{"id":614,"date":"2026-03-21T19:43:49","date_gmt":"2026-03-21T19:43:49","guid":{"rendered":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/remarks-to-a-pedal-point-problem-of-p-pech\/"},"modified":"2026-03-21T19:43:49","modified_gmt":"2026-03-21T19:43:49","slug":"remarks-to-a-pedal-point-problem-of-p-pech","status":"publish","type":"post","link":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/en\/remarks-to-a-pedal-point-problem-of-p-pech\/","title":{"rendered":"Remarks to a pedal point problem of P. Pech"},"content":{"rendered":"<p><em>Gunter Weiss<\/em><br \/><small>TU Vienna &amp; TU Dresden, Wien<\/small><\/p>\n<p>In 2025 P. Pech presented a special Wallace-Simson problem for quadrilaterals, namely that the four pedal points P_i with respect to a pole P form a quadrangle with parallel sides. It turns out that the locus of possible poles P is a circle. This can be proved without calculation by synthetic elementary geometric reasoning alone. Furthermore, P. Pech\u2019s idea can be generalized to 3D-problems for tetrahedra. In addition, it gives a hint how to formulate problems generalizing the classical Wallace-Simson problem for trilaterals, too. <\/p>\n","protected":false},"excerpt":{"rendered":"<p>Gunter WeissTU Vienna &amp; TU Dresden, Wien In 2025 P. Pech presented a special Wallace-Simson problem for quadrilaterals, namely that the four pedal points P_i with respect to a pole P form a quadrangle with parallel sides. It turns out that the locus of possible poles P is a circle. This can be proved without [&hellip;]<\/p>\n","protected":false},"author":13,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-614","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\/614","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\/13"}],"replies":[{"embeddable":true,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/comments?post=614"}],"version-history":[{"count":0,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/posts\/614\/revisions"}],"wp:attachment":[{"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/media?parent=614"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/categories?post=614"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/tags?post=614"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}