Quilted Math November 26, 2001
Piece by Piece
The earliest quilts may have been made from layers of animal skin sewn around material. In colonial and pioneer times, women often fashioned the scraps of homespun fabrics into quilts. In her novel, How to Make an American Quilt, Whitney Otto writes, "What you should understand when undertaking the construction of a quilt is that it is comprised of spare time as well as excess material." How do quilts use mathematical patterns?

A quilt refers to a fabric "sandwich" consisting of a quilt top, a layer of filling called "batting," and a backing. A block is the basic design unit of a quilt top. It is often square. Many blocks have names, which are used to describe the quilt designs. Some popular block names are Log Cabin, Irish Chain, or Wedding Ring. The rich pattern of the quilt top emerges as blocks are repeated over and over.

In some ways quilts can be thought of as pictures painted in fabric pieces. Quilt designs often honor a birth or a marriage, or mark the occasion of a special community or state event, like a centennial.

Sharon Cerny Ogden, a professional quilter in Pennsylvania, explains that before she begins a quilt she "normally has a person in mind who is going to receive the quilt" or, at the very least, she has "a particular reason for making it." Quilters today approach a quilting project in much the same way a journalist researches an article, by gathering information in order to tell a story. "Modern quilters get ideas from many sources," continues Ogden. Quilters spend many hours reviewing history, colors, fabrics, and patterns in order to arrive at their designs.

Ogden designs her quilts on graph paper and draws with colored pencils to get an idea of the "overall scheme," a process that can take hours or days. Some quilters prepare their designs on special quilt-design software, then print them on high-quality color printers to achieve accuracy of color not available decades ago. After Ogden buys and prepares the fabric, she "draws the actual pattern pieces on the back of the fabric, cuts them out and sews them together."

Geometry Glossary
Imagine a quilt as a plane. In geometry, when a shape is moved in a plane it is called a transformation. Some special types of transformations are isometries. The following are three common isometries:

Translation: sliding a shape the same distance in a given direction without changing its orientation, so it looks like an exact duplicate of itself

Reflection: flipping a shape over a mirror or line

Rotation: turning a shape a given direction and angle about a fixed point (like a corner)

The actual "quilting" doesn't occur until after the quilt top, batting, and backing have been stitched together, either by hand or on a sewing machine.

Taking Shape
While the entire process of making a quilt may not sound very time-consuming, one of Ogden's intricate patterns took her more than 600 hours to complete.

The mathematically rich pattern in the quilt shown at right has an unlikely name: Hearts and Gizzards.

  • What basic shapes do you see in this design?

Look at one block. Find two triangles in this small square. (For help locating the triangles, find the line that runs from the upper right to the lower left.) What can you say about these triangles and their angles?

Rotating the block about a corner generates a second square, as in the example at left. What happens to the pattern if you rotate the original block 90 degrees, either clockwise or counterclockwise about one its corners?

How many times do you need to repeat this rotation before you return to where you started?

Which isometry can you apply to the block to generate the pattern shown on the quilt itself?

The quilt to the right, which is about 100 years old, shows an example of the popular Irish Chain pattern.

  • If the dimensions of this quilt are 60 in x 72 in, and 60 equal blocks were used to make the quilt, what were the dimensions of each block?

The basic block consists of a checkerboard and a square with a rectangle inscribed in it.

  • Which transformation would you use to generate this pattern starting with the basic block: a translation, a reflection, or a rotation?

Quilt with a Conscience
Imagine a quilt comprised of 44,000, 3 ft x 6 ft panels, weighing more than 50 tons, and measuring the length of 16 football fields. Integrating a wide range of fabrics, pictures, and other materials, each panel of the AIDS Memorial Quilt pays tribute to a victim of AIDS. Each person's individuality comes to life in the panels' varied styles. A quilt of this type — where each panel is different — is known as an album or autograph quilt.

During a candlelight march in San Francisco, California, in 1985, Cleve Jones and others wrote the names of AIDS victims on cards and taped them to a wall. The resulting wall of names reminded Jones of a patchwork quilt. He made the first panel and then formed the NAMES Project Foundation to oversee the addition of individual panels. While anyone can add a panel, the Foundation has prepared guidelines for the types of fabrics and materials to use, as well as rules for submitting it for inclusion into the Quilt.

More Links
Take a look at the symmetry found in quilts by examining four different quilt blocks.

The American Quilter's Society site has information about shows, books, contests, and other news of interest to quilters.

The Web site for the PBS series America Quilts features sections on quilts in the classroom, an online gallery, and a glossary. There's also a section about the quilters and quilts featured on the show.

Mosaic Magic lets you discover important mathematical concepts such as symmetry, rotation, repetition, and transformation through content areas such as spatial perception and pattern recognition.

Related Resources

Get these books by Sharon Cerny Ogden:

Irish Chain Quilts : Single, Double and Triple

Optical Illusions Quilt Designs

In 1987, the original Quilt went on display for the first time in Washington, D.C. Its 1,920 panels made it just larger than a football field. After a 20-city United States tour, the number of panels increased to 6,000.

Today, there are approximately 50 NAMES Project chapters in the United States alone. Over the past 13 years, more than 13 million people have viewed the AIDS Memorial Quilt, and more than $3 million has been raised for AIDS service organizations. Widely recognized as the largest community project in the world, the Quilt was nominated for the Nobel Peace Prize in 1989.

  • Portions of the Quilt are on display in cities around the country in honor of World AIDS Day. Check the AIDS Memorial Quilt site for a display schedule.
Related Activities
Applying Properties of Real Numbers
Understand the way algebra is used to express and analyze patterns in general, and patterns on an American quilt in particular, with this Destination Math tutorial.
Tessellating Regular Polygons
Try your hand at reproducing the Grandmother's Flowers pattern with this Tangible Math activity.
Marrying Math and Art
In this Riverdeep archive article, see how artist Helaman Ferguson incorporates math into his medium: sculpture.
A Home for Math Problems
Learn about The Math Forum, an online community for students, teachers, and anyone interested in math, in this archive article.