sadashige","id":"6F7C4B96-A8E9-11E9-A7CA-09ECE5697425","last_name":"Ishida","first_name":"Sadashige"}],"day":"25","publication":"arXiv","type":"preprint","date_updated":"2023-04-25T06:51:21Z","external_id":{"arxiv":["2303.14555"]},"month":"03","article_processing_charge":"No","publication_status":"submitted","date_published":"2023-03-25T00:00:00Z","citation":{"short":"A. Chern, S. Ishida, ArXiv (n.d.).","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>","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>.","ista":"Chern A, Ishida S. Area formula for spherical polygons via prequantization. arXiv, 2303.14555.","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>","ieee":"A. Chern and S. Ishida, “Area formula for spherical polygons via prequantization,” <i>arXiv</i>. .","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>."},"main_file_link":[{"url":"https://arxiv.org/abs/2303.14555","open_access":"1"}],"abstract":[{"lang":"eng","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."}],"language":[{"iso":"eng"}],"department":[{"_id":"GradSch"},{"_id":"ChWo"}],"article_number":"2303.14555","_id":"12846","date_created":"2023-04-18T19:16:06Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"oa_version":"Preprint","year":"2023","status":"public","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).","title":"Area formula for spherical polygons via prequantization","project":[{"grant_number":"101045083","_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena"}]}