Prime Factorization Blanket – First Row

So, Tuesday I posted my plan for making a Prime Factorization Blanket for my new niece or nephew. I then learned that my brother and his wife may know the baby’s gender by December 17th. Did I want to wait that long to choose the colors and start?

Short answer: No. I got to thinking: It’s not like this won’t be a very multi-colored blanket. I had thought about using shades of blue or shades of pink at the beginning, but I don’t think that’s a good plan. Since the colors represent numbers, and since a baby’s going to see this, better to have distinct colors with distinct names as the prime factors that show up most often.

On top of that, I happen to have a full skein and more of a turquoise blue left over from another project. Turquoise worked out very well as the color for 2 in my prime factorization scarf. It doesn’t cry out “boy,” but neither is it a bad color for a girl. And best of all, it goes well with pretty much every other color. (And 2 has to do that.) I decided to go with bright, rich colors for the primes that will be most predominant.

Thanks to a fairly long management meeting and a day off today where I needed to read, I’ve already finished the first row. I’m very happy with the colors! Now, the first row consists of just knitting 9 squares. The next row of white will convert them into diamonds. I’m also proud to say that I sewed in the starting ends of all the yarn. And that’s my plan to go on with: At the end of each row, I’ll sew in all the ends that were loose at the start of that row. (I don’t want to sew in the ends right next to a live stitch.) That way, it won’t be a daunting task at the end of the blanket.

So here’s the first row, the numbers 1 through 9 (0 is a blank space.), with the numbers the colors represent written on the picture:

I admit it’s getting where I’m going to have a hard time giving this away! Good thing I’ve publicly said it’s for my new niece or nephew!

And that does remind me. If you’d like your own Prime Factorization T-shirt or Tote Bag, or if you have a friend or loved one who really needs one for Christmas, be sure to check my Cafe Press Prime Factorization Store! 🙂

My posts on Mathematical Knitting and related topics are now gathered at Sonderknitting.

Mathematical Knitting — Blessing Blanket

Alyssa Karise is here! And her blanket is ready to send! Here’s the finished blanket. It’s actually a rectangle, but I wanted the message to be in the picture, reading from the top to bottom, left to right, so the perspective warps it a little.

I used Base 5 math to code a message into the blanket, which I explained when I started. But now I can show you how it worked out.

You can see in the picture above that the blanket makes a sort of grid. The “smooth” squares in the blanket were knitted on the back side with the stitches P3, K1, P3 (purl 3, knit 1, purl 3). There are six of these squares in each row of the grid. I knitted my code on the back side so that the words would go from left to right. I coded letters into each square this way: P1, next two stitches are first digit of letter, K1, next two stitches are second digit of letter, P1.

I used two stitches for each digit of the letter, using a Base 5 code. I used P2 for 0 (since I was on the purl side); K2 for 1; yarn over, knit 2 together (ykt) for 2; ssk, yarn over (sky) for 3; and purl cable one stitch, holding to the back (cb) for 4. Here’s how the letters were made:

A: 01: p2 k2;
B: 02: p2 ykt;
C: 03: p2 sky;
D: 04: p2 cb;
E: 10: k2 p2;
F: 11: k2 k2;
G: 12: k2 ykt;
H: 13: k2 sky;
I: 14: k2 cb;
J: 20: ykt p2;
K: 21: ykt k2;
L: 22: ykt ykt;
M: 23: ykt sky;
N: 24: ykt cb;
O: 30: sky p2;
P: 31: sky k2;
Q: 32: sky ykt;
R: 33: sky sky;
S: 34: sky cb;
T: 40: cb p2;
U: 41: cb k2;
V: 42 – cb ykt;
W: 43: ykt cb;
X: 44: cb cb;
Y: 100: k2 p2 p2; (I knitted this as k2p1 (k1) p3, leaving the garter stitch in the middle.)
Z: 101: k2 p2 k2.

Here’s what I planned to have the blanket say (I added Alyssa’s name at the end when it was clear what that would be. Fortunately, I was knitting from bottom to top.):

Alyssa Karise,
Grace and Peace.
Grace and peace to you from God our Father and the Lord Jesus Christ.
Grace and Peace.

When I had the blanket all finished, ends sewn in, and I laid it out to take pictures — I discovered I’d left out a word! Urgh! But it’s still a Blessing Blanket. And I still thought about and prayed for Alyssa as I knitted. And it’s still warm and soft. I’m not going to say what word I left out, because I want to see if the baby’s parents can “read” it well enough to figure out! (I’m bad!) Astute readers of this blog who possess really really good eyesight might be able to tell as well.

To see how the coding actually looks, I took pictures of the top three rows. Here is AL – KA – GR:

Since the stitches are done on the purl side, k2 gives you straight bumps. So A = p2 k2 gives you a smooth panel, then bumps. L = ykt ykt gives you a hole from the yarnover, then two stitches together, in both sides. On the second row, K = ykt k2 combines both of those. Then we have A, which looks just like the first A. The third row has the same combination reversed in G = k2 ykt. Then R = sky sky. With sky, the stitches are knitted together before the yarn over, so the hole is on the right of the combined stitches.

The next section shows YS – RI – AC, and a fourth row, ND:

Y = k2 p2 p2, so I started on that first stitch I usually leave a purl stitch. So it looks the same as A, only shifted over one stitch to the left. S = sky cb shows us our final “digit”. The cable in back comes out as one stitch going over another with no hole. The second row is easier to see. R = sky sky, so you can see both sides have the hole on the right. Then I = k2 cb, and you can more easily see the cabled stitch crossing over. On the third row, we have A = p2 k2 and C = p2 sky. The fourth row, the end of the word AND, gives you a nice look at the cables again, with N = ykt cb and D = p2 cb.

I’ll give you the end of the top three rows, but I’ll leave it to the reader to work out that at least I didn’t make a mistake on the top of the blanket:

Making this was so much fun! In fact, I’ve been dragging my feet about sending it on. But tonight I noticed that the yarn label happens to have a pattern for a one-skein scarf, and I happen to have one skein left. So perhaps making myself a scarf out of this wonderful 85% cotton 15% angora yarn (Serenade) will remind me to send thoughts and prayers and blessings to my sweet little niece, Alyssa Karise.

And, meanwhile, my brother announced that his wife is expecting a baby. His baby needs a prime factorization blanket! I am swatching to figure out how best to accomplish this, and will definitely be letting my readers know!

My posts on Mathematical Knitting and related topics are now gathered at Sonderknitting.

Review of How Many Jelly Beans? by Andrea Menotti, illustrated by Yancey Labat

How Many Jelly Beans?

A Giant Book of Giant Numbers

by Andrea Menotti
illustrated by Yancey Labat

Chronicle Books, San Francisco, 2012. 26 pages.
Starred Review

Hooray! A book that really shows how completely huge the number one million is!

The story is simple. Emma and Aiden (with thoughts expressed by their dog) are asked how many jelly beans they’d like. Emma starts with ten, and we see a close-up of her hand with ten jelly beans.

Aiden, however, wants twenty, and the picture shows that, with ten in each hand.

Emma’s response seems quite realistic for a kid. “He can have twenty? I’ll have TWENTY-FIVE!” The responses escalate: fifty, seventy-five, one hundred. All of those amounts are shown on a tabletop. Since the tabletop in the pictures is the same every time, just with greater or fewer jelly beans distributed across them, this doesn’t really show the quantities viscerally. However, that will change by book’s end.

I like it when they get to details. Emma tells Aiden he can’t eat five hundred jelly beans, and he tells her that in a year he could eat a thousand jelly beans.

On the next big double-page spread, we see jelly beans distributed on pages of a calendar. Emma says, “Wait a second. That’s only two or three jelly beans a day.”

She comes to the logical conclusion: “I could eat FIVE THOUSAND jelly beans in a year.” Now the view pans out to Emma happily jumping on a bed covered with five thousand jelly beans. (Never mind that they would scatter all over the place if she really tried that.)

They go on. Ten thousand jelly beans. A hundred thousand jelly beans. Now the children are shown as quite small, with a hundred thousand tiny jelly beans spread out around them. I like it when Aiden tells us how he’d distribute the flavors if he had a hundred thousand jelly beans. Only one would be lemon.

But the truly marvelous part of this book, the tour de force, is the foldout section showing ONE MILLION jelly beans. In fact, when you first pull it out, the kids are saying, “Wow! A million jelly beans is a lot!” But then they say, “This is only HALF a million jelly beans! Look up there!” When you unfold the page further, then, at last, you see a million tiny jelly beans.

So here, at last, is a book that allows you to see one million things at one glance. The only way to truly give you the feel of this book was to take a picture:

Here’s the book closed, already an extra-large format:

And here’s the book opened up, showing a million jelly beans. I can hardly hold it up:

Now, I’ll be the first to admit that this book is not going to hold up well to library usage. It was not easy even for me to hold up the book with the page open without tearing the pages. And if you tear the page along the folds, it’s not going to be at all easy to mend.

But you know what? I don’t care! I love that someone did this, that Andrea Menotti and Yancey Labat made a book that truly shows kids just how enormous a million really is. And maybe, just maybe, a million jelly beans would be too many.

chroniclekids.com

Buy from Amazon.com

Find this review on Sonderbooks at: www.sonderbooks.com/Childrens_Nonfiction/how_many_jelly_beans.html

Disclosure: I am an Amazon Affiliate, and will earn a small percentage if you order a book on Amazon after clicking through from my site.

Source: This review is based on a library book from the Fairfax County Public Library.

Disclaimer: I am a professional librarian, but I write the posts for my website and blogs entirely on my own time. The views expressed are solely my own, and in no way represent the official views of my employer or of any committee or group of which I am part.

Review of Swirl by Swirl, by Joyce Sidman, pictures by Beth Krommes

Swirl by Swirl

Spirals in Nature

by Joyce Sidman
pictures by Beth Krommes

Houghton Mifflin Books for Children, 2011. 36 pages.

This is a gentle and soothing picture book that rewards reading and examining again and again. The text is unrhymed poetry, with only a few lines on a page, and very large print.

You could read this book to very young children with a short attention span, but it will also work with older children, who can notice new details on each page.

The beautiful pictures were created by Beth Krommes, Caldecott medalist for The House in the Night. She uses the same scratchboard technique here, with more colors. The technique works well for showing spirals, since the lines are distinct and clear.

Here’s the first page. It says:

“A spiral is a snuggling shape.
It fits neatly in small places.
Coiled tight, warm and safe, it waits . . .”

We’ve got a snow scene, but most of the picture is taken up with what’s underground. We see several animals curled up in their nests for the winter, and small print labels them: a bull snake, harvest mouse, eastern chipmunk, and woodchuck. All the animals are resting in a coiled shape.

The next page shows those same animals emerging into a springtime landscape, but the sharp reader will still spot some spirals.

The book goes on, gently and soothingly, showing seashells, ferns, ram’s horns, coiled tails and trunks, spiderwebs, and even gets much bigger in waves, whirlpools, and tornadoes. The climax takes us all the way out to galaxies, and then back to the cozy winter landscape again.

There are even two pages at the back that give some of the science (and math!) behind spirals.

This was one of the books we discussed at the Bill Morris Seminar in January, and my fellow attendees made me appreciate it all the more. It’s the sort of book into which you can delve much deeper than initially meets the eye, a book you and your children will want to look at and read again and again.

Buy from Amazon.com

Find this review on Sonderbooks at: www.sonderbooks.com/Childrens_Nonfiction/swirl_by_swirl.html

Disclosure: I am an Amazon Affiliate, and will earn a small percentage if you order a book on Amazon after clicking through from my site.

Source: This review is based on a library book from the Fairfax County Public Library.

Disclaimer: I am a professional librarian, but I write the posts for my website and blogs entirely on my own time. The views expressed are solely my own, and in no way represent the official views of my employer or of any committee or group of which I am part.

More Mathematical Knitting

I’m a math nut. I’ve always said that my prime factorization sweater proves it.

I finished knitting the sweater in 2005. It shows the color-coded prime factorization of all the whole numbers from 2 to 100. I’ve shown it to lots of people since then, with mixed amounts of appreciation. In 2009, I finally posted a blog explanation of it and how it works.

Last April, I wore it to the US Science and Engineering Festival. I showed it to Ivars Peterson, manning the Mathematical Association of America booth. He tweeted one tweet with a link to my blog post, and the next day I got 28,000 hits on my website.

And the post got so much attention, this month it’s appearing in Hacker News! In print! I’m happy that people are finding out about it. It’s just goes to show that Math is Beautiful.

Now, there’s no way I’m ever going to make a replica of the original sweater. It took way too long. But since then, I’ve designed a t-shirt for sale to all on Cafepress. I’ve knitted a scarf that uses color-coded stripes to represent the prime factorization of numbers up to 50. And I’ve begun work on a cuff-to-cuff cardigan that also uses color-coded stripes, similar to the scarf. I hope it will go up to 100.

But for now I’m taking a break from knitting the prime factorization cardigan, because my little sister is having a baby!

I wanted to knit something special for the little one, but not so blatantly mathematical. I decided to use a mathematical code to knit a blessing into the blanket.

Here’s how it works. I’m using the same pattern I used to knit my son a cotton blanket 18 years ago. It’s a simple knit-purl pattern. I didn’t want lace, since I wanted it to function as a warm blanket. I gave it to him whenever he ate and managed to get him very attached to it!

I want to knit a code into the blanket. The layout is a basic grid. It mimics a plaid, but with knits and purls. I decided to focus on the stockinette sections that show up on one side. These sections are seven stitches across, with the stitch in the middle purled on every other row. There are six sections across in the grid and a total of 20 sections vertically down the blanket.

The baby is a girl, and her middle name will probably be Karise, coming from the Greek word for grace. I decided to use the Christian blessing that shows up many times in the New Testament: “Grace and peace to you from God our Father and the Lord Jesus Christ.” After all, what more could you want for a baby than grace and peace?

That’s 14 words, so I decided to put one word on each row of the grid, with the words “Grace and Peace” before and after, using all 20 rows. Each word is six letters or less, so I can use the six stockinette sections to highlight the letters.

Now, how to do the letters? Simple! Years ago, I did a library program where I showed the kids that they could use the ideas from the sweater to make codes using colors or shapes for letters. You start with a simple 1 to 26 code for the letters A to Z. Then I will convert the numbers to base 5 and I only need 5 different coded digits.

Here’s how the letters will be represented:

A – 01 B – 02 C – 03 D – 04 E – 10
F – 11 G – 12 H – 13 I – 14 J – 20
K – 21 L – 22 M – 23 N – 24 O – 30
P – 31 Q – 32 R – 33 S – 34 T – 40
U – 41 V – 42 W – 43 X – 44 Y – 100
Z – 101

Then I assign certain stitches to represent each digit. Since knitting is done from right to left, I’m going to work the stitches on the purl side, so when I look at them, they will read left to right.

Here’s the code I’m using, with two stitches for each digit.

0 = purl 2 (p2)
1 = knit 2 (k2)
2 = yarn over, knit 2 together (ykt)
3 = ssk, yarn over (sky)
4 = cable one purl stitch in back (cb)

Since the purl sections I’m using have 3 purl stitches, one knit stitch and then 3 purl stitches, I’m putting in the code this way: one purl stitch, then the first digit of the coded letter,
then one knit stitch, then the second digit of the coded letter, then one purl stitch.
I’m doing this on the middle row of the section of the grid.

I am working the code from the bottom of the blanket, so I had to list all the words in backwards order.

Here’s how it’s working out!

This picture shows the bottom three rows of the large grid. So I encoded the words “Grace and Peace.” Here’s the detail:

Looking at the first two sections of each word, on the top row, we have G = 12 = k2, ykt; R = 33 = sky, sky.
Second row has a blank section to center “AND,” then A = 01 = p2, k2.
Third row has P = 31 = sky, k2; E = 10 = k2, p2.

Here’s the middle section:

For the middle, on the top row, we have A = 01 = p2, k2; C = 03 = p2, sky.
Second row has N = 24 = ykt, cb; D = 04 = p2, cb
Third row has A = 01 = p2, k2; C = 03 = p2, sky

And finally, the last two sections in the row:

This just has the end of each word. On the first and third row, that’s E = 10 = k2, p2. We’ve got “blank” sections in the other slots.

Oh, and I should mention that on yarn.com, I purchased some fabulously soft yarn on sale. It’s Artful Yarns Serenade, and it’s 70% pima cotton, and 30% angora. There’s one strand of pink, one of purple, and one of brown, which I thought more interesting than straight pink. It’s ending up so beautiful and wonderful to touch. I always say that knitting with soft yarn is like therapy. And this time, I get to knit in a mathematical blessing.

My posts on Mathematical Knitting and related topics are now gathered at Sonderknitting.

My Prime Factorization Scarf

I finished it! Last week, I finished sewing the ends in on my new Prime Factorization Scarf.

The scarf is similar to my Prime Factorization Sweater, using a new color for each prime factor. For the scarf, though, instead of making a grid of squares representing each number, I used two-row stripes for each factor. I separated each number with two rows of black, which represented the number 1 (since 1 times anything doesn’t change the value.)

I like the way the scarf gives the flow of the numbers. You can look closely at the blue color for 2 and watch it repeat. Then notice how the pink color for 3 repeats a little more slowly. And 5 a little more slowly than that. The scarf goes all the way up to 50.

Here are some sections up close. First, this picture shows 1 through 21:

2 is blue.
3 is pink.
4 = 2 x 2, so it’s two stripes of blue.
5 is yellow.
6 = 2 x 3, so it’s a stripe of blue and a stripe of pink.
7 is purple.
8 = 2 x 2 x 2, so it’s three stripes of blue.
9 = 3 x 3, so it’s two stripes of pink.
10 = 2 x 5, so it’s a stripe of blue and a stripe of yellow.
11 gets a new color, green.
12 = 2 x 2 x 3, so it’s two stripes of blue and a stripe of pink.
And so on….

Here is a picture showing 17 (light pink) through 35:

And finally, 33 to 50:

My earlier posts explained why I chose the pattern I did. I wanted the scarf to be reversible, but it’s not quite as easy to read as plain garter stitch stripes.

What’s next? A cuff-to-cuff cardigan! Only, I want to go higher than 50, so I decided to combine factors in one stripe — unless you have perfect powers of a number. Here’s a preview. I’m working on 33 now. (You can see that since 32 = 2^5, it’s 5 rows of blue.) It’s going to be flamboyantly bright, but I plan to wear my primes with pride!

My posts on Mathematical Knitting and related topics are now gathered at Sonderknitting.

Review of Just a Second, by Steve Jenkins

Just a Second

A Different Way to Look at Time

by Steve Jenkins

Houghton Mifflin Harcourt, Boston, 2011
Starred Review

I think this is the first time I’ve read a book by Steve Jenkins where I pored over the words without noticing the exquisite art the first time through. Make no mistake, his cut-paper art is as detailed and amazing as ever. It’s so realistic, I’m not sure I noticed at first that it was his usual cut-paper art and not drawings.

But the text! This is a practical way to explain time. He mentions where seconds, minutes, hours, days, weeks, months, and years came from (most being a long-time-ago invention of man). Then he tells some things that happen in each amount of time.

Did you know that in one second “A peregrine falcon in a dive, or stoop, plunges more than 300 feet”?

Did you know that in one week “Moose antlers, the fastest-growing tissue of any mammal, can add 6 inches to their length”?

Did you know that in one year “More than 2,000,000 people are killed by mosquito-borne diseases”? “Humans cut down 4,000,000,000 trees”?

The book is full of facts like that: some fascinating, some surprising, some disturbing. Some, like “In one year an estimated 50 people are killed by sharks,” may be included because the accompanying illustrations are so much fun.

This book definitely succeeds as a “Different Way to Look at Time.” Good for children learning about time, as well as for science buffs, as well as for the simply curious.

stevejenkinsbooks.com
hmhbooks.com

Buy from Amazon.com

Find this review on Sonderbooks at: www.sonderbooks.com/Childrens_Nonfiction/just_a_second.html

Disclosure: I am an Amazon Affiliate, and will earn a small percentage if you order a book on Amazon after clicking through from my site.

Source: This review is based on a library book from the Fairfax County Public Library.

Prime Progress

Woo-hoo! After getting my prototype Prime Factorization t-shirt from my new Cafepress Shop, I tweaked the colors to make the chart brighter. I also made shirts on different colored backgrounds. As luck would have it, the new shade for 2 almost perfectly matches the “Caribbean Blue” background. My new revised shirt came this week, and I love it!

For those just coming in on this, the chart is 10 rows of 10, beginning at the bottom left. (Because I can’t bring myself to have higher numbers down lower on the shirt.) Each prime number gets its own color, and the prime factors of each number are displayed by color. Unlike the sweater, the numbers are listed on the shirt.

Like the sweater, I couldn’t resist putting rows of 8 on the back. And of course, I had to list those numbers in their Octal representation. But since that adds to the cost, I’m also offering t-shirts that have only the chart on the front.

Now, as long as I was so happily wearing my prime factorization t-shirt, I had to spend some time making progress on my prime factorization scarf. The biggest problem with the scarf is that I need to carry around lots of skeins of yarn. Fortunately, I ordered a Prime Factorization Tote Bag from my Cafepress Shop! (The pictured one was ordered before I brightened up the colors.)

I am super happy about how the prime factorization scarf is turning out. The original sweater is kind of pointless if you don’t know what it represents, but the scarf is aesthetically pleasing totally aside from the mathematics.

Here is my progress earlier this week, up to 24. (Today I finished 30, and, honestly, it’s hard to stop, because it’s so much fun to see how the next number will turn out!)

This one starts at the bottom. Though with a scarf, you can hold it any direction you like.

Once again, the background color, black, represents 1. It’s used between the other numbers.

The first stripe of blue is our first prime, 2.

Then we have pink for 3.

4 = 2 x 2. It’s not quite as easy to tell on the scarf, but the next blue stripe is twice as wide as the original.

5 gets a new color, yellow.

6 = 2 x 3, so a stripe with blue, then pink.

7 gets purple.

8 = 2 x 2 x 2, so that stripe of blue is three times as wide as the original.

And so it goes. I love the way the colors flow. You can quickly see that blue is showing up every second stripe, and that every second blue stripe is fatter. You can see the pinks showing up every third stripe and the yellows every fifth. As I said, I think it makes a lovely art object totally apart from the math behind it. And the math makes it completely cool.

Also, with a scarf, you don’t have to decide your colors ahead of time. I am using a certain progression. I’m afraid going to 100 is going to be ridiculously long, but I may do it anyway. After all, I’m doing it more for the math than anything else. But when I’m done, I’m planning to make a cuff-to-cuff cardigan using the same design, and that one cannot go so high.

I’ll continue to show my progress. Such fun!

My posts on Mathematical Knitting and related topics are now gathered at Sonderknitting.

My Prime Factorization T-Shirt Shop Is Ready!

My Prime Factorization T-shirt Shop is ready!

Now, the motivation was that when the math community found out about my Prime Factorization Sweater, many commenters said I should make a T-shirt. I “happen” to have several of the charts already created in Word, because I’ve written a children’s book about using these ideas to learn about other mathematical bases and make cyphers and patterns using the mathematical principles. So I used two of those charts to make a shirt. But I did want to see if the colors came out distinct enough before I offered it for sale.

Monday night, the shirt I ordered arrived, so I wore it to work yesterday:

And here I am among the Math books:

On the back, as with the sweater, I’ve got rows of 8, so you can see that the patterns change.

Now, there were two things I wasn’t quite happy about with the shirt.

First, one thing I was happy about was that the colors came out exactly as they looked when I printed out the charts. However, that was also the first thing I was not happy about. The blue shade for 2, on my computer screen, is nice and bright and easy to spot. On the print-out, and on the shirt, it looks much darker.

The second thing I was unhappy about was that the numbers were blurry. This was because I hadn’t been able to save my Word table as a jpeg file. My son came up with the solution of taking a screenshot and merging the two pictures into a jpeg. It was good enough, but I really noticed the little imperfections.

Then, at work, wearing the shirt, I had a brainstorm. Surely in publisher, you can turn files into jpeg files? Sure enough! So yesterday evening I went home, opened my book manuscript, and pasted the prime factorization table into publisher. It worked! My test shirt hasn’t arrived yet, but I’m confident the numbers will be more clear.

While I was at it, I changed the colors, and lightened up some factors that are used several times in the chart, particularly the blue for 2. Since my graphic looks different when it’s printed, I’ll post a picture of how the print-out looks, because that’s how it will look on the shirt:

I also added various colors, by popular demand. I now have a Caribbean Blue shirt on order with the new charts.

One other thing I should mention. For “Super Geeks” (like me), I did put rows of 8 on the back. All the charts have the numerical values under the color code, but on the back, I gave those numbers their Octal representation. So after 7 comes 10, after 10 comes 11, after 17 comes 20, after 77 comes 100, and so on. A couple times, when I was looking at the back, I forgot I was looking at the back and thought I had factored incorrectly! With the colors, you could use this as a handy-dandy way to convert from decimal to octal! (Just what everyone needs, right? But if you’re ever on an alien planet….)

I do like the way the two charts with the same colors show how the patterns change. Particularly look at yellow (5). In the decimal chart, because it’s a factor of 10, it lines up. In the octal chart, because it’s relatively prime with 8, it does not line up.

So, I’m looking forward to my new shirt coming in! And I do feel ready to offer my shirts for sale!

The URL is http://www.cafepress.com/sonderbooks.

Prime Factorization Swatches

I finished three swatches and decided on how I’m going to approach my new Prime Factorization Scarf.

First, I tried garter stitch. It’s a reversible stitch, and I thought it would work for the scarf. No pun intended, I thought I’d begin with the primary colors, since they are clearly “red,” “blue,” and “yellow.” Here’s how that swatch turned out:

The colors do stand out in this version. Black is 1, the background color. The pattern starts on the left. 2 is red. One ridge clearly stands out for the factor. When you get to 1 again, you stop multiplying and start a new number. Primes will always be one ridge. Next is 3, which is blue. Then comes 4, clearly showing as two ridges of red, 2 x 2. Then black, so you start a new number. Then comes 5, a new color, yellow. Then black. Then we have a ridge of red with a ridge of blue, 2 x 3 = 6. A ridge of black. Then 7, a new color. Black. Three ridges of red, 2 x 2 x 2 = 8. Black. Two ridges of blue, 3 x 3 = 9. Black. A ridge of red and a ridge of yellow, 2 x 5 = 10.

What I like about this swatch? The colors pop out and clearly show how many of each factor you want.

Problems with this swatch? Well, I completely forgot that garter stitch with colors is not reversible. Here’s the other side:

The garter stitch pattern would work great in a sweater, where you only see one side. But a scarf is better when it’s reversible, since it’s not easy to keep only one side of a scarf showing.

One other problem was that I didn’t like the colors. In the picture on the web, the red looked like a pretty cherry red. In real life, it was so bright, it almost glowed in the dark. Next to black, it feels glaring.

So I decided to experiment with the colors I think are the prettiest of all the ones in the box. After all, the color for 2 is going to get used in every other stripe. Might as well use a color I like to look at, right?

I needed to pick a stitch that would be reversible in color. I chose the Double Seed Stitch, which gives a nice textured look. You alternate two knit stitches with two purl stitches, and you do two rows that line up with each other. Then you do two rows with the stitches staggered from the first two — The knit stitches in the two top rows are lined up with the purl stitches in the bottom two rows, and the purl stitches in the two top rows are lined up with the knit stitches in the bottom two rows.

You can’t really tell the colors I used in the next swatch, but it’s a turquoise for 2 and pink for 3, yellow for 5, and purple for 7. I got happier and happier as I knitted. I think this is beautiful, and it will be the pattern I use for the scarf. Here’s that swatch:

Now, I acknowlege that it’s not nearly as easy to tell exactly where the numbers separate or exactly which factors are in the number. But it’s pretty. And I know which factors are where. And it’s completely reversible. The back looks exactly the same as the front.

I did one more swatch, to be absolutely sure I wanted to use a black background. I also wanted to see if using larger needles would make the fabric more drapey. The yarn band suggests size 8 needles, and that’s what I’d been using, and I think it would be nice for a sweater. But for a scarf, I’d like a little less firmness. So I made the next swatch with a cream-colored background and size 10 needles, but the same stitch and the same colors for the numbers. Here’s that swatch:

Yes, this combination is pretty. But I think it reminds me too much of my original prime factorization sweater, and I’m ready for something different. So I’m going to go with the black background.

So I’ve begun! I’m using Size 10 needles, a black background, double seed stitch, and 26 stitches across. (The swatches used 20 stitches.)

Oh, one more thing: I hereby resolve that I will, I WILL, sew the ends in as I go, so that I don’t have to do them all at the end, like I did with the sweater. (Sigh. The worst thing about this whole project!)

I also plan to make a black edging along the sides, to hide the carried-along yarn. I can practice on the swatches.

And while I’m knitting, my mind will be spinning with ideas for a cardigan.

Stay tuned and watch my progress! One of the fun things about it is that I can wait to choose colors as I go. I don’t even have to stop at 100….

My posts on Mathematical Knitting and related topics are now gathered at Sonderknitting.