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I've been working on my very own pattern for a knit circle, with each row acting as a radius rather than a loop. Heavily inspired by this placemat that my parents own. The only gripe I have with them is that the very edge curls, so it's not 100% flat like I want.
WIP
Circumference: 15in. Radius: 14sts/2.5in.
Circumference: 17in. Radius: 12sts/3in.
Circumference: 19in. Total radius: 12sts/3in. Inner radius: 3sts/0.75in. Obviously this has a massive hole in the center, as this was my first attempt at the project. The hole comes from the fact that I used 16 slices instead of 8.
Circumference: 10in. Radius: 8sts/1.5in. This was the first disk I made without a hole in the middle, and the smallest overall. I fell like you can see the 8 slices very easily, but it's hard to avoid at this scale.