{"version":"1.0","provider_name":"SOUL OF MATHEMATICS","provider_url":"https:\/\/soulofmathematics.com","author_name":"Rajarshi Dey","author_url":"https:\/\/soulofmathematics.com\/index.php\/author\/rajarshidey1729gmail-com\/","title":"KNOT THEORY - SOUL OF MATHEMATICS","type":"rich","width":600,"height":338,"html":"<blockquote class=\"wp-embedded-content\" data-secret=\"GZBzGYznX2\"><a href=\"https:\/\/soulofmathematics.com\/index.php\/knot-theory\/\">KNOT THEORY<\/a><\/blockquote><iframe sandbox=\"allow-scripts\" security=\"restricted\" src=\"https:\/\/soulofmathematics.com\/index.php\/knot-theory\/embed\/#?secret=GZBzGYznX2\" width=\"600\" height=\"338\" title=\"&#8220;KNOT THEORY&#8221; &#8212; SOUL OF MATHEMATICS\" data-secret=\"GZBzGYznX2\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\" class=\"wp-embedded-content\"><\/iframe><script type=\"text\/javascript\">\n\/* <![CDATA[ *\/\n\/*! This file is auto-generated *\/\n!function(d,l){\"use strict\";l.querySelector&&d.addEventListener&&\"undefined\"!=typeof URL&&(d.wp=d.wp||{},d.wp.receiveEmbedMessage||(d.wp.receiveEmbedMessage=function(e){var t=e.data;if((t||t.secret||t.message||t.value)&&!\/[^a-zA-Z0-9]\/.test(t.secret)){for(var s,r,n,a=l.querySelectorAll('iframe[data-secret=\"'+t.secret+'\"]'),o=l.querySelectorAll('blockquote[data-secret=\"'+t.secret+'\"]'),c=new RegExp(\"^https?:$\",\"i\"),i=0;i<o.length;i++)o[i].style.display=\"none\";for(i=0;i<a.length;i++)s=a[i],e.source===s.contentWindow&&(s.removeAttribute(\"style\"),\"height\"===t.message?(1e3<(r=parseInt(t.value,10))?r=1e3:~~r<200&&(r=200),s.height=r):\"link\"===t.message&&(r=new URL(s.getAttribute(\"src\")),n=new URL(t.value),c.test(n.protocol))&&n.host===r.host&&l.activeElement===s&&(d.top.location.href=t.value))}},d.addEventListener(\"message\",d.wp.receiveEmbedMessage,!1),l.addEventListener(\"DOMContentLoaded\",function(){for(var e,t,s=l.querySelectorAll(\"iframe.wp-embedded-content\"),r=0;r<s.length;r++)(t=(e=s[r]).getAttribute(\"data-secret\"))||(t=Math.random().toString(36).substring(2,12),e.src+=\"#?secret=\"+t,e.setAttribute(\"data-secret\",t)),e.contentWindow.postMessage({message:\"ready\",secret:t},\"*\")},!1)))}(window,document);\n\/* ]]> *\/\n<\/script>\n","thumbnail_url":"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2020\/10\/giphy-2.gif?fit=480%2C480&ssl=1","thumbnail_width":480,"thumbnail_height":480,"description":"In&nbsp;topology,&nbsp;knot theory&nbsp;is the study of&nbsp;mathematical knots. In mathematical language, a knot is an&nbsp;embedding&nbsp;of a&nbsp;circle&nbsp;in 3-dimensional&nbsp;Euclidean space, R3 (in topology, a circle isn&#8217;t bound to the classical geometric concept, but to all of its&nbsp;homeomorphisms). Two mathematical knots are equivalent if one can be transformed into the other via a deformation of R3 upon itself (known as an&nbsp;ambient isotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting the string or passing the string through itself. Although people have been making use of knots since the dawn of our existence, the actual mathematical study of knots is relatively young, closer to 100 years than 1000 years. In contrast, Euclidean geometry and number theory, which have been studied over a considerable number of years, germinated because of the cultural &#8220;pull&#8221; and the strong effect that calculations and computations generated. It is still quite common to see buildings with ornate knot or braid lattice-work. However, as a starting point for a study of the mathematics of a knot, we need to excoriate this aesthetic layer and concentrate on the shape of the knot. Knot theory, in essence, is the study of the geometrical aspects of these shapes. Not only has knot theory developed and grown over the years in its own right, but also the actual mathematics of knot theory has been shown to have applications in various branches of the sciences, for example, physics, molecular biology, chemistry. A knot is not perceptively changed if we apply only one elementary knot move. However, if we repeat the process at different places, several times, then the resultant knot seems to be a completely different knot. For example, let us look at the two knots K1 and K2 which may be called Perko&#8217;s pair. In appearance Perko&#8217;s pair of knots looks completely different. In fact, for the better part of 100 years, nobody thought otherwise. However, it is possible to change the knot K1 into the knot K2 by performing the elementary knot moves a significant number of times. This was only shown in 1970 by the American lawyer K.A. Perko. Knots that can be changed from one to the other by applying the elementary knot move are said to be equivalent or equal. Therefore, the two knots are equivalent."}