{"id":261,"date":"2026-09-13T07:32:46","date_gmt":"2026-09-13T07:32:46","guid":{"rendered":"https:\/\/borovik.net\/selecta\/?p=261"},"modified":"2026-09-13T07:32:46","modified_gmt":"2026-09-13T07:32:46","slug":"yin-and-yang-of-elementary-geometry","status":"publish","type":"post","link":"https:\/\/borovik.net\/selecta\/2026\/09\/13\/yin-and-yang-of-elementary-geometry\/","title":{"rendered":"Yin and Yang of elementary geometry"},"content":{"rendered":"<p>A new paper on my <a href=\"https:\/\/borovik.net\/selecta\/journal\/\" target=\"_blank\" rel=\"noopener\">Journal<\/a>:<\/p>\n<p>A. Borovik, <a href=\"https:\/\/borovik.net\/selecta\/wp-content\/uploads\/2026\/09\/Selected_14_1_Borovik_Yin-and-Yang-of-elementary-geometry_12.09.26.pdf\">Yin and Yang of elementary geometry<\/a>,\u00a0 Selected Passages from Correspondence with Friends 14 no. 2 (2026), 5-13.<\/p>\n<p><strong>Abstract:<\/strong><\/p>\n<blockquote><p>Triangles and many other geometric figures in the plane could be <em>chiral<\/em>, not superimposable on their mirror symmetry images. This paper is a sketch of a rigorous treatment of the concepts of chirality and orientation which could be used in more deep or advanced streams of school level mathematics. It is based on treating the Euclidean plane as<\/p>\n<p><em>A<\/em> 2-<em>dimensional real vector space with two non-degenerate bilinear forms on it, one symmetric and positive definite and another -antisymmetric<\/em> (<em>symplectic)<\/em>.<\/p>\n<p>These two bilinear forms are the eponymous <em>Yin <\/em>and<em> Yang<\/em> of the title of the paper.<\/p>\n<p>Most proofs are omitted &#8211; they are fairly obvious. The paper contains some historic comments and my personal stories, quite relevant to this topic.<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>A new paper on my Journal: A. Borovik, Yin and Yang of elementary geometry,\u00a0 Selected Passages from Correspondence with Friends 14 no. 2 (2026), 5-13. Abstract: Triangles and many other geometric figures in the plane could be chiral, not superimposable on their mirror symmetry images. This paper is a sketch of a rigorous treatment of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-261","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/borovik.net\/selecta\/wp-json\/wp\/v2\/posts\/261","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/borovik.net\/selecta\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/borovik.net\/selecta\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/borovik.net\/selecta\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/borovik.net\/selecta\/wp-json\/wp\/v2\/comments?post=261"}],"version-history":[{"count":1,"href":"https:\/\/borovik.net\/selecta\/wp-json\/wp\/v2\/posts\/261\/revisions"}],"predecessor-version":[{"id":262,"href":"https:\/\/borovik.net\/selecta\/wp-json\/wp\/v2\/posts\/261\/revisions\/262"}],"wp:attachment":[{"href":"https:\/\/borovik.net\/selecta\/wp-json\/wp\/v2\/media?parent=261"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/borovik.net\/selecta\/wp-json\/wp\/v2\/categories?post=261"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/borovik.net\/selecta\/wp-json\/wp\/v2\/tags?post=261"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}