Rabbit Hole: Minimum L-seams

I was trying to write a post about art with squarable numbers, and so I thought quilting a Mrs. Perkins Quilt might be a nice addition to the exploration. With 1500 words almost ready to hit send, I ended up down a rabbit hole. This post is rather long and has a lot of data, so bear with me, or skip it. I will have an artsy post with a quilt in the next week. The quilt:Ok, first off, Mrs Perkin's quilt is a lovely math problem. The challenge is to slice a square of side n into smaller squares with integer side lengths, use the fewest squares possible, and make sure the side lengths share no common factor. The website squaring.net has a lot more on the problem, including the original wording, and Wolfram has a demonstration to explore. "For Christmas, Mrs. Potipher Perkins received a very pretty patchwork quilt constructed of 169 square pieces of silk material. The puzzle is to find the smallest number of square portions of which the quilt could be composed and show how they might be…