Thursday, August 16, 2012

Math of the Granny Square

I'm a nerd, there, I admit it. (Though it never was truly a secret, but only we know that.) I love Sci-fi Novels, my favorite being "Fahrenheit 451" by Ray Bradbury, of whom just recently passed away. I love to figure things out. One of my friends nicknamed my "DIY Dawn" a couple of years ago. I found it so true. I don't just want to know the end result, but the process of how it is achieved.

For the past year, I have been working on the most glorious afghan. It a simple Granny Square, really.   Start with four stitches of three double chains, and add an extra group to turn each corner. I've taken it across the United States to various Fiber Festivals and friends homes to work on (and show off on occasion, since I love it so much). It started out as a way to use up all those 20 yards sock yarn Phat Fibers samples I had been gathering from the various participants. I had a basketful of tiny hanks of bright and plain yarn love. I decided to make a mammoth project of these tidbits. Heck, the artists worked so hard to bring me a sample of their colors and fibers from the shops, I had to pay homage somehow. Thus, the Great Granny Blanket began.

For months I worked on this blanket. First it was big enough to make a pillow. Okay, that was great, but I wanted bigger! Then, it was a baby blanket size. No way in heck was I giving this beauty away! Soon, I ran out of samples. Okay. . . I looked in my scrap pile from various projects and pulled out all those left over bits. 50 yards leftover from the shawl I knit last Fall. . . another 100 yards from the socks I knit my mom for Christmas. This blanket kept growing and growing. I finally had to halt all production since I didn't have any more yarn. Gasp! How can that happen? It sat in a basket for several months before I purchased a special hank of yarn at a fiber festival from a friend. It's the only hank so far that I've bought for it. I finally gathered enough samples to work on it again on my 12 hour drive to visit my Grandmother. Yay!

While busily hooking away on my baby. I start thinking about how much time I actually put into this. I hadn't been keeping a log or anything. It's that project that you pick up whenever you have a few extra minutes. So, I started pondering about an equation to figure out the estimated time. (Did I mention, I'm a geek?) For the life of me, I couldn't figure it out. I knew with the simplicity of the math (starting with four groupings, and adding four on every row) a solution was possible. I looked everywhere online for the solution to come up empty. There might be an answer somewhere, but not where I could find it.  So, in my infinite wisdom (insert laugh here) I posed the question to my father. Now, this could be unusual for some, but my Daddy has an Engineering Degree and was a Captain/Pilot in the Air Force. He loves math and thinks very logically. He and I played around for about a half and hour discussing different equations. It was always that first increase from 4 to 8 bunches that got us off kilter. I actually even started writing down what the total stitches would be for each row completed by simply adding four each time. Let me tell you, that took 15 minutes, in and of itself!

Here's the basic Granny square diagram:

Finally, though, we figured it out.

You want to know the answer? Here it is...

The answer is:
1/2 (4X+4) x X = total groups
X = the amount of rows. 

Yep, that's it. To me it's like God finally answering, "What is the meaning of life?". Now, here's how to figure out, roughly, the amount of time you put into your simple Granny Square.

So, if you plug what row you just finished as x. You will be able to figure out how many groups of three you get. Remember, simple granny squares start with 4 groups of 3, then go to 8 groups of three, then 12 groups of 3, and so on.

With this number, all you need to estimate the amount of time you've put into a blanket is to time how long it takes you to do a bunch of groups.

For example, I was on row 95 when I figured this out.

1/2 (4X+4) x X
1/2 ([4x95]+4) x 95
1/2 (380+4) x 95
1/2 (384) x 95
192 x 95 = 18,240

Then, let's say, I can complete 6 groups in a minute.
18240 divided by 6 = 3040 total minutes
3040 minutes divided by 60 (minutes per hour) = 50.66666 hours total time
So, it roughly took me 50 hours to complete the afghan to row 95.

ALSO, you could also use the total groups number to estimate yardage. Let's say it take one yard of fingering yarn for two groups.

Divide 18,240 groups by 2 (groups per yard) = 9,120 total yards.

Of course, this would be an estimate since joins would add some more yards that don't contribute to the groups or if I were falling asleep and slowing down, my time would increase. At least, though, you can know get an idea of how much time it takes to make a simple granny blanket.

Who said Algebra would never come be handy in the real world? Now, grab your calculators and get to work!