{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,22]],"date-time":"2025-05-22T23:03:37Z","timestamp":1747955017991},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2012,8,2]],"date-time":"2012-08-02T00:00:00Z","timestamp":1343865600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2012,10]]},"DOI":"10.1007\/s00454-012-9448-y","type":"journal-article","created":{"date-parts":[[2012,8,1]],"date-time":"2012-08-01T13:20:32Z","timestamp":1343827232000},"page":"580-595","source":"Crossref","is-referenced-by-count":6,"title":["Affine Properties of Convex Equal-Area Polygons"],"prefix":"10.1007","volume":"48","author":[{"given":"Marcos","family":"Craizer","sequence":"first","affiliation":[]},{"given":"Ralph C.","family":"Teixeira","sequence":"additional","affiliation":[]},{"given":"Moacyr A. H. B.","family":"da Silva","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,8,2]]},"reference":[{"key":"9448_CR1","volume-title":"Affine Differential Geometry","author":"S. Buchin","year":"1983","unstructured":"Buchin, S.: Affine Differential Geometry. Science Press, New York (1983)"},{"key":"9448_CR2","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1023\/A:1004903818702","volume":"69","author":"J.C. Fischer","year":"1998","unstructured":"Fischer, J.C., Jamison, R.E.: Properties of affinely regular polygons. Geom. Dedic. 69, 241\u2013259 (1998)","journal-title":"Geom. Dedic."},{"key":"9448_CR3","doi-asserted-by":"crossref","first-page":"581","DOI":"10.2307\/2313773","volume":"75","author":"H. Flanders","year":"1968","unstructured":"Flanders, H.: A proof of Mankowski\u2019s inequality for convex curves. Am. Math. Mon. 75, 581\u2013593 (1968)","journal-title":"Am. Math. Mon."},{"key":"9448_CR4","unstructured":"http:\/\/www.geogebra.org\/cms"},{"key":"9448_CR5","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1023\/A:1005099011913","volume":"71","author":"P.J. Giblin","year":"1998","unstructured":"Giblin, P.J., Sapiro, G.: Affine-invariant distances, envelopes and symmetry sets. Geom. Dedic. 71, 237\u2013261 (1998)","journal-title":"Geom. Dedic."},{"key":"9448_CR6","series-title":"Banach Center Publications","doi-asserted-by":"crossref","first-page":"71","DOI":"10.4064\/bc82-0-5","volume-title":"Geometry and Topology of Caustics (Caustics 06)","author":"P.J. Giblin","year":"2008","unstructured":"Giblin, P.J.: Affinely invariant symmetry sets. In: Geometry and Topology of Caustics (Caustics 06). Banach Center Publications, vol. 82, pp. 71\u201384 (2008)"},{"key":"9448_CR7","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1007\/s00454-007-9010-5","volume":"39","author":"P. Gronchi","year":"2008","unstructured":"Gronchi, P., Longinetti, M.: Affinely regular polygons as extremals of area functionals. Discrete Comput. Geom. 39, 272\u2013297 (2008)","journal-title":"Discrete Comput. Geom."},{"key":"9448_CR8","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-5858-8","volume-title":"Convexity and Its Applications","author":"P. Gruber","year":"1983","unstructured":"Gruber, P.: Approximation of convex bodies. In: Convexity and Its Applications, vol. 131. Birkh\u00e4user, Basel (1983)"},{"key":"9448_CR9","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/B978-0-444-89596-7.50015-8","volume-title":"Handbook of Convex Geometry","author":"P. Gruber","year":"1993","unstructured":"Gruber, P.: Aspects of approximation of convex bodies. In: Handbook of Convex Geometry, pp. 319\u2013346. North-Holland, Amsterdam (1993)"},{"key":"9448_CR10","doi-asserted-by":"crossref","first-page":"606","DOI":"10.2307\/3647745","volume":"110","author":"G. Harel","year":"2003","unstructured":"Harel, G., Rabin, J.M.: Polygons whose vertex triangles have equal area. Am. Math. Mon. 110, 606\u2013619 (2003)","journal-title":"Am. Math. Mon."},{"key":"9448_CR11","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1007\/BF01189576","volume":"63","author":"M. Ludwig","year":"1994","unstructured":"Ludwig, M.: Asymptotic approximation of convex curves. Arch. Math. 63, 377\u2013384 (1994)","journal-title":"Arch. Math."},{"key":"9448_CR12","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1016\/0022-247X(75)90125-0","volume":"51","author":"D. McClure","year":"1975","unstructured":"McClure, D., Vitale, R.: Polygonal approximation of plane curves. J. Math. Anal. Appl. 51, 326\u2013358 (1975)","journal-title":"J. Math. Anal. Appl."},{"key":"9448_CR13","first-page":"3","volume":"47","author":"V. Ovsienko","year":"2001","unstructured":"Ovsienko, V., Tabachnikov, S.: Projective geometry of polygons and discrete 4-vertex and 6-vertex theorems. Enseign. Math. 47, 3\u201319 (2001)","journal-title":"Enseign. Math."},{"issue":"1","key":"9448_CR14","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1006\/jfan.1994.1004","volume":"119","author":"G. Sapiro","year":"1994","unstructured":"Sapiro, G., Tannenbaum, A.: On affine plane curve evolution. J. Funct. Anal. 119(1), 79\u2013120 (1994)","journal-title":"J. Funct. Anal."},{"key":"9448_CR15","series-title":"Encyclopedia of Mathematics","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511526282","volume-title":"Convex Bodies: The Brunn\u2013Minkowski Theory","author":"R. Schneider","year":"1993","unstructured":"Schneider, R.: Convex Bodies: The Brunn\u2013Minkowski Theory. Encyclopedia of Mathematics, vol.\u00a044. Cambridge University Press, Cambridge (1993)"},{"key":"9448_CR16","doi-asserted-by":"crossref","first-page":"830","DOI":"10.2307\/2695738","volume":"107","author":"S. Tabachnikov","year":"2000","unstructured":"Tabachnikov, S.: A four-vertex theorem for polygons. Am. Math. Mon. 107, 830\u2013833 (2000)","journal-title":"Am. Math. Mon."},{"key":"9448_CR17","unstructured":"Teixeira, R.C.: Personal home page. http:\/\/www.professores.uff.br\/ralph"}],"container-title":["Discrete &amp; Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-012-9448-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-012-9448-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-012-9448-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,28]],"date-time":"2019-05-28T23:50:36Z","timestamp":1559087436000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-012-9448-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,8,2]]},"references-count":17,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2012,10]]}},"alternative-id":["9448"],"URL":"https:\/\/doi.org\/10.1007\/s00454-012-9448-y","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,8,2]]}}}