PROBLEM:  Can the length of a curved surface be determined?

PREDICTION:

PROCEDURE:

MATERIALS:  1 tangle per student

EXERCISE 1.  In the space below, make 3 shapes that are topologically related using 16 snaps from a Tangle.  Trace the area inside.  If you think you have a "neat" shape, show your teacher before you change the shape.

EXERCISE 2.  See if you can make a knot from the closed curve of 16 segments.  Draw the difference between a knot and a closed curve.

EXERCISE 3.  Keeping the tangles closed, make a coil.  Show your instructor and have them check this item to verify you completed this exercise.  

EXERCISE 4.  Can you make a curved surface flat?  You may unsnap one of the links on the tangle.  Show your instructor to verify. 

EXERCISE 5.  How many complete circles can you make from the 16 curved snaps?_________  If the diameter of the circle (in cm) is multiplied by pi or 3.14, you can determine the circumference of the circle.  Can you determine the outer length of the entire curved surface?  Can you determine the inner length of the entire tangle?  Use the space below and try to compute the length of a curved surface.

CONCLUSIONS: