The Fair Mathematics of Fair Isle Knitting: A Study of Knitting Patterns
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Fair Isle knitting is a unique knitting style that follows a set of general rules. These rules include its use of only two colors within a knit row, its simple color changes, its repeats in pattern structure, and its formation of geometric shapes through the color changes and repeated patterns used. Alongside these standards comprising what a makes a Fair Isle knitting pattern, it is important to understand that Fair Isle knitting is knit in a circle. The patterns formed are therefore cyclical. Due to the nature of Fair Isle knitting patterns, it came into question whether or not it would be possible to count the total number of pattern possibilities that can be created for various stitch lengths. In simplifying complex patterns, a series of patterns within patterns became apparent. Using the information discovered, an algorithm was formulated for finding an upper bound for the total number of potential patterns per stitch length. This study went further in developing a method for finding an approximate number of possible patterns for odd numbered stitch lengths.
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