"Grandmother" here probably refers simply to "a good old pattern," as noted in Ruby McKim's 100 PATCHWORK PATTERNS, published in 1931. Numerous versions for this applique "fan" design are listed in the compendiums, with names like FAN PATCHWORK (Ladies Art Company Catalogue, #296, late 19th c.) and GRANDMOTHER'S FAN, also FORMOSA FAN (Nancy Cabot's version left) and A FAN OF MANY COLORS etc.
See Barbara Brackman's ENCYCLOPEDIA OF PIECED QUILT PATTERNS, (#3305-#3308) and Jinny Beyer's QUILTER'S ALBUM OF PATCHWORK PATTERNS (p. 386). Maggie Malone's 5,500 QUILT BLOCK DESIGNS has a stunning full-color, fifty-page section on geometric quilt patterns with circles or curves (pp. 267-317) — for GRANDMOTHER'S FAN see pg. 290.
If the designs are worked out with a compass, or via a right-angle triangle, the number of panels (or
"sticks") that make up the fan can be highly flexible and there are endless variations for the arrangement in the tiling. The rendering here has more than most, 11 sticks, but the block called ART DECO FAN has 13 (Malone #3764). When drafted as illustrated lower left, the number of divisions per side of the square grid always equals the number of sticks — the center of the fan progressively opens the sticks wider, naturally (in terms of geometry) and beautifully. A dover reprint of Ruby McKim's beloved 101 PATCHWORK DESIGNS includes templates for all 101, including a beautiful 6-stick version of GRANDMOTHER'S FAN (P.53).
Some variations use colors and scraps to add an accordion effect (upper left), providing at least a vague suggestion of the folds in the fan. The following is edited from Cabot's enthusiastic comments (Chicago Tribune, August, 1936):
"FORMOSA FAN is another applique quilt pattern of the fan variety, but most attractive and simple to make. The sticks of the fan may be gleaned from the scrap bag, with each a different color, or there may be alternate shades in the fan. Variety may be had by making each block different in a quilt composed entirely of applique designs."
Related circle designs at this site include:
BUTTERFLY IN CIRCLES
SUNSHINE AND STAINED GLASS
SNAKE IN THE HOLLOW
(A) WINDING TRAIL