{"id":122,"date":"2018-11-09T12:09:13","date_gmt":"2018-11-09T14:09:13","guid":{"rendered":"http:\/\/www.professores.uff.br\/vitorbalestro\/?page_id=122"},"modified":"2018-11-09T12:09:13","modified_gmt":"2018-11-09T14:09:13","slug":"geometric-properties-of-a-sine-function-extendable-to-arbitrary-normed-planes","status":"publish","type":"page","link":"https:\/\/www.professores.uff.br\/vitorbalestro\/publications\/geometric-properties-of-a-sine-function-extendable-to-arbitrary-normed-planes\/","title":{"rendered":"Geometric properties of a sine function extendable to arbitrary normed planes"},"content":{"rendered":"<p id=\"h.p_z5_N2QyMKcbZ\" class=\"zfr3Q\">V. Balestro, H. Martini and R. Teixeira, <strong>Geometric properties of a sine function extendable to arbitrary normed planes, <\/strong>Monatshefte f\u00fcr Mathematik 182(4), pp. 781-800, 2017. (<a class=\"dhtgD\" href=\"https:\/\/www.google.com\/url?q=https%3A%2F%2Farxiv.org%2Fabs%2F1601.06287&amp;sa=D&amp;sntz=1&amp;usg=AFQjCNHiwtbEZauosGY_qTsiyhW0pK1vcA\" target=\"_blank\" rel=\"noopener noreferrer\">arXiv link<\/a>) (<a class=\"dhtgD\" href=\"https:\/\/www.google.com\/url?q=https%3A%2F%2Flink.springer.com%2Farticle%2F10.1007%2Fs00605-016-0916-y&amp;sa=D&amp;sntz=1&amp;usg=AFQjCNEZh_93ER99hvxFbqHQr6wQctz3zg\" target=\"_blank\" rel=\"noopener noreferrer\">journal link<\/a>)<\/p>\n<p id=\"h.p_cbyQfBVRKd9n\" class=\"zfr3Q\">Comments: In this paper we study a sine function which as a simple formulation in terms of the norm, and which agrees with the usual sine function in the Euclidean subcase. We study its properties and also use it to define a geometric constant to measure how far a plane is from being Radon. This constant can be also regarded as a modulus of asymmetry of supporting directions in the unit circle. Further on, we relate the sine function to angular measures in the sense of Brass, proving that they only can &#8220;agree&#8221; if the norm is Euclidean and if the angular measure is the standard one.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>V. Balestro, H. Martini and R. Teixeira, Geometric properties of a sine function extendable to arbitrary normed planes, Monatshefte f\u00fcr Mathematik 182(4), pp. 781-800, 2017. (arXiv link) (journal link) Comments: In this paper we study a sine function which as a simple formulation in terms of the norm, and which agrees with the usual sine [&hellip;]<\/p>\n","protected":false},"author":205,"featured_media":0,"parent":12,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"categories":[],"tags":[],"class_list":["post-122","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/122","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/users\/205"}],"replies":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/comments?post=122"}],"version-history":[{"count":1,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/122\/revisions"}],"predecessor-version":[{"id":123,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/122\/revisions\/123"}],"up":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/12"}],"wp:attachment":[{"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/media?parent=122"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/categories?post=122"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/tags?post=122"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}