Wandering through the county fair this past August, my wife and I enjoyed some of the quilt patterns. Many of them involved mathematical ideas, some geometrical interpretations, and some flights of imagination.
If you want to both see and explore the mathematics of quilt patterns, I suggest Elaine Ellison's Mathematical Quilts website. I have heard her give a conference talk on the same at a NCTM Conference.
Eight pages of quilt patterns to explore, with multiple quilts and brief descriptions on each page. The mathematics involved is broad: golden rectangles, Pythagorean motifs, conic sections, spirals, fractals, non-Euclidean geometry, cartography, tesselations, Fibonacci numbers, and even more.
A browse introduces the various quilts...I expect you will pause to focus on your favorites! You may even be tempted to buy the Mathematical Quilt Cards offered on the website as well.
With co-author Diana Venters, Elaine Ellison has written two books on mathematical quilt-making. See the Resource Section for this week.