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

Children's Nonfiction Review, Mathematical, Picture Book Review, Poetry, Science 0

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

Mathematical, Prime Factorization 0

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

Mathematical, Prime Factorization 2

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

Children's Nonfiction Review, Mathematical, Science, Starred Review 0

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

Mathematical, Prime Factorization 0

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!

Mathematical, Prime Factorization 0

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

Mathematical, Prime Factorization 0

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.

Review of Edgar Allan Poe’s Pie, by J. Patrick Lewis

Children's Nonfiction Review, Humorous, Mathematical, Poetry 0

Edgar Allan Poe’s Pie

Math Puzzlers in Classic Poems

by J. Patrick Lewis
illustrated by Michael Slack

Harcourt Children’s Books, 2012. 37 pages.

I feel a tiny bit sheepish by how much fun I find in this book. J. Patrick Lewis, Children’s Poet Laureate, has parodied 14 classic poems that children may well be familiar with and has inserted… a math problem.

These problems are not particularly tricky. Though I suppose that depends on the child’s age. (There is some multiplication and division, so this is more for upper elementary grades.) At times it’s not totally clear exactly what they want you to figure out (though that is given in the upside-down answers on the next page). But the parodies are definitely playful.

Could there possibly be a better way to get a kid to do word problems for fun and without fear?

The poems, after the title, list the poem they are inspired by.

Here’s the end of “Edgar Allan Poe’s Apple Pie,” the one inspired by “The Raven”:

I ignored the frightful stranger
Knocking, knocking . . . I, sleepwalking,
Pitter-pattered toward the pantry,
Took a knife from the kitchen drawer,
And screamed aloud, “How many cuts
Give me ten pieces?” through the door,
The stranger bellowed, “Never four!”

Another favorite for me is the one that plays off a poem I love, “Us Two,” by A. A. Milne. Here’s the beginning:

Wherever I am, there’s always Boo.
Boo in the flowers with me.
The size of our garden is eight by two.
“How much wire for the fence,” says Boo,
“If it wraps all around as it ought to do?
Let’s guess together,” says Boo to me.
“Let’s guess together,” says Boo.

With some, like “Robert Frost’s Boxer Shorts,” he goes for silly. “Langston Hughes’s Train Trip” uses some trickier math. “Edward Lear’s Elephant with Hot Dog” is just a limerick.

That should give you an idea of what’s going on here. Some quite silly fun. With math!

Buy from Amazon.com

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


Ready to Start My Prime Factorization Scarf!

Mathematical, Prime Factorization 1

My yarn arrived tonight! 26 shades of Plymouth Encore yarn (on sale at yarn.com), so I can make a Prime Factorization Scarf that goes all the way up to 100!

Now, a lot of the shades ended up looking more alike than I hoped they would. But I can always hold those toward the end where they only turn up once. I also didn’t realize what large skeins I was getting — I will need to make a sweater after this, because I’m going to have all kinds of leftover yarn. But I can change the color scheme to keep it interesting.

My mission first: Decide which colors will be most dominant. I’m planning on black for 1 this time, but I’m going to swatch out some different combinations for 2, 3, 5, and 7, to decide how I like it. I was planning on red for 2, but it’s so bright — I might not want that much red in the scarf. And I really like the turquoise blue that came. So we shall see… I’ll make some small swatches before I try the actual scarf.

If anyone wants to play along and make a scarf with me, let me know! It might be a lot smarter to make this as a leftover-yarn project and use up old yarn, instead of buying all the same yarn. I wish I’d thought of that! Anyway, I will think in terms of using the yarn for a cardigan later. For now, I’m looking forward to playing with some swatches!

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

Prime Factorization Knitting Revisited

Mathematical, Prime Factorization 4

Yesterday I went to the US Science and Engineering Festival in DC, and made sure to stop at the Mathematical Association of America booth. I knew they’d be there because every day I make sure to do MAA Minute Math.

I was hoping it would be cool enough (weatherwise) to wear my prime factorization sweater (For the explanation, follow the link!), and to my joy it was. I was happy to get a picture taken at the MAA booth.

Well, that got the attention of many more math people, and today I found four new comments on my blog post about the sweater and a page about me on Hacker News!

Now, the good people at Hacker News did misread my age, so I will post something I just realized that will be true this year after my younger son and I have our birthdays. (I was so delighted when I realized it, I ran to tell my son, not realizing he’d just gone to bed.)

My age will have five prime factors.
My oldest son’s age will have four prime factors.
My youngest son’s age will have three prime factors.

A picture of the three of us should enable you to narrow it down. (I am not 72, and my youngest son is not 8.)

I’ll add one more cool set of facts to definitely set our ages:

In the year my oldest son was born, my age had four prime factors (as his does now).
In the year my youngest son was born, my age had three prime factors (as his will this year).

Let’s see. My youngest son’s age is still ambiguous. So I’ll add the clue that there are only three distinct prime factors in all the expressions above. That should do it.

So, all this establishes that I was thinking about prime numbers yesterday. And, yes, I think it’s time to make a prime factorization cardigan, which I can wear in warmer weather.

Some have said I should sell these. But let’s be honest. Having to buy all those shades of yarn costs around $100. Then it was definitely not my only knitting project, but it took me more than a year to knit. (Fun time, but not worth spending if it were for monetary gain and not for the fun of it.) Then it took me more than a month just to sew in all the yarn ends. Granted, if I made more with the same color scheme, that would spread out the cost. But by the time I finished, I’d had quite enough of the project. It has taken ten years for me to be at all interested in doing anything similar, and I’m NOT going to use the same yarn and color scheme as before; you can be sure of that.

With a cardigan, you wouldn’t have room for a chart on both sides. So I was thinking about how else to express it. Last night, I ordered some Plymouth Encore yarn from yarn.com to make a scarf.

Why Plymouth Encore? Well, first, it’s on sale right now. Needing 26 different colors to go up to 100, any savings per ball helps. I also decided that my cotton sweater (the original was made in Cotton Classic), while soft and comfortable, is a little bit droopy, and wasn’t the greatest choice for the intarsia work. Wool by itself risks being too scratchy. Most of all, this had enough colors, which I hope will be distinct.

This is my plan this time:
I think I’ll use a black background this time. I don’t look good in black is the one reason I didn’t use that on my sweater. (The original partial picture of a blanket that gave me the idea used a black background.) But in a scarf, the background won’t be as prominent.

I’m thinking I’ll use garter stitch, with two rows and one ridge for each factor. I will probably put two stitches of black (one) along the sides, in order to (I hope) hide the two and three factor colors being carried along the edge of the sweater. (I absolutely WILL sew in ends as I go this time. I will. I WILL!)

So here’s how it will work. I’ll start with however many rows of black looks good at the beginning. This is 1. Then I’ll choose a color for 2 and knit two rows (one ridge) in that color. Then I’ll do two rows of black. That represents a factor of 1, and also tells you that we’re starting on a new number. 3 will get two rows of a new color. Then two rows of 1. 4 is 2 x 2. So 4 will be expressed with four rows (two ridges) of the 2 color. Then two rows of 1. Then a new color for 5. Then two rows of 1. Then 6 = 2 x 3, so two rows of 2 directly followed by two rows of 3. Then two rows of 1.

Get the idea? Numbers with lots of prime factors will take up more space than prime numbers.

Mind you, I’ll swatch it out, with some different color choices, and see what looks best. (You definitely want your favorite colors as 2 and 3.) I will post pictures when I get there.

Once I have a scarf done? Well, what I might try with a cardigan is a chart like the old sweater on the back (in new colors and yarn) and maybe stripes as in the scarf on the front sides. Or maybe I’ll be sick of it and give it a rest for awhile.

Based on the new comments, it’s time for me to design a t-shirt! Stay tuned. I have written a children’s book which I called Colors and Codes that talks about using these ideas to make cyphers and patterns using colors or shapes combined with math. As part of the book, I made several charts on my computer. I will see how hard it is to transfer these charts to a t-shirt in Cafe Press.

By the way, I haven’t tried to sell this book yet. I had been working on selling a middle grade novel, and lately I’ve been letting both efforts rest while I dealt with some medical issues. But if anyone knows of an agent or a publisher who’d like to take on something a little unorthodox but extremely cool to math geeks, let me know!

It’s been about ten years since I designed and knitted the sweater. (So I was WAY young then!) Let me stress that the idea of visualizing the prime numbers through colors in knitting was not my own. By all means, spread the word! The article I read (and I should definitely track it down. It was in Interweave Knits in the late 90’s or 2000 or so.) talked about how the blanket that had been made inspired kids who didn’t think they were good in math. As I say in my book, you can attach the numbers to the letters of the alphabet and use these ideas to knit or color messages into things. The sky’s the limit, and it’s lots of fun.

Once I have some swatches, I’ll take some pictures and post the results!

Edited to add: I found the inspiration! It was an article in the Fall 2003 issue of Interweave Knits, called “geekchic” by Brenda Dayne, regarding the work of Pat Ashcroft and Steve Plummer. They have a fabulously cool website at woollythoughts.com. Here’s what the article said about an afghan they created:

“Across the Atlantic Ocean and far from the research laboratories and hallowed halls of Academia, a young girl, age thirteen, stands mesmerized in front of a knitted afghan displayed at the annual North-East Math Fair in Lancashire, England. Constructed of one hundred brightly colored squares, the intricately striped fabric is the creation of Pat Ashforth and Steve Plummer (www.woollythoughts.com). Knitters, teachers, mathematicians, and partners, Pat and Steve have found that basic mathematical principles make for beautiful knitwear designs, and that knitting is an excellent way of explaining complex theorems to their students.

“Vibrating with color, and reminiscent of African Kente cloth, the Counting Panes afghan is so beautiful it’s hard to accept that it was created as a teaching tool. Within its one hundred brightly colored squares, in ten columns and ten rows, however, lie lessons in multiplication, division, pattern, and numerical relationships… If a square contains yellow, it contains a number divisible by two, if it contains red, then the number divides by three. The more colors in a square, the more numbers it divides by.”

Now, they only had a photograph of a very small part of the afghan, so I couldn’t see how it worked. That part would not work on my sweater at all — there are several squares that appear to just be dark blue, and it’s stated elsewhere that green always appears with baby blue. So maybe that quilt is just showing factors of numbers, and not the prime factorization? Maybe beyond a certain point primes don’t get new colors?

But anyway, having the fondness for math that I do, that much information made me realize that I could knit a prime factorization chart. But I wanted to wear it, not just look at it! I still can’t make sense of what, exactly, their afghan was doing, but they are the ones who gave me the idea behind my design. I graphed it out, figured out how many stitches across I needed, and then found a basic sweater pattern from the book Picture Knitting to use as my canvas. Thank you so much for the germ of the idea!

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