Math and Quilting

 Quilts have been a part of American history since people came over in the 17th century.  Various patterns have developed, some are said to have been used to direct escaping slaves while others tell us more about the material of the times.  I have relatives who made quilts but we don't always look at the math behind quilting.

One thing about quilting is the number of books on quilt blocks.  A quilt block is one square with one complete pattern.  Each pattern has a unique name and is made out of polygons.

The majority of shapes used are triangles and squares which are put together in different patterns to create trapezoids, rectangles, pentagons, and parallelograms.  Eventually they are connected together to create a quilt block.  These blocks are then connected together into rows and the rows are sewn together until the whole quilt is built.  Usually, its big enough to cover a bed.

Regular quilting pattern.

A mathematics professor, Irena Swanson, created a new method of quilting which uses fewer seams and much quicker than the traditional method.  Usually, you cut the individual shapes, sew the pieces together, slowly.  Rather than doing this, she created "Tube Piecing".  In this method, she sews together strips of alternating light and dark fabrics that are slightly offset to create parallelograms.  Then she sews the strips of parallelograms together to form tubes.  As the last step, she cuts the tubes into rings so the cuts are perpendicular to the seams forming quadrilaterals.  These quadrilaterals are repositioned and sewn together to make quilts.

If you look past the standard forms, you can find patterns made out of hexagons, or hex rings made out of 18 equilateral triangles.  In fact, some quilters have not restricted themselves to traditional patterns.  If you look, you'll see this beautiful Mobius quilt that has no backing because of the way it was designed.  Its classified under topology.

Some artists have used tessellation's to create beautiful repeating patterns such as this one.  Furthermore, the same page has identified quilting material with tessellation's on an isometric grid.  If you take time to explore the Math Quilts site, you find quilts based on factals such as the one inspired by a Martin Gardener article from Scientific American, or even one based on the Pythagorean theorem.

Of course one can always find quilts created as optical illusions so the two dimensional blocks appear as three dimensional.  At mathwire, they offer some wonderful quilting activities you can easily include in your classroom. If you don't have material handy, you can use colored paper.  In my geometry class I had students create their own quilting pattern made out of polygons.  Unfortunately, most wanted to take a large square with like 8 triangles of 8 different colors and glue them to the paper.  This lead to a long discussion on numerical patterns versus quilting patterns.  Both have repeating parts.

One nice thing about this topic is the math part can be done in math class while the actual construction of quilts can be done in the home economics class. Check it out, Let me know what you think, I'd love to hear.  Have a great day.