Bias tape
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Bias tape or bias binding is a narrow strip of fabric, cut on the bias (UK cross-grain). The strip's fibers, being at 45 degrees to the length of the strip, makes it stretchier as well as more fluid and more drapeable compared to a strip that is cut on grain. Many strips can be pieced together into a long "tape". The tape's width varies from about 1/2" to about 3" depending on applications. Bias tape is used in making piping, binding seams, finishing raw edges, etc. It is often used on the edges of quilts, placemats, and bibs, around armhole and neckline edges instead of a facing, and as a simple strap or tie for casual bags or clothing.
Commercially available bias tape is available as a simple bias tape, single-fold bias tape, and double-fold bias tape. Single-fold bias tape is bias tape that is folded in half lengthwise on its center line, wrong side together, and pressed. Double-fold bias tape is single-fold bias tape where each half is again folded in half lengthwise (to the center fold), wrong sides together, and pressed.
Devices are available commercially to aid the home sewer in making folded bias tape. The fabric strip is fed through the device, which folds the fabric. The folds are then pressed into place. The resulting folded tape will be 1/4 the width of the original fabric strip.
How to Make Continuous Bias Tape, by Shelley Rodgers
See also trim (sewing).