{"id":771,"date":"2026-04-30T16:34:05","date_gmt":"2026-04-30T16:34:05","guid":{"rendered":"https:\/\/home.pf.jcu.cz\/~csgg2026\/?p=771"},"modified":"2026-04-30T16:36:15","modified_gmt":"2026-04-30T16:36:15","slug":"petrs-theorem-and-harmonic-analysis-of-polygons","status":"publish","type":"post","link":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/en\/petrs-theorem-and-harmonic-analysis-of-polygons\/","title":{"rendered":"Petr&#8217;s theorem and harmonic analysis of polygons"},"content":{"rendered":"\n<p><strong>prof. RNDr. Pavel Pech, CSc.<\/strong><\/p>\n\n\n\n<p><em>University of South Bohemia<\/em><\/p>\n\n\n\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\n\n\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.&nbsp;<\/p>\n\n\n\n<p>Then we will investigate plane linear polygon transformations. We will study two kinds of transformations \u2013&nbsp;<em>S<\/em>-transformation which is described by means of complex numbers and preserves similarity and&nbsp;<em>A<\/em>-transformation which is defined by real numbers and is invariant under any affinity.<\/p>\n\n\n\n<p>In the next part, we use&nbsp;<em>A<\/em>-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>prof. RNDr. Pavel Pech, CSc. University of South Bohemia 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 polygons are [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-771","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/posts\/771","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\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/comments?post=771"}],"version-history":[{"count":1,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/posts\/771\/revisions"}],"predecessor-version":[{"id":772,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/posts\/771\/revisions\/772"}],"wp:attachment":[{"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/media?parent=771"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/categories?post=771"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/tags?post=771"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}