In Which I Discover My Maths Teacher Did Not Lie

I wasn't very good at maths at school. I was a rather scared and dutiful child, though, so I did my best to understand it - but to no avail. Of course, now that I am designing knitting patterns, I find myself using maths all the time, and I am just about mastering the easy stuff. Working out what tension (or GAUGE, as Elizabeth Zimmerman would have it) I am using by calculating the amount of stitches per centimetre on a tension swatch, then multiplying that by the measurement of the garment I want to knit - yep, I can do that. And the things I make now fit, most of the time. I know about how to custom shape things so they will fit better. So, on the whole, this kinda stuff wasn't a problem for me.

Then, I discovered this book. It's an amazingly beautiful and inspiring book by Maie Landra of Koigu Yarns , and all the patterns in it are created with mosaic knitting - little pieces of knitting which are created by means of cunning decreasing, and which form various shapes which, when knitted together, form larger geometric shapes. I had an idea of a hat formed in this way, maybe with a hexagon crown, and squares for the sides. I worried at this idea for a long time, wondering how on earth I could work out how big the hexagon had to be. Then I remembered pi. Of course! In theory, I know how to work out the diameter and radius of a circle, if I have the circumference - remember that? Circumference of circle = pi (3.14) x diameter. Halve the diameter, and you get the radius. The little triangle segments which form the hexagon are each the length of the radius, from point to base. Knitting being fairly flexible, I thought, does it matter if it's a circle or a hexagon? It was worth a go. I knitted a sample hexagon, and blow me down, I found that it worked. To say I was gobsmacked is an understatement. Who knew that this would ACTUALLY WORK? So they weren't lying to me at school after all. Wow.

(Bit blurry, and this is actually a later version than the original, but it does show the segments quite well.)

Inspired, I did the rest of the maths for the hat, and knitted away with trepidation. Was it going to work? Errr...
Well, it turned out exactly the size I had wanted it to, but what I hadn't factored in is that hats fit best on a person's head if they are about an inch smaller than the actual circumference measurement of the wearer's bonce... I seem to have knitted something that looks more like a lampshade.

I'm trying again. Meanwhile, if there's anyone of my acquaintance with an absolutely enormous head, I've got a hat for them.