Like a lot of people, remembering ratios and formulas for most things in geometry always felt like something that I had to learn just for math class, but I would never use it outside class. Surprisingly, I was wrong. The ratio of the hypotenuse to the sides of a isosceles right triangle, also known as a 45-45-90 triangle, is useful for knitting.
Granted, it shouldn't be surprising that geometry is useful for knitting. Knitting is probably one of the most math based fiber crafts out there. I've actually known several people who do not like knitting because you are so dependent on math. They would rather crochet, where you can free form any shape you want relatively easily, compared to knitting, where you need to calculate how many increases and where in order to create curves and diagonals. You can still free form with knitting, it just tends to take some more trial and error than crochet, since crochet can move in any direction.
So to get back on topic, the ratio for an isosceles right triangle is very helpful when knitting a blanket, or anything really, on a bias because it lets you figure out how many stitches you need in order to get the width you want for each side. Since each side started out the same length and grows at the same length, it is an isosceles triangle. The growth rate with the garter stitch, makes it a right triangle. Here is the blanket I am using it for:
Of course, this trick really only works if you know your gauge and are using mostly garter stitch. But it still worked! And it almost makes up for having to sit through geometry on a daily basis in high school.
