Monday, March 14, 2011

inspired Monday: in which we discuss Pi

::PART 1::
(this is the 1st of a 2 part post which I hope will help designers to calculate yardage requirements for hats)

I'm inspired this week by π (or pi or 3.14).  Today is 3/14, and I'm not the only one observing this quasi-holiday.  I had every intention of baking a lemon meringue pie for today, but our Girl Scout cookie order arrived and, well, we're swamped in treats.

Just last week, I had to google how to calculate the area of a circle, and I was reminded of the formula pi times radius squared.  I'm a complete math nerd and seeing the formula made me wonder how I ever forgot it because it's really so simple.

I wanted to know how to calculate the area of a circle because I was trying to estimate how many yards of yarn it would take to knit each size of the Lucia Hat pattern that I'm designing.

To do this, I need to start with two questions:
  1. How many square inches are there in the sample hat I knit?
  2. How many yards of yarn does it take to knit 1 square inch of the hat?

    To answer the 1st question, I need to use some geometry to turn my hat into simple shapes so that I can calculate the area—or square inches—of each shape.

So let's answer Question 1 first.

How many square inches are in my sample hat size?

Let's imagine that the hat, laying flat and 2-dimensional, is made up of rectangles and a circle.  (It's not perfect, but it's close enough for our purposes.)

Area of a rectangle (square inches) = height x width.  

Area of circle (square inches) = 3.14 x radius x radius 

The circumference of the hat I knit was 14."5.  So if the hat were laying flat, the width would be 7.25", or half of the circumference.  The height of the rectangle is 4.1", which includes all of my knitting from the bottom of the hat up until I begin my decreases.  

The area of that rectangle is 7.25 x 4.1 or 29.725 square inches.  The bottom of the hat is essentially 2 rectangles, so I can double that figure to make 59.45 square inches.

radius copy

The top of the hat (the portion made up of all of the decrease rounds) is a circle.  The circle at the top of the hat has a radius of 2.6" (this is the distance from where the decreases began to the center of the hat).  So the area of the circle is 3.14 x 2.6 x 2.6, or 21.25 square inches.  

The total number of square inches in the hat are then 59.45 + 21.25 = 81 square inches (I rounded up).

Now let's answer Question 2: How many yards of yarn does it take to knit 1 square inch of the hat?

I first need to know how many yards it took me to knit this sample hat. The hat weighed 1 ounce. And the yarn I used is 250 yards per 4 ounces. So I set up a formula like this and solved for Y:

250 yards / 4 ounces =  Y yards / 1 ounce

250 x 1 = 4 x Y

250 ÷ 4 = Y

Y = 62.5

So a 1 ounce hat contains 63 yards of yarn.

How do you figure out how many yards of yarn are in each square inch? I know that it took 63 yards for me to knit the hat which is 81 square inches. So,

63 yards ÷ 81 square inches =  .77 yards per square inch.

In Part 2, which I'll next Monday, I'll show you how to take this information and estimate yardage requirements for each size of a hat you're designing.

I'd love to hear your comments on this post--is it helpful, confusing, or what?  Thanks!

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