Introduction to Curve Stitching - Line Designs

Wilhelm L. Lilly             Kenwood Academy
1629 E. Hyde Park Blvd.      5015 S. Blackstone Ave.
Chicago, IL 60615            Chicago, IL 60615
                             (312) 535-1409

Objectives:

     To develop the students' awareness that straight line segments can produce 
the illusion of a curve.

     To develop the students' ability to recognize and describe number patterns.

     To experience the beauty of mathematics and to introduce geometric 
fundamentals.

Materials needed:

     1/8" hardboard squares approx. 10" x 10" (or 24cm x 24cm) for each student.
     1/8" hardboard figures (equilateral triangle, regular pentagon, regular 
       hexagon, circle) one shape for each student.
     11" pieces of brightly colored yarn (approx. 25 pieces per figure).
     Overhead projector transparencies of suggested designs for each figure.
     Plastic demonstration figure (optional).
     Observation worksheets - one per student.

Strategy:

     Obtain the 1/8" hardboard at a major hardware store.  Hardboard usually 
comes in 4ft. x 12ft. sheets.  However, most stores can section it for more 
convenient transport.  A shop teacher or student/parent can assist with cutting 
10" x 10" squares if power tools present an area of difficulty.  Tracing large 
regular polygonal shapes on the hardboard with pencil will make cutting simpler. 
     Once the shapes are cut, measure and mark each side so as to obtain 8, 10, 
12 or 15 divisions as you desire.  Each mark will then need to be notched with 
a saw to create a 1/4" slit. 
     Line designs are formed by connecting sequences of notches with yarn pulled 
taut as a line segment.  The basic pattern is to connect equally-spaced notches 
along the two adjacent sides of a square: 

 8 |-
 7 |-                     (1) Divide each side into an equal number of 
 6 |-                         segments, notch and number them.
 5 |-
 4 |-                     (2) Connect notch "8" on the vertical with 
 3 |-                         notch "1" on the horizontal.
 2 |-
 1 |-                     (3) Connect notch "7" on the vertical with
     -+-+-+-+-+-+-+-+-+-      notch "2" on the horizontal and so on 
      1 2 3 4 5 6 7 8         until all pairs of notches whose sum is
                              9 are connected.

A greater number of notches on the side of the square will result in a design
which is higher in density but has the same curve.  The numbering of the 
notches can be varied to create different number patterns or can be used to 
discuss the Cartesian Coordinate System.  Another variation is to use a 
rectangle and divide each side into the same number of equal parts.
     An effective approach to teaching this lesson could include using 
cooperative learning groups of two.  The teacher would demonstrate the line 
segment connection (a few segments) on a model at the overhead projector, 
discussing number patterns, if desired.  One student from each group can then 
obtain their "notched" square and yarn bundle.  Squares should be notched on all
sides to allow each student to complete their own line design.  Once the squares
are completed and discussed, each group can obtain a second polygonal shape for 
creative experimentation.  Suggested designs can be shown on the overhead 
projector or copies made to hand out with the polygonal shapes. 
     
Conclusions:

     While the mathematical concepts built into this lesson are important, it is
equally important that students see that mathematics underlies much of the 
design and art of our modern culture.  Students find much joy in expressing 
their creativity through these line designs.  Since few prerequisite skills are 
required, students who have failed in previous mathematical activities find 
success and recognition on par with or above high achievers. 

References:

     Dale Seymour, Linda Silvey and Joyce Snider. LINE DESIGNS.
     Palo Alto, Calif.: Creative Publications, 1974.