Mathematical Quilting

I got hooked on origami sometime after Math Craft admin Cory Poole posted instructions for creating modular origami, but I had to take a break to finish a quilt I've been working on for a while now. It's my first quilt, and very simple in its construction (straight up squares, that's about it), but it got me thinking about the simple geometry and how far you could take the design to reflect complex geometries. Below are a few cool examples I found online.

I never really thought about the tie to math, and what a homage the quilt is to the mathematical shape. Travis over at Komplexify does a good job elaborating on this. First, he shows a fairly typical looking quilt:

And then he delves into complexities that are a bit beyond me (forgive me… ironically I'm rather math illiterate, but since obtaining a BFA in textiles / print design, I've grown pretty fascinated with repitition, geometry, etc.). Travis says:

"Note that the design of the whole quilt is merely a tiling of the plane by a single square design, sequentially rotated and/or reflected. Even more, the basic "atomic" square, called a log cabin in quilter's terms, is actually a nice proof without words that the sum of consecutive odd numbers is always a perfect square; here is a proof with words demonstrating the general idea with applets…

…Further inspection shows that the "top-stitching"—the threading used to connect the top patterns to the back of the quilt through the padding—takes the form of very basic polar rose curves of the from  and $r=\cos(2t)$."

Cory, maybe you can explain… or maybe I'll just let it float over my head. Regardless, here are more mathematically inspired quilts that I found interesting.

• A Piece of Hyperspace by Serena Mylchreest and Mark Newbold (pattern available here)

• Penrose Tiling by Serena Mylchreest and Mark Newbold

• Möbius Triangle by Renate Soltmann with quilting by Bethany Pease

• Escher Quilt Close-Up by Wendy Sheridan

• Cubed by Angela