knitting a Pie for Pi Day

The round dish cloth I am knitting not only resembles a pie, with its eight wedges and peaked edging; it also follows the revered number Pi in several ways. First, anything circular, including my cotton dishcloth, already has a connection to pi. Pi is the ratio of the circumference to the diameter of a circle.

The circumference is the outer edge, the line you draw when you draw a circle. imagine walking along the perfectly curved outer edge and measuring it as you go. The diameter is the straight line you draw to split the circle in half. Measuring it can be done easily with a ruler.

The magic of mathematics has determined that the ratio between these two numbers is a “constant.” No matter how big or small the circle is, that ratio will always be the same. And who said you can’t count on anything anymore?

Pi, an Overview

According to Pi.org, “Pi Day is celebrated on March 14th (3/14) around the world. Pi (Greek letter “π”) is the symbol used in mathematics to represent a constant — the ratio of the circumference of a circle to its diameter — which is approximately 3.14159.

Pi has been calculated to over one trillion digits beyond its decimal point. As an irrational and transcendental number, it will continue infinitely without repetition or pattern.” http://www.piday.org/

Knitter’s Pi Chart: 3.141592653

Blue Variagated Round Dishcloth w Peaks: photo by Rich Hill

I like the image of “an irrational and transcendental number,” that will continue infinitely without repetition or pattern. In fact, I might just make that my life’s goal. For today, however, I will share my musings on knitting Pi.

  • 3 = the number of peaks in each wedge of my round dishcloth.
  • 1 = the number of central points per wedge – well, duh!
  • 4 = the number of rows in each peak were the stitch-count changes.
  • 15 = the number of stitches needed to start the project. Is it OK to use two digits at once?
  • 9 = the number of wedges I had last night, when I realized that I had one more wedge than I needed. Arg!
  • 2 = the number of rows in each wedge where you actually have the original number of stitches.
  • 6 = the number of letters in “Albert.” Hey, Einstein’s birthday is March 14, so why can’t I think of him while I’m knitting?
  • 5 = the number of stitches left to cast on after you place a marker to separate the ten short-row stitches, which create the pointed wedge shape, from the edging stitches – the ones that make the peaks around the outside.
  • 3 = the number of increase rows in each peak… and no, that’s not a contradiction to 4, the number of rows in which the stitch-count changes. After all, what goes up, must come down; right?

Knitting a Round Dishcloth

Round Dishcloth on Needles Shows Curve of Short-row Knitting: photo by Rich Hill.

Now, for you knitters who want to give it a try. The pictures show the original Round Dish Cloth from Mielke’sFiber Arts: http://www.mielkesfarm.com/dishclth.htm

I made many of these before deciding to see if I could make something that was less open and therefore less fragile. yes, I use them as dishcloths, and we don’t have a dishwasher, so they get a lot of use. And, no, I am not complaining; I had a dishwasher once & I prefer doing them myself.

This pattern which is done back and forth and not in the round, relies on a technique called short-row knitting to create a curved shape. It is also used in making heels in socks, darts in sweaters etc. In short-row knitting, we have two choices – either knit less stitches every right-side row or knit more.

Mielke’s folks decided to do the former. That’s why the dishcloth is so lacey looking with a starburst of open-work flanking the eight wedges. I tried that and now exclusively use the opposite approach – knit one more stitch every right-side row. The most amazing thing is that it doesn’t change the overall shape.

Materials

Use your favorite cotton yarn (any fiber will due, if you’re going to use it as a doily), and your favorite size needles for working with that yarn. I like Peaches and Creme cotton yarn on size 7 needles. You’ll need one marker, one yarn needle and one stitch saver to use to pin the work together for finishing. BTW, “SM” means “slip marker.”

Instructions

CO 15 sts using the knit-on method. Place a marker on the needle after you’ve cast on 10 stitches to separate the short-row area from the edging. Your yarn tail will be at the center of what will soon become a circle.

  • Row 1 (rs): k3, YO, k2 (6 sts. prior to marker), SM, k1, turn.
  • Row 2 and all even-numbered rows: k.
  • Row 3: k3, YO, k3 (7 sts prior to marker), SM, k2, turn.
  • Row 5: k3, YO, k4 (8 sts prior to marker), SM, k3, turn.
  • Row 7 (ends first peak of wedge and begins second): k1, (k1, slip first st. on rh needle over second) 3 times, k2, YO, k2 (6 sts prior to marker), SM, k4, turn.
  • Row 9: k3, YO, k3 (7 sts prior to marker), SM, k5, turn.
  • Row 11: k3, YO, k4 (8 sts prior to marker), SM, k6, turn.
  • Row 13 (ends second peak of wedge and begins third): k1, (k1, slip first st. on rh needle over second) 3 times, k2, YO, k2 (6 sts prior to marker), SM, k7, turn.
  • Row 15: k3, YO, k3 (7 sts prior to marker), SM, k8, turn.
  • Row 17: k3, YO, k4 (8 sts prior to marker), SM, k9, turn.
  • Row 19 (ends third peak and ends wedge): k1, (k1, slip first st. on rh needle over second) 3 times, k4 (5 sts prior to marker), SM, k10 (all 15 sts are now on one needle.
  • Row 20: k.

Repeat these 20 rows 7 more times for a total of 8 wedges (24 peaks)

Finishing

You can use a 3-needle bind-off to join the beginning and end, but I prefer grafting (aka Kitchener stitch). What I do is to start the grafting in the 19th row of the final wedge. I cast off the 3 stitches for the final peak and replace the stitch to the left-hand needle.

Then, pick up 15 sts. along the cast on edge. Line up the two needles with the points to your right and the yarn coming out of the first stitch on the back needle. I like pinning the work together a couple of inches below the needles.

Cut the yarn giving yourself about four-times the length of the 15 stitches. Thread working yarn into yarn needle.

Prep Row

leaving the stitches on the needles, enter the yarn needle as if to purl on the first stitch on the front needle, and pull it through. Repeat for the first stitch on the back needle.

Garter grafting Chant

Front needle, knit, purl; back needle, knit, purl.

Garter Grafting Explanation

Front needle:
insert the yarn needle into the first stitch as if to knit and remove the stitch from the needle pulling the yarn through.
Insert the yarn needle as if to purl into the next stitch on the front needle; leave the stitch on the needle, but pull the yarn through. You now have 14 stitches on the front needle and 15 on the back.

Repeat for back needle so only 14 stitches remain on each needle. Then, do this whole thing over and over until only one stitch remains on each needle. Enter the front as if to knit and remove from the needle and do the same for the one on the back.

Center Finishing

Work the yarn needle through the inner edge stitches in the center of the circle and adjust the tension to your liking before tying together with the original tail yarn and working in the ends.

Advertisements

About Donna W. Hill

Donna W. Hill is a writer, speaker, animal lover and avid knitter from Pennsylvania's Endless Mountains. Her first novel, The Heart of Applebutter Hill, is an adventure-mystery with excursions into fantasy for general audiences. Professionals in the fields of education and the arts have endorsed it as a diversity, inclusion and anti-bullying resource for junior high through college. A songwriter with three albums, Hill provided educational and motivational programs in the Greater Philadelphia area for fifteen years before moving to the mountains. Her essay, "Satori Green" appears in Richard Singer's Now, Embracing the Present Moment (2010, O-Books), and her cancer-survivor story is in Dawn Colclasure’s On the Wings of Pink Angels (2012). From 2009 through 2013, Hill was an online journalist for numerous publications, covering topics ranging from nature, health care and accessibility to music, knitting and chocolate. She is an experienced talk show guest and guest blogger and presents workshops about writing and her novel for school, university, community and business groups. The Heart of Applebutter Hill is available in print and e-versions at Amazon, B&N, Apple, Sony, Smashwords, Create Space and other outlets. It is also available through Bookshare for readers with print disabilities.
This entry was posted in Knitting, Mathematics, Uncategorized and tagged , , , , . Bookmark the permalink.

So, what do you think?

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s