About Topology Tricks About the module In this module children experiment with some basic ideas in topology at an elementary level. Children can enjoy playing with some of the simpler ideas in topology, such as classifying shapes or classifying knots. The hairy ball theorem lends itself to an activity with great kid appeal--smoothing the hair on a hairy ball. The Moebius band is always a popular topic and appears in many children's puzzle books. Equipment The equipment needed for this module includes a lump of clay or playdough, strips of paper, tape, scissors, a collection of knots, several lengths of rope for tying knots, an inside-out ball and an inside-out doughnut, and a hairy ball and a hairy doughnut. Here's a photo of the equipment we used. A collection of knots, some clay, the hairy ball, the hairy doughnut, the inside-out ball and the inside-out doughnut are shown in the picture. I'm not sure it is possible to purchase a hairy ball or a hairy doughnut. I went to the local fabric store and bought a quarter yard of some very hairy material and made my own. Here are the instructions: Hairy Ball: use the pattern from the "Printable Materials" page. Sew it like a baseball. Leave a small opening so that you can turn it right-side-out. Turn it right-side-out and stuff it with your favorite stuffing material and sew up the opening by hand. Hairy Doughnut: You can use a LARGE coffee can for a pattern (or something else which is round and roughly the right size). Cut two circles from the hairy fabric. Cut a radial slit in the two circles. Sew them together close to the outside edge with right sides together and slits aligned. Sew a very small circle, about 2 1/2 inches in diameter, around the center. Cut away the fabric inside the smaller circle (shaded in the diagram). Turn the doughnut inside out through the slit to get a circular tube with the ends open. Stuff it with your favorite stuffing material and sew the two ends of the tube together. I also made the ball and doughnut for turning inside out. The instructions for the ball are the same, except you can use any material you like and you stop before turning it right-side-out. The instructions for the inside-out doughnut are different because the trick here is that the doughnut cannot be turned right-side out unless you are very careful about where you leave the opening. To make the doughnut cut two circles but DO NOT cut a radial slit. Sew the circles together with right sides facing, about 7/8 of the way around the outside circle. Sew completely around the inside circle. Cut the fabric away in the center of the inside circle. You will not be able to turn this inside out. Knot collection: Tie several trefoil (overhand) knots in a short (6" or 8") piece of rope (clothesline works well) and join the ends of each knot with duct tape. Tie several figure eight knots and join the bitter ends of each of these. Several cinquefoil knots are also nice: these are overhand knots with an extra twist. Once the knots have been tied and the ends taped, twist and tangle all of them so that it is not immediately obvious which ones are the same. Any of the other simple knots from the Knot Catalogue would be a good addition to the collection. Some topology for kids on the web: This site is full of good activities for children. Untangling the Mathematics of Knots It's in the Workbook section of the MegaMath website. This site is a bit more technical but is good background reading. The KnotPlot Site This site has topology games on it--tictactoe and mazes on a Klein bottle and on a torus. Exploring the Shape of Space A very useful source for this module was Martin Gardner's Sixth Book of Mathematical Games from Scientific American. The poem was found in this book. The Topology Tricks module was written 12/6/01 by Janet A. Dixon. Revised 1/10/06