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     		<h2>Mathematical knots</h2>
-    		<p>Mathematical knots, or</p>
+    		<p>Mathematical knots, or knots which are studied in the field of knot theory, are based on the embedding of a circle within three-dimensional space. They are different from the usual idea of a knot, that is a string with free ends. Therefore, mathematical knots are (almost) always considered to be closed loops.</p>
     		<h2>Knotworks</h2>
-    		<p>Knotworks are visualisations of network topologies which use mathematical knots to represent a collapsing of the distinction between node and link. Just as a knot is a complication in which the tangle can conceal parts contained (as in <a href="http://b-e-e-t.r-o-o-t.net/readings/cybernetic_guerilla_warfare.html" target="_blank">klein worm topologies</a>), unravelling the knot reveals that it is homeomorphic to a continuous link. The link and the node are the same, unravelled.</p>
+    		<p>Knotworks are visualisations of network topologies which use mathematical knots to represent a collapsing of the distinction between node and link. Just as a knot is a complication in which the tangle can conceal parts contained (as in <a href="readings/cybernetic_guerilla_warfare.html" target="_blank">klein worm topologies</a>), unravelling the knot reveals that it is homeomorphic to a continuous link. The link and the node are the same, unravelled.</p>
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