---
OA_place: repository
OA_type: green
_id: '12846'
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.
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.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Albert
  full_name: Chern, Albert
  last_name: Chern
- first_name: Sadashige
  full_name: Ishida, Sadashige
  id: 6F7C4B96-A8E9-11E9-A7CA-09ECE5697425
  last_name: Ishida
  orcid: 0000-0002-3121-3100
citation:
  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>
  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>
  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>.
  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.
  ista: Chern A, Ishida S. 2024. Area formula for spherical polygons via prequantization.
    SIAM Journal on Applied Algebra and Geometry. 8(3), 782–796.
  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>.
  short: A. Chern, S. Ishida, SIAM Journal on Applied Algebra and Geometry 8 (2024)
    782–796.
corr_author: '1'
date_created: 2023-04-18T19:16:06Z
date_published: 2024-09-23T00:00:00Z
date_updated: 2026-04-07T12:02:22Z
day: '23'
ddc:
- '516'
department:
- _id: GradSch
- _id: ChWo
doi: 10.1137/23M1565255
external_id:
  arxiv:
  - '2303.14555'
  isi:
  - '001342265800009'
has_accepted_license: '1'
intvolume: '         8'
isi: 1
issue: '3'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2303.14555
month: '09'
oa: 1
oa_version: Preprint
page: 782-796
project:
- _id: 34bc2376-11ca-11ed-8bc3-9a3b3961a088
  grant_number: '101045083'
  name: Computational Discovery of Numerical Algorithms for Animation and Simulation
    of Natural Phenomena
publication: SIAM Journal on Applied Algebra and Geometry
publication_identifier:
  eissn:
  - 2470-6566
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
related_material:
  record:
  - id: '20551'
    relation: dissertation_contains
    status: public
scopus_import: '1'
status: public
title: Area formula for spherical polygons via prequantization
tmp:
  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)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 8
year: '2024'
...