Archive for the ‘Knitting’ Category

Mathematical Colors and Codes, Episode Two: Prime Factorization Codes

Thursday, July 2nd, 2020

Episode Two of my Mathematical Virtual Program Series is up!

In Episode Two, I talk more about prime factorization and ways to show it with colors. Then I show how you can use that idea to make a prime factorization code.

This video has a downloadable coloring page to help you make your own prime factorization code.

Here’s this week’s video:

Here are links to the entire Mathematical Colors and Codes series:

Episode One, Prime Factorization
Episode Two, Prime Factorization Code

Mathematical Colors and Codes

Monday, June 22nd, 2020

My Mathematical Virtual Program Series is up!

This program is a series of six videos with downloadable coloring pages. New videos will post on Mondays at 3 pm.

They will show kids how to use math to make colorful patterns and coded messages, learning about prime factorization and nondecimal bases along the way.

They’ll post on Fairfax County Public Library’s website, but I’ll post them here as well.

These will be best for kids who already understand multiplication.

And this week, Episode One is up! It covers Prime Factorization, with an explanation of my Prime Factorization Sweater. And it explains how you can color your own chart, using this downloadable coloring page.

I hope you enjoy it!

Here are links to the entire Mathematical Colors and Codes series:

Episode One, Prime Factorization
Episode Two, Prime Factorization Code

Baby Martin’s Normal Distribution Blanket

Saturday, January 11th, 2020

I finished a Normal Distribution Blanket for my new little nephew, Martin!

This is the same idea I used to make a blanket for my little niece Kara, but that one was in shades of pink.

Unfortunately, I didn’t get to try the blanket out on Martin in person, but I gave the blanket to my brother, his Daddy, to give to Martin.

Here’s the method. The blanket is simply a series of entrelac squares (diamonds). I knit one row of squares in one direction, then pick up stitches along an edge to make another row of squares in the other direction, and knit back and forth, with squares in between the squares of the previous row. The nice thing about it is that each square is knitted completely before you move on to the next square, so you don’t have to carry different yarns across the row.

I used Tahki’s Cotton Classic yarn because they have many, many shades, and I already had some spare yarn from previous projects — Cotton Classic is my go-to yarn for mathematical knitting projects. All those shades!

Choosing the shade of the yarn for each square is where the normal distribution math comes in.

I simply generated a list of random numbers from the normal distribution (using google to find a random number generator). The normal distribution is a bell-shaped curve, so I’ll get more numbers in the middle of the distribution.

I took five shades of purple and labeled them A through E. For numbers in the middle, I used lighter colors, and got gradually darker as the numbers went out from the middle. For numbers that were outliers, I added a sparkly silver yarn to color E — because it’s the outliers that make life beautiful. And aren’t we all outliers in some way?

Here’s the specific math for those who care or who want to reproduce the method:

I set the middle of the distribution as zero, with a standard deviation of one. For positive numbers, I did a garter stitch square, and for negative numbers I did a seed stitch square.

Here’s how I assigned the colors:
Color A: Absolute values between 0 and 0.5
Color B: Absolute values between 0.5 and 1.0
Color C: Absolute values between 1.0 and 1.5
Color D: Absolute values between 1.5 and 2.0
Color E (with sparkles!): Absolute values greater than 2.0

Now, I didn’t have a perfect progression from light to dark. Color D was the reddish purple. And it’s not obvious in the photo that E was definitely much darker than Color C. Making D the reddish purple seemed to get the weight of the colors to progress better. I should have done a close-up of the sparkles, but didn’t think of it this time.

One thing I like about visualizing a normal distribution this way is you get a more visceral feel for how the colors are distributed than just looking at the curve. There are almost as many B-colored squares as A squares — and there really are a lot of outliers. (It might be a better representation if I had gone out one more level and used six colors. But this worked.)

I’ve also done scarves this way (with stripes) and of course the pink blanket. And it always comes out pleasing to the eye. The normal distribution really is the way so much of nature is arranged.

You can find links to explanations of all my mathematical knitting at!

Review of Knitting Pearls, edited by Ann Hood

Friday, November 9th, 2018

Knitting Pearls

Writers Writing About Knitting

edited by Ann Hood

W. W. Norton & Company, 2016. 260 pages.

This is a book of essays about knitting, and the essays are written by twenty-seven distinguished writers. Not all of the writers are knitters, but all of the writers do have something interesting to say about knitting. Maybe they had a relative who knitted for them. Maybe there’s a particular knitted object that starts their musings.

I took a long time to read this book. But that’s the beauty of essays – you can read one at a time and come away smiling. Or just musing about life.

Here’s a paragraph from the introduction, with the editor telling us what to expect. (There are several more paragraphs, so this is just a taste.)

And speaking of swooning, here’s what you have to look forward to when you read Knitting Pearls. Like me, some of the contributors knit their way through adversity. Caroline Leavitt’s first husband asked her to make him a sweater with brontosauruses on it, but as she knit the marriage began to crumble. Lily King’s daughter knit a hat during their year living in Italy, which eased her homesickness. Cynthia Chinelly knits to help her escape the worry she has for her son. Melissa Coleman hoped that knitting a sweater for everyone in her family would remove the curse of divorce. An on-again, off-again knitter, Robin Romm returned to it when her mother was dying, and now knits as she waits for a baby. Back at Ithaca College in the 1970s, Bill Roorbach joined the knitting club to get over his broken heart – and to meet girls.

If you love knitting, you’re going to enjoy this book.

Buy from

Find this review on Sonderbooks at:

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 Fairfax County Public Library.

Disclaimer: I am a professional librarian, but I maintain my website and blogs 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.

What did you think of this book?

Review of How to Knit a Monster, by Annemarie van Haeringen

Monday, November 5th, 2018

How to Knit a Monster

by Annemarie van Haeringen

Clarion Books, 2018. First published in the Netherlands in 2014. 32 pages.
Starred Review

This book was first published in the Netherlands in 2014. It is not eligible for the Newbery. I should not have taken time to read it. On top of that, I have a pet peeve against books that show someone knitting a complete sweater in less than a month – and this book does much, much worse than that.

And yet, all that said — I did read this book today and was enchanted. The speedy knitting is all part of this amazing goat’s magic.

Here’s how the book begins:

Greta is a goat, a white goat. When she goes outdoors in wintertime, she’s almost invisible.

She is a very, very good knitter. She knits socks for everyone she knows and for many she doesn’t know.

Today Greta decides to knit something different. How about a whole goat?

She tries a little one first.

Click, click, clickety click go her knitting needles, and before long a little goat slides off her needle.

What fun! Greta knits more little goats so they can play together.

The illustration here shows several goats, with splashes of color in various places and trailing yarn. They are cavorting about happily, with two butting heads.

But then “mean Mrs. Sheep” comes by and badmouths Greta’s knitting.

Greta is upset. She isn’t watching her knitting.

We’ll see who knits the fastest, Greta thinks angrily. Clickclickclicketyclick go her needles.

Mrs. Sheep keeps talking. Greta still isn’t watching her knitting.

She decides it’s finished and ends it off . . .

. . . and a wolf jumps off the needle!

The little goats run away.

Well, the wolf deals with Mrs. Sheep. Greta hides just in time – in a closet with more yarn, thankfully. Because next she knits a tiger to catch the wolf. But the tiger is hungry….

And what is especially lovely about this book is how it all comes together – or, um, apart – at the end. (No one is permanently damaged, but Mrs. Sheep does learn a lesson.) Though Greta does need to learn to pay more attention to what she knits!

So this knitter, for one, truly appreciates the genius of Greta, whose knitting is just plain magical. Besides this being a really fun story to tell, all the better to convince children that knitters have magical powers, right?

Buy from

Find this review on Sonderbooks at:

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 Fairfax County Public Library.

Disclaimer: I am a professional librarian, but I maintain my website and blogs 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.

What did you think of this book?

Outliers Blanket!

Sunday, October 22nd, 2017

I did some more mathematical knitting for my new niece Kara!

For this blanket, I used the entrelac squares format I’d used in the prime factorization blankets, but the concept I’d used in the outliers scarves.

I took numbers from a normal distribution, using the generator at

Then I chose five colors in shades of pink, since we already knew Kara would be a girl.

For numbers in the middle of the curve (part of the bell), I used lighter colors. (z-scores of -0.5 to 0.5) For every half a z-score, I used a darker color. For the true outliers, numbers with a z-score bigger than 2 (or less than -2), I used the darkest color – but I added a sparkly silver thread.

This is to show that the outliers are what make life beautiful.

And aren’t we all outliers in some way or other?

I also distinguished between negative and positive numbers by using garter stitch for positive numbers and seed stitch for negative numbers.

It was a huge treat to try out the blanket with Kara. It wasn’t as big as I originally intended, but with random numbers I was able to stop when I decided it was done.

Kara’s big sister Zoe really enjoyed the blanket, too!

Another Coded Blessing Blanket!

Saturday, March 11th, 2017

I finished another Mathematical Knitting Project!

This is another Coded Blessing Blanket.

This time, though, it’s for my 22-year-old son.

I’d finished knitting for babies in the family. (Though now it’s time to knit again.) So I asked my son if there were anything he’d like me to knit for him. He said, “Blue Blankie could use a stunt double.”

Blue Blankie is the blanket I knitted him when I was expecting his birth and I was on bed rest. After he was born, I gave him the blanket every time I fed him. I was happy when he took Blue Blankie with him to college, but yes, sadly, Blue Blankie is falling apart.

However, Tim said he’d like a purple blanket this time. And I’d already used the same pattern to knit a blanket for my niece Alyssa with a blessing coded in the stitches. So I decided to do the same for Tim.

Here’s how it works. The stitches make a sort of plaid pattern with knits and purls. The pattern has a sequence of 12 rows that make one large pattern-row. Each pattern-row has seven smooth panels on the front side of the blanket. And each smooth panel is split into two parts. So I used those panels to code words of seven letters or less.

The code I used was base 5. So A = 01, B = 02, C = 03, D = 04, E = 10, F = 11, and so on. So I only need 5 stitch patterns, using three stitches.

I used some simple patterns. 0 is knit each stitch. This matches the background.

1 is purl each stitch, making a bumpy row.

2 is a cable made by holding 2 stitches to the back.

3 is a cable made by holding 1 stitch to the front. (Making the cable go the opposite direction from 2.)

4 is a yarnover and knit 2 together — making a hole.

Here’s a closer look at how the stitches turned out.

And an even closer look.

The first four rows are my son’s name, Timothy Ronald John Eklund. So the first row, for example, is 40 14 23 30 40 13 100. (To knit Y, I began one stitch ahead of the 7-stitch panel, using 9 stitches for 100.)

I’m not going to tell what the rest of the blanket says, except to say it’s a blessing. Can Tim read the code?

Now, this is exactly the same way I made Alyssa’s Blessing Blanket, but it turned out that hers had an error. I had almost finished Tim’s at Christmas time, but finally proofread it — and found an error, took out about 50 rows, and reknitted them. But now it’s done, and it’s error-free!

And it was a wonderful thing to knit a blanket full of love for my 22-year-old son who had just moved to the other side of the country.

May you thrive, Tim!

Review of A Hat for Mrs. Goldman, by Michelle Edwards, illustrated by G. Brian Karas

Thursday, February 2nd, 2017

A Hat for Mrs. Goldman

A Story About Knitting and Love

by Michelle Edwards
illustrated by G. Brian Karas

Schwartz & Wade Books, 2016. 36 pages.
Starred Review
2016 Sonderbooks Stand-out: #5 Picture Books
2017 Sydney Taylor Book Award Silver Medalist

Oh, here is a picture book for knitters to love!

Unlike many stories about knitting, it acknowledges that knitting is difficult and takes a long time. And this ends up being a beautiful story about showing love by knitting.

Mrs. Goldman knits hats for the whole neighborhood, including Sophia.

“Keeping keppies warm is our mitzvah,” says Mrs. Goldman, kissing the top of Sophia’s head. “This is your keppie, and a mitzvah is a good deed.

Sophia goes with Mrs. Goldman when she walks her dog Fifi, and Sophia notices that Mrs. Goldman doesn’t have a hat any more. She gave it to Mrs. Chen.

Sophia gets an idea.

Last year, Mrs. Goldman taught Sophia how to knit.
“I only like making pom-poms,” decided Sophia after a few days.
“Knitting is hard. And it takes too long.”

Now Sophia digs out the knitting bag Mrs. Goldman gave her. And the hat they started.
The stitches are straight and even. The soft wool smells like Mrs. Goldman’s chicken soup.

Sophia holds the needles and tries to remember what to do. She drops one stitch. She drops another.

Still Sophia knits on. She wants to make Mrs. Goldman the most special hat in the world.

Sophia works hard on that hat. For a long time. Finally she finishes knitting and sews it up.

I love that the hat doesn’t look very good. In fact, it looks like a monster hat.

But Sophia’s solution is wonderful, and fits with what went before. She covers the hat with red pom-poms. When she gives it to Mrs. Goldman, she says it reminds her of Mr. Goldman’s rosebushes.

And now her keppie is toasty warm. And that’s a mitzvah.

The book finishes up with instructions for knitting a simple hat and for making pom-poms.

(Hmmm. Now as I post this, I think it’s pretty much a Pussy hat. But you can cover it with pom-poms if you like. Or not.)

This is a beautiful story, as it says, about knitting and love.

Buy from

Find this review on Sonderbooks at:

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 Fairfax County Public Library.

Disclaimer: I am a professional librarian, but I maintain my website and blogs 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.

What did you think of this book?

Normal Distribution Scarf

Friday, August 12th, 2016

Today I finished a second Normal Distribution Scarf.


The first one I made was designed to highlight outliers to show that outliers are what makes the world beautiful.

For this one, I only wanted to show the Normal Distribution. I decided to knit it the long way so this time I wouldn’t have to sew any ends in.

I took colors from light to dark, in shades of pink. Colors B and C were a little closer than I wanted them to be, but it still gave the idea.


I generated numbers from a normal distribution and made a big list. For positive values, I purled the row, and for negative values, I knitted — so those values should be about even, making random ridges.

For the color, I used the absolute value, from light to dark. Since the normal distribution is a bell curve, there should be many more values in the lighter colors.

For 0 to 0.5, I used White.
0.5 to 1.0 was Victorian Pink.
1.0 to 1.5 was Blooming Fuchsia (only a little darker than Victorian Pink).
1.5 to 2.0 was Lotus Pink — a bright, hot pink.
Above 2.0 was Fuchsia — a dark burgundy.


Naturally, I used a lot more of the lighter colors. So for my next project after my current one, I think I’m going to do another normal distribution scarf, but this time reversing the values. So the new scarf would be mainly dark colors with light highlights.

In fact, if I weren’t using pink (maybe purple or blue), it would be fun to make scarves for a couple this way. Use dark, staid, sedate colors for the man, with light highlights. Use pastel shades for the woman — with dark highlights. [Hmmm. If I knit a scarf for a boyfriend before he exists, would the boyfriend jinx not apply?]


In this version, the lighter colors were more prominent.

Here’s a view of the scarf draped over my couch, showing both sides.


The different look has to do with where the knits and purls were placed and which side has a ridge and which is smooth.

Here’s a closer look:


I like the way the color combinations turned out so pleasing.


The only real problem is that the scarf is made out of wool, and it was almost 100 degrees outside today. So for now, I’m going to have to enjoy it draped over my couch rather than wearing it. I’ll look forward to this winter!


Update: I made an opposite scarf to this one, also generating random numbers and using the same exact yarn, but going from dark to light. Together, they make a matched set, so I gave them to my daughter and her wife-to-be!

Coded Affirmations Scarf

Saturday, February 27th, 2016

affirmations_scarfThe one knitted object in my Sonderknitting Mathematical Knitting Gallery which I haven’t explained is the Coded Affirmations Scarf.

I knitted the scarf with a small ball of leftover yarn before I knitted Alyssa’s Coded Blessing Blanket, but after it had occurred to me that you could use mathematical bases to make coded messages, as in this Base Six Code Coloring Sheet. With knitting, instead of colors, you use a different two-stitch stitch pattern for the code.

I’m pretty sure I used a similar code for the Affirmations Scarf as I did for the Blessing Blanket later. The patterns would have involved knit and purl stitches, cables to the front or back, and yarn overs with decreases. But to be honest, the scarf is much harder to read because it’s not as clear where the letters begin and end. (It was nice in the blanket that I had a built-in grid to use.)

Anyway, the idea wasn’t to be able to decipher it. The idea was that I would know what the scarf said.

What does the scarf say? My name — my full name, my nickname — and words that I believe describe me. (Along the lines of “Loved,” “Joyful” — you get the idea.)

And the effect is just a seemingly random lacy pattern.

This was my first experiment. And looking at it now, years later — well, I still haven’t been able to decipher it. (I’m hoping I wrote down the code somewhere!)

But the idea — to knit meaning into a scarf with a coded message — was a complete success.

And I still say you could do this with colors on the edge of a picture or anywhere else you want a secret meaning hidden in a pretty pattern.


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