Magicians sometimes use mathematics to do magic tricks. One such trick is to get a ring dropped around the outside of a loop of string to become tied to that loop with a knot. While some skill is involved in performing this trick, the real secret to doing it is to figure out the underlying mathematics of how the knot gets tied. To help you do this, place the ring and string on a flat surface as shown. While holding one end of the loop, grab the ring and slowly pull it in the opposite direction. If you hold the correct end and grab the ring in exactly the right place, you should be able to knot the ring to the string. Now that you've watched the trick happen horizontally and slowly, try it vertically. Be prepared because this will happen much more quickly. Study the illustration on the left. This shows the starting point of the ring and loop. Your challenge is to drop the ting in such a way that the ring becomes tied to the loop as illustrated above. Once you have figured out how the trick works, you will need to practice it until you can perform it consistently. Good luck!