{"version":"1.0","provider_name":"Matem\u00e1ticas y sus fronteras","provider_url":"https:\/\/www.madrimasd.org\/blogs\/matematicas","author_name":"Matem\u00e1ticas y sus fronteras","author_url":"https:\/\/www.madrimasd.org\/blogs\/matematicas\/author\/matematicas","title":"La circunferencia de los nueve puntos - Matem\u00e1ticas y sus fronteras","type":"rich","width":600,"height":338,"html":"<blockquote class=\"wp-embedded-content\" data-secret=\"ybiLz7F0dz\"><a href=\"https:\/\/www.madrimasd.org\/blogs\/matematicas\/2020\/03\/07\/147433\">La circunferencia de los nueve puntos<\/a><\/blockquote><iframe sandbox=\"allow-scripts\" security=\"restricted\" src=\"https:\/\/www.madrimasd.org\/blogs\/matematicas\/2020\/03\/07\/147433\/embed#?secret=ybiLz7F0dz\" width=\"600\" height=\"338\" title=\"\u00abLa circunferencia de los nueve puntos\u00bb \u2014 Matem\u00e1ticas y sus fronteras\" data-secret=\"ybiLz7F0dz\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\" class=\"wp-embedded-content\"><\/iframe><script>\n\/**\n * WordPress inline HTML embed\n *\n * @since 4.4.0\n * @output wp-includes\/js\/wp-embed.js\n *\n * This file cannot have ampersands in it. This is to ensure\n * it can be embedded in older versions of WordPress.\n * See https:\/\/core.trac.wordpress.org\/changeset\/35708.\n *\/\n(function ( window, document ) {\n\t'use strict';\n\n\tvar supportedBrowser = false,\n\t\tloaded = false;\n\n\t\tif ( document.querySelector ) {\n\t\t\tif ( window.addEventListener ) {\n\t\t\t\tsupportedBrowser = true;\n\t\t\t}\n\t\t}\n\n\t\/** @namespace wp *\/\n\twindow.wp = window.wp || {};\n\n\tif ( !! window.wp.receiveEmbedMessage ) {\n\t\treturn;\n\t}\n\n\t\/**\n\t * Receive embed message.\n\t *\n\t * @param {MessageEvent} e\n\t *\/\n\twindow.wp.receiveEmbedMessage = function( e ) {\n\t\tvar data = e.data;\n\n\t\tif ( ! data ) {\n\t\t\treturn;\n\t\t}\n\n\t\tif ( ! ( data.secret || data.message || data.value ) ) {\n\t\t\treturn;\n\t\t}\n\n\t\tif ( \/[^a-zA-Z0-9]\/.test( data.secret ) ) {\n\t\t\treturn;\n\t\t}\n\n\t\tvar iframes = document.querySelectorAll( 'iframe[data-secret=\"' + data.secret + '\"]' ),\n\t\t\tblockquotes = document.querySelectorAll( 'blockquote[data-secret=\"' + data.secret + '\"]' ),\n\t\t\tallowedProtocols = new RegExp( '^https?:$', 'i' ),\n\t\t\ti, source, height, sourceURL, targetURL;\n\n\t\tfor ( i = 0; i < blockquotes.length; i++ ) {\n\t\t\tblockquotes[ i ].style.display = 'none';\n\t\t}\n\n\t\tfor ( i = 0; i < iframes.length; i++ ) {\n\t\t\tsource = iframes[ i ];\n\n\t\t\tif ( e.source !== source.contentWindow ) {\n\t\t\t\tcontinue;\n\t\t\t}\n\n\t\t\tsource.removeAttribute( 'style' );\n\n\t\t\t\/* Resize the iframe on request. *\/\n\t\t\tif ( 'height' === data.message ) {\n\t\t\t\theight = parseInt( data.value, 10 );\n\t\t\t\tif ( height > 1000 ) {\n\t\t\t\t\theight = 1000;\n\t\t\t\t} else if ( ~~height < 200 ) {\n\t\t\t\t\theight = 200;\n\t\t\t\t}\n\n\t\t\t\tsource.height = height;\n\t\t\t}\n\n\t\t\t\/* Link to a specific URL on request. *\/\n\t\t\tif ( 'link' === data.message ) {\n\t\t\t\tsourceURL = document.createElement( 'a' );\n\t\t\t\ttargetURL = document.createElement( 'a' );\n\n\t\t\t\tsourceURL.href = source.getAttribute( 'src' );\n\t\t\t\ttargetURL.href = data.value;\n\n\t\t\t\t\/* Only follow link if the protocol is in the allow list. *\/\n\t\t\t\tif ( ! allowedProtocols.test( targetURL.protocol ) ) {\n\t\t\t\t\tcontinue;\n\t\t\t\t}\n\n\t\t\t\t\/* Only continue if link hostname matches iframe's hostname. *\/\n\t\t\t\tif ( targetURL.host === sourceURL.host ) {\n\t\t\t\t\tif ( document.activeElement === source ) {\n\t\t\t\t\t\twindow.top.location.href = data.value;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\t};\n\n\tfunction onLoad() {\n\t\tif ( loaded ) {\n\t\t\treturn;\n\t\t}\n\n\t\tloaded = true;\n\n\t\tvar isIE10 = -1 !== navigator.appVersion.indexOf( 'MSIE 10' ),\n\t\t\tisIE11 = !!navigator.userAgent.match( \/Trident.*rv:11\\.\/ ),\n\t\t\tiframes = document.querySelectorAll( 'iframe.wp-embedded-content' ),\n\t\t\tiframeClone, i, source, secret;\n\n\t\tfor ( i = 0; i < iframes.length; i++ ) {\n\t\t\t\/** @var {IframeElement} *\/\n\t\t\tsource = iframes[ i ];\n\n\t\t\tsecret = source.getAttribute( 'data-secret' );\n\t\t\tif ( ! secret ) {\n\t\t\t\t\/* Add secret to iframe *\/\n\t\t\t\tsecret = Math.random().toString( 36 ).substr( 2, 10 );\n\t\t\t\tsource.src += '#?secret=' + secret;\n\t\t\t\tsource.setAttribute( 'data-secret', secret );\n\t\t\t}\n\n\t\t\t\/* Remove security attribute from iframes in IE10 and IE11. *\/\n\t\t\tif ( ( isIE10 || isIE11 ) ) {\n\t\t\t\tiframeClone = source.cloneNode( true );\n\t\t\t\tiframeClone.removeAttribute( 'security' );\n\t\t\t\tsource.parentNode.replaceChild( iframeClone, source );\n\t\t\t}\n\n\t\t\t\/*\n\t\t\t * Let post embed window know that the parent is ready for receiving the height message, in case the iframe\n\t\t\t * loaded before wp-embed.js was loaded. When the ready message is received by the post embed window, the\n\t\t\t * window will then (re-)send the height message right away.\n\t\t\t *\/\n\t\t\tsource.contentWindow.postMessage( {\n\t\t\t\tmessage: 'ready',\n\t\t\t\tsecret: secret\n\t\t\t}, '*' );\n\t\t}\n\t}\n\n\tif ( supportedBrowser ) {\n\t\twindow.addEventListener( 'message', window.wp.receiveEmbedMessage, false );\n\t\tdocument.addEventListener( 'DOMContentLoaded', onLoad, false );\n\t\twindow.addEventListener( 'load', onLoad, false );\n\t}\n})( window, document );\n<\/script>\n","description":"Desde la publicaci\u00f3n de mi libro La enga\u00f1osa sencillez de los tri\u00e1ngulos (De la f\u00f3rmula de Her\u00f3n a la criptograf\u00eda) he impartido varias conferencias sobre el mismo, en diferentes contextos, y en cada una han surgido nuevos temas que en su d\u00eda no se trataron en el libro pero que pod\u00edan haber sido parte de su contenido. Una muestra m\u00e1s de lo acertado del t\u00edtulo. En esta entrada trataremos una de estas curiosas propiedades de los tri\u00e1ngulos. \u00a0 Consideremos un tri\u00e1ngulo arbitrario, y sobre \u00e9l los siguientes nueve puntos: los puntos medios de los tres lados del tri\u00e1ngulo, los pies\u2026","thumbnail_url":"http:\/\/www.madrimasd.org\/blogs\/matematicas\/files\/2020\/03\/1920px-Nine-point_circle.svg_-1024x1024.png"}