Geometry: An Interactive Journey to Mastery

Study Tip
x This lesson is purely optional. There are no recommended study tips for this lesson other than to enjoy
the lesson and let the thinking about it strengthen your understanding of geometry as a whole.
Pitfall
x Don’t forget to have fun in your thinking of mathematics. This is a fun topic.

1. 7LHWKUHHVWULQJVWRWKHEDFNRIDFKDLUDQGEUDLGWKHPLQDQ\KDSKD]DUGPDQQHU\RXFKRRVHͼ௘'RQ¶W
   alternately cross the left two strands, then the right two strands. Try crossing the left two a few times, then
   WKHULJKWWZRDIHZWLPHVDQGVRRQEDFNDQGIRUWK௘ͽ0DNHVXUHWKDWWKHPLGGOHVWUDQGHQGVEDFNLQWKH
   middle position. Next, tie the three loose ends to a wooden spoon, again with the middle string tied in the
   middle position.
   Is it now possible to maneuver the wooden spoon through the tangle of strings and completely undo the
   braid? Try it.


2. Show that, with three strands in a braid, a single overcrossing
   is physically equivalent to a single undercrossing.
   ͼ௘6HHFigure 33.1௘ͽ


3. Show that, with three strands in a braid, two crossings in
   a row between the same pair of strings is physically
   HTXLYDOHQWWRQRFURVVLQJVͼ௘6HHFigure 33.2௘ͽ

Problems

Figure 33.1

Figure 33.2