{"id":753,"date":"2026-04-30T14:03:09","date_gmt":"2026-04-30T14:03:09","guid":{"rendered":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/petrs-theorem-and-harmonic-analysis-of-polygons-plenary-lecture\/"},"modified":"2026-04-30T14:06:32","modified_gmt":"2026-04-30T14:06:32","slug":"petrs-theorem-and-harmonic-analysis-of-polygons-plenary-lecture","status":"publish","type":"post","link":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/en\/petrs-theorem-and-harmonic-analysis-of-polygons-plenary-lecture\/","title":{"rendered":"Petr&#039;s theorem and harmonic analysis of polygons (plenary lecture)"},"content":{"rendered":"<p><em>Pavel Pech<\/em><br \/>\n<small>University of South Bohemia, Faculty of Education, \u010cesk\u00e9 Bud\u011bjovice<\/small><\/p>\n<p>Over 120 years have elapsed since K. Petr, the professor of Charles's university in Prague, established a theorem which is called after him Petr's theorem. So, it is a good occasion to remind some results which are connected with this theorem.<\/p>\n<p>First, plane dosed polygons are harmonically analyzed, i.e. they are expressed in the form of the sum of fundamental k-regular polygons. Using this harmonic analysis the Petr's theorem is studied.<\/p>\n<p>Then we will investigate plane linear polygon transformations. We will study two kinds of transformations \u2013 S-transformation which is described by means of complex numbers and preserves similarity and A-transformation which is defined by real numbers and is invariant under any affinity.<\/p>\n<p>In the next part, we use A-transformations to generalization of linear polygon transformations into a space which leads to a space analog of harmonic analysis of polygons.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pavel Pech University of South Bohemia, Faculty of Education, \u010cesk\u00e9 Bud\u011bjovice Over 120 years have elapsed since K. Petr, the professor of Charles&#8217;s university in Prague, established a theorem which is called after him Petr&#8217;s theorem. So, it is a good occasion to remind some results which are connected with this theorem. First, plane dosed [&hellip;]<\/p>\n","protected":false},"author":14,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-753","post","type-post","status-publish","format-standard","hentry","category-presentations"],"_links":{"self":[{"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/posts\/753","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/users\/14"}],"replies":[{"embeddable":true,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/comments?post=753"}],"version-history":[{"count":1,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/posts\/753\/revisions"}],"predecessor-version":[{"id":755,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/posts\/753\/revisions\/755"}],"wp:attachment":[{"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/media?parent=753"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/categories?post=753"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/tags?post=753"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}