{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T17:21:27Z","timestamp":1771003287750,"version":"3.50.1"},"reference-count":11,"publisher":"SAGE Publications","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JCM"],"published-print":{"date-parts":[[2021,11,1]]},"abstract":"<jats:p>The inverses of Jacobi elliptic functions possess an apparently-non-crucial property: they provide almost-everywhere-conformal maps on a hemisphere onto a torus and so, onto a parallelogram. Thus, they produce map projections on the sphere generalizing the famous quincuncial projection of Charles S. Peirce. Besides providing a general practical definition of n-uncial map and proving that all the considered inverse elliptic functions are n-uncial, we give operative handy formulas to calculate these maps. To the best of our knowledge, these useful formulas have not been all together published before, except for Pierce projection. We look forward to their numerical implementation. By the way, we also classify the resulting map projections according the number of singularities.<\/jats:p>","DOI":"10.3233\/jcm-215014","type":"journal-article","created":{"date-parts":[[2021,6,4]],"date-time":"2021-06-04T12:02:35Z","timestamp":1622808155000},"page":"1469-1483","source":"Crossref","is-referenced-by-count":0,"title":["Inverses and n-uncial property of Jacobian elliptic functions"],"prefix":"10.1177","volume":"21","author":[{"given":"Leonardo","family":"Solanilla","sequence":"first","affiliation":[]},{"given":"Jhonny Andr\u00e9s","family":"Leal","sequence":"additional","affiliation":[]},{"given":"Diego Mauricio","family":"Tique","sequence":"additional","affiliation":[]}],"member":"179","reference":[{"key":"10.3233\/JCM-215014_ref1","first-page":"263","article-title":"Recherches sur les fonctions elliptiques","volume":"2\u20133","author":"Abel","journal-title":"Journal f\u00fcr die Reine und Angewandte Mathematik, Herausgeben vor Crelle"},{"key":"10.3233\/JCM-215014_ref6","first-page":"15","article-title":"New methods to project panoramas for practical and aesthetic purposes","author":"German","year":"2007","journal-title":"Computational Aesthetics in Graphics, Visualization, and Imaging"},{"key":"10.3233\/JCM-215014_ref7","doi-asserted-by":"crossref","unstructured":"B. Grieger, Quincuncial adaptive closed kohonen (QuACK) map for the irregularly shaped comet 67P\/Churyumov-Gerasimenko, Astronomy & Physics, special issue A1 (2019).","DOI":"10.1051\/0004-6361\/201834841"},{"key":"10.3233\/JCM-215014_ref12","doi-asserted-by":"crossref","first-page":"563","DOI":"10.2307\/212415","article-title":"Some conformal projections based on elliptic functions","volume":"55","author":"Lee","year":"1965","journal-title":"Geographical Review"},{"key":"10.3233\/JCM-215014_ref15","doi-asserted-by":"crossref","first-page":"394","DOI":"10.2307\/2369491","article-title":"A quincuncial projection of the sphere","volume":"2","author":"Peirce","year":"1879","journal-title":"American Journal of Mathematics"},{"key":"10.3233\/JCM-215014_ref16","doi-asserted-by":"crossref","first-page":"145","DOI":"10.2307\/2369678","article-title":"Note on the C.S. Peirce\u2019s Paper on \u2018A Qincuncial Projection of the Sphere\u2019","volume":"18","author":"Pierpont","year":"1896","journal-title":"American Journal of Mathematics"},{"key":"10.3233\/JCM-215014_ref17","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.cub.2018.11.029","article-title":"Y chromosome sequences reveal a short beringian standstill, rapid expansion, and early population structure of native american founders","volume":"29","author":"Pinotti","year":"2019","journal-title":"Current Biology"},{"key":"10.3233\/JCM-215014_ref19","first-page":"225","article-title":"Darstellung einer beliebigen gegebenen Gr\u00f6\u00dfe durch \ud835\udc60\ud835\udc56\ud835\udc5b\ud835\udc4e\ud835\udc5a\u2062(u+w,k)","volume":"45","author":"Richelot","year":"1853","journal-title":"Journal f\u00fcr die Reine und Angewandte Mathematik"},{"key":"10.3233\/JCM-215014_ref21","doi-asserted-by":"crossref","first-page":"23","DOI":"10.18273\/revint.v34n1-2016002","article-title":"Peirce quincuncial projection","volume":"34","author":"Solanilla","year":"2016","journal-title":"Revista Integraci\u00f3n"},{"issue":"1","key":"10.3233\/JCM-215014_ref23","first-page":"19","article-title":"A quincuncial projection of the world","volume":"6","author":"Stanley","year":"1946","journal-title":"Surveying and Mapping"},{"key":"10.3233\/JCM-215014_ref24","doi-asserted-by":"crossref","unstructured":"D.B. Taylor and S.A. Bell, Astronomical applications of the quincuncial map projection, Astronomy & Geophysics 54 5 (2\u201913), 5.13\u20135.15.","DOI":"10.1093\/astrogeo\/att161"}],"container-title":["Journal of Computational Methods in Sciences and Engineering"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/JCM-215014","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T16:31:50Z","timestamp":1771000310000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/JCM-215014"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,1]]},"references-count":11,"journal-issue":{"issue":"5"},"URL":"https:\/\/doi.org\/10.3233\/jcm-215014","relation":{},"ISSN":["1472-7978","1875-8983"],"issn-type":[{"value":"1472-7978","type":"print"},{"value":"1875-8983","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,1]]}}}