Quilting
A quilt consists of two layers of fabric—the quilt top and the backing—with a third layer of soft insulating material between them, called the batting. Hand or machine stitching holds the three layers together. A quilt can be "whole cloth" (which means the top is one piece of material) but the more colorful and popular forms are patchwork and appliqué.
In patchwork, small patches are sewn together to form larger patterns, while in appliqué the motifs are stitched onto a background fabric. Patchwork quilts are more likely to be arrangements of geometric figures, such as squares and triangles. Appliqué is more frequently used for freeform or representational designs. In either style, the quiltmaker first completes the top by piecing, then quilts together the sandwich of two layers of fabric with batting in between by stitching through all three layers.
Quilts were made even in the earliest civilizations—for example, in ancient Egypt and Central America. In Europe, the Crusaders brought the idea back from the Holy Land around the twelfth century. However, it was in America that the patchwork quilt blossomed into a distinctive and ubiquitous folk art form.
On the frontier, fabric was a valuable commodity, and quilts were a practical way to use leftover scraps and worn-out clothing. Pioneer women soon discovered the artistic possibilities of quiltmaking, and it became one of the few outlets for creativity and beauty in a difficult life. Quilts also became a valuable cultural record. To those who often did not have access to written media, quilts were a way of chronicling important life events: births, marriages, or even something so humble as a treasured friendship.
Over the generations, the practical importance of quilts diminished. Today, anyone can go to the store and buy a factory-made comforter. But over the last 30 years quilting has enjoyed a tremendous renaissance as a hobby and as a form of artistic and social expression. Fabrics and tools are now available that would have astounded previous generations of stitchers.
Patchwork Mathematics
Many traditional quilt designs are mathematically based, even if their inventors had no formal training in mathematics. A common geometric motif is the square. In the nineteenth century, many girls' first sewing project was a "nine-patch," a simple arrangement of nine squares in a grid. Another common figure is the isosceles right triangle, obtained by cutting a square along the diagonal. Hundreds of traditional blocks consist of these figures, arranged in different sizes and orientations to form stars, animals, buildings, or whatever the quilter's imagination suggested.
A traditional full-sized quilt is often composed of many copies of one basic block. Sometimes two blocks are alternated in checkerboard fashion, as shown in Figure 1. In both quilts, the individual blocks are difficult to discern once they have been incorporated into the completed quilt.
Quilters have learned that the skillful use of contrasting fabrics can lead the eye to see larger "secondary patterns," camouflaging the underlying grid. The traditional pattern called Jacob's Ladder illustrates this technique. As Figure 1 shows, the quilter can use the same geometric pattern yet can make the quilt look completely different by varying the colors. In the quilt on the left, the dominant color creates an illusion of two rectangles with broad borders, positioned diagonally across the quilt and intersecting one another at right angles. In the quilt on the right, the rectangles are barely visible because the color is muted. Instead, the dominant feature on the right is the series of long gray ladders ascending diagonally across the quilt.
Circular symmetry is another common geometric theme. Many quilts, instead of using a repeated pattern of square blocks, feature an elaborate
symmetric "medallion" in the center, such as an 8-pointed Lone Star or a 16-pointed Mariner's Compass. The quilt shown on the cover of this encyclopedia shows an 8-pointed star.
Measurements and Tools. In order to make the pieces of a quilt fit together correctly, quilters depend on precise measurements. If the diagonal lines in Jacob's Ladder were off by even a quarter inch, the sense of continuity from one block to the next would be ruined. The finished quilt can also develop unsightly ripples or bulges if the patches are not measured and cut with accuracy.
A little mathematics comes in handy, too. Because it is impossible to sew two patches together edge-to-edge, quilters cut out each patch a little larger than it will appear in the final quilt. To make a 1-inch square, quilters know they need to cut out a 1½ inch square, adding in a ¼-inch seam allowance (a standard amount) on each side. But it is trickier to figure out the correct cutting size for an isosceles right triangle. Adding ½ inch to the length of the short side is not enough, because this leaves no seam allowance on the long side, as shown in the figure below. The extra length needed, inches, can be computed from the Pythagorean Theorem, making a total of inches to add to the short sides of the triangle. Most quilters know the "rule of thumb," even if they do not know that they owe it to Pythagoras.
Modern quilters have access to an array of specialized tools for design and execution. The rotary cutter, a device somewhat like a pizza slicer, can cut more swiftly and accurately than scissors. When used with special see-through rulers that have grids and oblique angles marked on them, the
rotary cutter also allows quilters to skip the tedious step of marking fabric with a pencil. Other measuring devices associated with mathematics include protractors, compasses, and both rectilinear and isometric (triangular) graph paper. In recent years, some quilt designers have begun to use computer programs to design, preview, and calculate yardage.
Mathematics in Design. In addition to using mathematics as a tool, a few quilters have begun to use mathematics as their inspiration. In Caryl Bryer Fallert's Fibonacci Series #3, the long rectangles have side lengths that form a Fibonacci progression: 1, 2, 3, 5, 8, and so on. (See Figure 2.) Although not shown here, Jane LeValley Kerns's prizewinning Fractal ingeniously ties together the mathematical concept of a fractal (in this case, a cube made of smaller cubes made of smaller cubes) with a well-known optical illusion called the Necker cube. Other quilts with mathematical themes have been based on space-filling curves, logarithmic spirals, and nonperiodic tessellations. The mathematical motifs provide an inherent sense of rhythm and balance that partners well with the color and tactile satisfaction of the quilting medium.
