Rare Singer Sewing Machine Single Foot #160845/15429 Left Toe. Here is a foot that will set off your vintage sewing machine.   Back in the day...  

The function of this attachments was to allow the needle to pass close to the edge of a cord placed under a folded-over piece of fabric.  This decorative finish can be found on many pillows and cushions, and is useful for other sewing projects as well.  I'll bet zippers hadn't been invented when they first designed this foot, though nowadays the foot also allow a seamstress to sew close to the edge of a zipper during garment construction. 

This is a single foot #160845/15429 is the left toe.  This came from a closed Singer Company Store closed in Fairmont WV. These will fit all of Singer's Vertical Shank machines.