{"id":38403,"date":"2026-10-07T05:12:28","date_gmt":"2026-10-07T03:12:28","guid":{"rendered":"https:\/\/xmau.com\/notiziole\/?p=38403"},"modified":"2026-10-06T21:25:14","modified_gmt":"2026-10-06T19:25:14","slug":"il-teorema-di-miquel","status":"publish","type":"post","link":"https:\/\/xmau.com\/notiziole\/2026\/10\/07\/il-teorema-di-miquel\/","title":{"rendered":"Il teorema di Miquel"},"content":{"rendered":"<figure id=\"attachment_38404\" aria-describedby=\"caption-attachment-38404\" style=\"width: 300px\" class=\"wp-caption alignright\"><a href=\"https:\/\/i0.wp.com\/xmau.com\/notiziole\/wp-content\/uploads\/sites\/6\/2026\/10\/Miquel_Circles.png?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-38404\" src=\"https:\/\/i0.wp.com\/xmau.com\/notiziole\/wp-content\/uploads\/sites\/6\/2026\/10\/Miquel_Circles.png?resize=300%2C264&#038;ssl=1\" alt=\"il teorema di Miquel\" width=\"300\" height=\"264\" srcset=\"https:\/\/i0.wp.com\/xmau.com\/notiziole\/wp-content\/uploads\/sites\/6\/2026\/10\/Miquel_Circles.png?resize=300%2C264&amp;ssl=1 300w, https:\/\/i0.wp.com\/xmau.com\/notiziole\/wp-content\/uploads\/sites\/6\/2026\/10\/Miquel_Circles.png?resize=768%2C676&amp;ssl=1 768w, https:\/\/i0.wp.com\/xmau.com\/notiziole\/wp-content\/uploads\/sites\/6\/2026\/10\/Miquel_Circles.png?w=960&amp;ssl=1 960w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-38404\" class=\"wp-caption-text\">Po immagine di inductiveload, da https:\/\/commons.wikimedia.org\/wiki\/Image:Miquel_Circles.svg<\/figcaption><\/figure>\n<p>Potreste pensare che dal Rinascimento, a esser buoni, non si possa pi\u00f9 trovare alcun nuovo teorema &#8220;simpatico&#8221; in geometria euclidea. Occhei, potreste anche pensare che il concetto di &#8220;teorema simpatico&#8221; sia un ossimoro, ma tralasciamo. E invece non \u00e8 cos\u00ec.<\/p>\n<p>Un po&#8217; prima della met\u00e0 del XIX secolo, il francese <a href=\"https:\/\/fr.wikipedia.org\/wiki\/Auguste_Miquel\">Auguste Miquel<\/a> (non lo trovate neppure nella Wikipedia in lingua inglese, il che \u00e8 tutto detto) scopr\u00ec il teorema che ha preso il suo nome, noto anche come il teorema del perno (pivot). Dato un qualunque triangolo\u00a0<em>ABC<\/em>, si prendano tre punti\u00a0<em>A&#8217;, B&#8217;, C&#8217; <\/em>sui lati o sui loro prolungamenti, e si costruiscano i tre cerchi che passano per un vertice del triangolo e per i due punti costruiti sui lati che partono da quel vertice. Bene: i tre cerchi si incontrano in un punto, detto (maval\u00e0?) punto di Miquel.<\/p>\n<p>\u00c8 vero che non ce ne facciamo molto di un teorema come questo: ma non trovate inaspettato che ci sia un vincolo cos\u00ec forte sulla costruzione fatta?<span hidden class=\"__iawmlf-post-loop-links\" data-iawmlf-links=\"[{&quot;id&quot;:388,&quot;href&quot;:&quot;https:\\\/\\\/fr.wikipedia.org\\\/wiki\\\/Auguste_Miquel&quot;,&quot;archived_href&quot;:&quot;http:\\\/\\\/web-wp.archive.org\\\/web\\\/20251116221207\\\/https:\\\/\\\/fr.wikipedia.org\\\/wiki\\\/Auguste_Miquel&quot;,&quot;redirect_href&quot;:&quot;&quot;,&quot;checks&quot;:[{&quot;date&quot;:&quot;2026-10-06 18:20:18&quot;,&quot;http_code&quot;:200}],&quot;broken&quot;:false,&quot;last_checked&quot;:{&quot;date&quot;:&quot;2026-10-06 18:20:18&quot;,&quot;http_code&quot;:200},&quot;process&quot;:&quot;done&quot;}]\"><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ancora nell&#8217;Ottocento si scoprirono nuovi teoremi di geometria. 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