Curve Stitching, or String Art, is a way to create patterns from modular arithmetic, and curves from straight lines.

In this activity we "stitch" patterns by joining points around a regular polygon.



Polygon String Art
Patterns from polygons and strings using modular arithmetic
Choose a number of points to generate a polygon. Then, supposing that each vertex point on the polygon is a pin, select a join number to determine how to select the pins in turn while connecting them with a string. For example, given 7 points and a join number of 3, the polygon is a heptagon, and the string is wrapped around every third pin to make the pattern.

Select different values from the menus, or by using the up and down arrows, and see how the pattern changes.

If you think about the points and join numbers using your knowledge of the times tables, you might be able to come up with a way to predict the pattern that results.

If Repeat is selected, the whole cycle is repeated starting on any free pins until no unconnected pins remain.

Points:     Join: 

        

Heading

About the activity

Some things to ponder:
  • What pairs of numbers make the most interesting patterns?
  • Are you able to predict features of a pattern from the numbers alone?
  • If the number of points is n, and the join value is k, what happens if you change the join value to n − k?
  • Can you explain this relationship?

Curve stitching was invented by Mary Boole—a leading early proponent of the role of fun in maths and science education. Her husband was George Boole, the inventor of Boolean Algebra, which is the mathematics used to describe logic, and to design digital electronics and computer hardware.